AU760205B2 - Physiological monitor and method of minimizing noise - Google Patents

Description

AUSTRALIA

PATENTS ACT 1990 DIVISIONAL APPLICATION NAME OF APPLICANT: Masimo Corporation ADDRESS FOR SERVICE: DAVIES COLLISON CAVE Patent Attorneys 1 Little Collins Street Melbourne, 3000.

o .INVENTION TITLE: "Physiological monitor and method of minimizing noise" **o The following statement is a full description of this invention, including the best method of performing it known to us: pr P:\OPER\DH\725063 div.do-20/1 1/00 -2- A METHOD OF IMPROVING THE DETERMINATION OF A PHYSIOLOGICAL PARAMETER Background of the Invention Field of the Invention The present invention relates to the field of signal processing. More specifically, the present invention relates to a method of improving the determination of a physiological parameter based upon physiological signals.

Description of the Related Art Signal processors are typically employed to remove or derive either the primary or secondary signal portion from a composite measured signal including a primary signal portion and a secondary signal portion.

For example, a composite signal may contain noise and desirable portions. If the secondary signal portion occupies a different frequency spectrum than the primary signal portion, then conventional filtering techniques such as low pass, band pass, and high pass filtering are available to remove or derive either the primary or the secondary signal portion from the total signal. Fixed single or multiple notch filters could also be employed if the primary andlor secondary signal portion(s) exist at a fixed frequency(s).

It is often the case that an overlap in frequency spectrum between the primary and secondary 20 signal portions exists. Complicating matters further, the statistical properties of one or both of the primary *and secondary signal portions change with time. In such cases, conventional filtering techniques are ineffective in extracting either the primary or secondary signal. If, however, a description of either the primary or secondary signal portion can be derived, correlation canceling, such as adaptive noise canceling, can be employed to remove either the primary or secondary signal portion of the signal isolating the other portion. In other words, given sufficient information about one of the signal portions,that signal portion can be extracted.

Conventional correlation cancelers, such as adaptive noise cancelers, dynamically change their transfer function to adapt to and remove portions of a composite signal. However, correlation cancelers require either a secondary reference or a primary reference which correlates to either the secondary signal 30 portion only or the primary signal portion only. For instance, for a measured signal containing noise and desirable signal, the noise can be removed with a correlation canceler if a noise reference is available. This is often the case. Although the amplitude of the reference signals are not necessarily the same as the -3amplitude of the corresponding primary or secondary signal portions, they have a frequency spectrum which is similar to that of the primary or secondary signal portions.

In many cases, nothing or very little is known about the secondary andlor primary signal portions.

One area where measured signals comprising a primary signal portion and a secondary signal portion about which no information can easily be determined is physiological monitoring. Physiological monitoring generally involves measured signals derived from a physiological system, such as the human body. Measurements which are typically taken with physiological monitoring systems include electrocardiographs, blood pressure, blood gas saturation (such as oxygen saturation), capnographs, other blood constituent monitoring, heart rate, respiration rate, electro-encephalograph (EEG) and depth of anesthesia, for example. Other types of measurements include those which measure the pressure and quantity of a substance within the body such as cardiac output, venous oxygen saturation, arterial oxygen saturation, bilirubin, total hemoglobin, breathalyzer testing, drug testing, cholesterol testing, glucose testing, extra vasation, and carbon dioxide testing, protein testing, carbon monoxide testing, and other in-vivo measurements, for example.

Complications arising in these measurements are often due to motion of the patient, both external and internal (muscle movement, vessel movement, and probe movement, for example), during the measurement process.

Many types of physiological measurements can be made by using the known properties of energy attenuation as a selected form of energy passes through a medium.

A blood gas monitor is one example of a physiological monitoring system which is based upon the measurement of energy attenuated by biological tissues or substances. Blood gas monitors transmit light into the test medium and measure the attenuation of the light as a function of time. The output signal of a blood gas monitor which is sensitive to the arterial blood flow contains a component which is a waveform representative of the patient's arterial pulse. This type of signal, which contains a component related to the patient's pulse, is called a plethysmographic wave, and is shown in Figure 1 as curve s.

Plethysmographic waveforms are used in blood gas saturation measurements. As the heart beats, the amount of blood in the arteries increases and decreases, causing increases and decreases in energy attenuation, illustrated by the cyclic wave s in Figure 1.

Typically, a digit such as a finger, an ear lobe, or other portion of the body where blood flows close to the skin, is employed as the medium through which light energy is transmitted for blood gas attenuation measurements. The finger comprises skin, fat, bone, muscle, etc., shown schematically in Figure 2, each of which attenuates energy incident on the finger in a generally predictable and constant manner. However, when fleshy portions of the finger are compressed erratically, for example by motion of the finger, energy attenuation becomes erratic.

SP: OPER\DH2358282 sp.l.doc-12/02/03 -4- An example of a more realistic measured waveform S is shown in Figure 3, illustrating the effect of motion. The primary plethysmographic waveform portion of the signal s is the waveform representative of the pulse, corresponding to the sawtooth-like pattern wave in Figure 1. The large, secondary motion-induced excursions in signal amplitude obscure the primary plethysmographic signal s. Even small variations in amplitude make it difficult to distinguish the primary signal component s in the presence of a secondary signal component n.

A pulse oximeter is a type of blood gas monitor which non-invasively measures the arterial saturation of oxygen in the blood. The pumping of the heart forces freshly oxygenated blood into the arteries causing greater energy attenuation. As well understood in the art, the arterial saturation of oxygenated blood may be determined from the depth of the valleys relative to the peaks of two plethysmographic waveforms measured at separate wavelengths.

Patient movement introduces motion artifacts to the composite signal as illustrated in the plethysmographic waveform illustrated in Figure 3. These motion artifacts distort the measured signal.

Summary of the Invention In accordance with the present invention, there is provided a method for the improvement of the determination of a physiological parameter having a predetermined range of possible values based upon physiological signals, said method comprising the steps of: sensing first and second physiological signals, each of said physiological signals having a desired portion and an undesired portion; based upon said physiological signals, determining at least two possible values of said physiological parameter based on at least two alternative calculation methods for AI said physiological parameter; and determining a resulting value for the physiological parameter from the at least two possible values.

In another aspect, there is provided a method of improving the determination of a physiological parameter based ulon physiological signals, said method comprising the steps of: sensing a physiological signal indicative of the physiological parameter, said physiological parameter having a predetermined range of possible values; providing at least two possible calculation methods far calculating said physiological parameter; and utilising at least one of the first and the second methods to determine a resulting value PA\OPER\DHcf358232 sp.Ldo.-I2/J3 for the physiological parameter.

P:\OPER\DH\39623-95.DIV 17/3/99 -6- Brief Description of the Drawings Figure 1 illustrates an ideal plethysmographic waveform.

Figure 2 schematically illustrates a typical finger.

Figure 3 illustrates a plethysmographic waveform which includes a motion-induced erratic signal portion.

Figure 4a illustrates a schematic diagram of a physiological monitor to compute primary physiological signals.

Figure 4b illustrates a schematic diagram of a physiological monitor to compute secondary signals.

Figure 5a illustrates an example of an adaptive noise canceler which could be employed in a physiological monitor, to compute primary physiological signals.

Figure 5b illustrates an example of an adaptive noise canceler which could be employed in a physiological monitor, to compute secondary motion artifact signals.

Figure 5c illustrates the transfer function of a multiple notch filter.

Figure 6a illustrates a schematic of absorbing material comprising N constituents within the absorbing material.

Figure 6b illustrates another schematic of absorbing material comprising N constituents, including one mixed layer, within the absorbing material.

Figure 6c illustrates another schematic of absorbing material comprising N constituents, 20 including two mixed layers, within the absorbing material.

Figure 7a illustrates a schematic diagram of a monitor, to compute primary and ooasol secondary signals.

ooo° ooooo* -7- Figure 7b illustrates the ideal correlation canceler energy or power output as a function of the signal coefficients r 1 r 2 "rn. In this particular example, r 3 r a and r 7 r v Figure 7c illustrates the non-ideal correlation canceler energy or power output as a function of the signal coefficients r 1 r 2 In this particular example, r 3 ra and r 7 r v Figure 8 is a schematic model of a joint process estimator comprising a least-squares lattice predictor and a regression filter.

Figure 8a is a schematic model of a joint process estimator comprising a ORD least-squares lattice (LSL) predictor and a regression filter.

Figure 9 is a flowchart representing a subroutine for implementing in software a joint process estimator as modeled in Figure 8.

Figure 9a is a flowchart representing a subroutine for implementing in software a joint process estimator as modeled in Figure 8a.

Figure 10 is a schematic model of a joint process estimator with a least-squares lattice predictor and two regression filters.

Figure 10a is a schematic model of a joint process estimator with a ORD least-squares lattice predictor and two regression filters.

Figure 11 is an example of a physiological monitor.

Figure 1 la illustrates an example of a low noise emitter current driver with accompanying digital to analog converter.

Figure 12 illustrates the front end analog signal conditioning circuitry and the analog to digital conversion circuitry of the physiological monitor of Figure 11.

Figure 13 illustrates further detail of the digital signal processing circuitry of Figure 11.

Figure 14 illustrates additional detail of the operations performed by the digital signal processing circuitry of Figure 11.

Figure 15 illustrates additional detail regarding the demodulation module of Figure 14.

Figure 16 illustrates additional detail regarding the decimation module of Figure 14.

Figure 17 represents a more detailed block diagram of the operations of the statistics module of 30 Figure 14.

30 Figure 18 illustrates a block diagram of the operations of one embodiment of the saturation transform module of Figure 14.

Figure 19 illustrates a block diagram of the operation of the saturation calculation module of Figure -8- Figure 20 illustrates a block diagram of the operations of the pulse rate calculation module of Figure 14.

Figure 21 illustrates a block diagram of the operations of the motion artifact suppression module of Figure Figure 21a illustrates an alternative block diagram for the operations of the motion artifact suppression module of Figure Figure 22 illustrates a saturation transform curve.

Figure 23 illustrates a block diagram of an alternative to the saturation transform in order to obtain a saturation value.

Figure 24 illustrates a histogram saturation transform in accordance with the alternative of Figure 23.

Figures 25A-25C illustrate yet another alternative in order to obtain the saturation.

Figure 26 illustrates a signal measured at a red wavelength Aa-Ared-660nm for use in a processor for determining the secondary reference or the primary reference and for use in a correlation canceler. The measured signal comprises a primary portion sAa(t) and a secondary portion nAa(t).

Figure 27 illustrates a signal measured at an infrared wavelength Ab-AlR- 9 1 0nm for use in a processor for determining the secondary reference or the primary reference and for use in a correlation canceler. The measured signal comprises a primary portion sAb(t) and a secondary portion nAb(t) Figure 28 illustrates the secondary reference a Figure 29 illustrates a good approximation s"Aa(t) to the primary portion sAa(t) of the signal SAa(t) measured at Aa-Ared-660nm estimated by correlation cancellation with a secondary reference Figure 30 illustrates a good approximation s"Ab(t) to the primary portion sAb(t) of the signal Sb(t) measured at Ab-AIR-910nm estimated by correlation cancellation with a secondary reference Figure 31 depicts a set of 3 concentric electrodes, Le., a tripolar electrode sensor, to derive electrocardiography (ECG) signals, denoted as S 1

S

2 and S 3 for use with the present invention. Each of the ECG signals contains a primary portion and a secondary portion.

Figure 32 shows a tapped delay line FIR filter.

Figure 33 shows phasor summation of FIR filter output for two frequencies.

Figure 34 shows an M-th order all-pass subfilter.

-9- Figure 35 shows complementary lowpass and highpass filters from a 2-path all-pass network.

Figure 36 shows a Hilbert transform all-pass filter realization as a transformed half band filter.

Figure 37 shows a resampling 2-path all-pass filter.

Figure 38 shows the spectrum of an iterated 2-path filter with polynomials in Z.

Figure 39 shows the spectra of four channel quadrant centered and cardinal centered filter banks.

Figure 40 shows a lowpass transformation of an all-pass filter.

Figure 41A shows an all-pass filter structure.

Figure 41B shows a polyphase all-pass structure.

Figure 42 shows the pole-zero distribution for M-th order all-pass subfilters.

Figures 43A-43D show typical phase responses of all-pass filter paths, and correspionding magnitude responses.

Figures 44A and 44B show the pole-zero plot and magnitude response for 2-path and polyphase all-pass networks.

Figure 45 shows a bandpass transformation of an all-pass filter.

Detailed Description of the Invention The system described below utilizes first and second measured signals that each contain a primary signal portion and a secondary signal portion. In other words, given a first and second .e e composite signals Sl(t) Sl(t) nl(t) and S 2

S

2 n 2 the system can be used to isolate either the primary signal portion s(t) or the secondary signal portion Following processing, the output of the system provides a good approximation to the secondary signal portion n(t) or a good approximation s(t) to the primary signal portion s(t).

The system is particularly useful where the primary and/or secondary signal portion n(t) may contain one or more of a constant portion, a predictable portion, an erratic portion, a random portion, etc. The primary signal approximation or secondary signal approximation is derived by removing as many of the secondary signal portions n(t) or primary signal portions s(t) from the composite signal S(t) as possible. The remaining signal forms either the primary signal approximation s"(t) or secondary signal approximation respectively. The constant portion and predictable portion of the secondary signal n(t) are easily removed with traditional filtering techniques, such as simple subtraction, low pass, band pass, and high pass filtering. The erratic portion is more difficult to remove due to its unpredictable nature. If something is known about the erratic signal, even statistically, it could be removed, at least partially, from the measured signal via traditional filtering techniques. However, often no information is known about the erratic portion of the secondary signal In this case, traditional filtering techniques are usually insufficient.

In order to remove the secondary signal a signal model in accordance with the following is defined for the first and second measured signals S1 and S 2 S, s +n,

S

2

S

2 +n 2 with s, ras 2 and n 1 r, n 2 n1 Or ra and a S 2 n2 where s 1 and n 1 are at least somewhat (preferably substantially) uncorrelated and s 2 and n 2 are at least somewhat (preferably substantially) uncorrelated. The first and second measured signals S 1 and S 2 are -11related by correlation coefficients r, and r, as defined above. The use and selection of these coefficients is described in further detail below.

This signal model is used in combination with a correlation canceler, such as an adaptive noise canceler, to remove or derive the erratic portion of the measured signals.

Generally, a correlation canceler has two signal inputs and one output. One of the inputs is either the secondary reference or the primary reference which are correlated, respectively, to the secondary signal portions n(t) and the primary signal portions s(t) present in the composite signal The other input is for the composite signal Ideally, the output of the correlation canceler or n"(t) corresponds, respectively, to the primary signal s(t) or the secondary signal n(t) portions only. Often, the most difficult task in the application of correlation cancelers is determining the reference signals and which are correlated to the secondary n(t) and primary s(t) portions, respectively, of the measured signal S(t) since, as discussed above, these portions are quite difficult to isolate from the measured signal In the signal processor of the present invention, either a secondary reference or a primary reference is determined from two composite signals measured simultaneously, or nearly simultaneously, at two different wavelengths, Aa and Ab.

A block diagram of a generic monitor incorporating a signal processor and a correlation canceler is shown in Figures 4a and 4b. Two measured signals, SAa(t) and SAb(t), are acquired by a detector 20. One skilled in the art will realize that for some physiological 20 measurements, more than one detector may be advantageous. Each signal is conditioned by a signal conditioner 22a and 22b. Conditioning includes, but is not limited to, such procedures as filtering the signals to remove constant portions and amplifying the signals for ease of manipulation. The signals are then converted to digital data by an analog-to-digital converter 24a and 24b. The first measured signal SAa(t) comprises a first primary signal portion, labeled herein sAa(t), and a first secondary signal portion, labeled herein nAa(t). The second measured signal SAb(t) is at least partially correlated to the first measured signal SAa(t) and comprises a second primary signal portion, labeled herein sAb(t), and a second secondary signal portion, labeled herein nAb(t). Typically the first and second secondary signal portions, nAa(t) and nAb(t), are uncorrelated andlor erratic with respect to the primary signal portions sAa(t) and sAb(t). The secondary signal portions nAa(t) and nAb(t) are often caused by motion of a patient in S 30 physiological measurements.

The signals SAa(t) and SAb(t) are input to a reference processor 26. The reference processor 26 multiplies the second measured signal SAb(t) by either a factor ra sAa(t)IsAb(t) or a factor r, nAa(t)InAb(t) and then subtracts the second measured signal SAb(t) from the first measured signal SAa(t).

-12- The signal coefficient factors ra and r, are determined to cause either the primary signal portions sAa(t) and sAb(t) or the secondary signal portions nAa(t) and nAb(t) to cancel, respectively, when the two signals SAa(t) and SAb(t) are subtracted. Thus, the output of the reference processor 26 is either a secondary reference signal nAa(t) rnAb(t), in Figure 4a, which is correlated to both of the secondary signal portions nAa(t) and nAb(t) or a primary reference signal sAa(t) rvsAb(t), in Figure 4b, which is correlated to both of the primary signal portions sAa(t) and sAb(t). A reference signal or is input, along with one of the measured signals SAa(t) or SAb(t), to a correlation canceler 27 which uses the reference signal or to remove either the secondary signal portions nAa(t) or nAb(t) or the primary signal portions sAa(t) or sAb(t) from the measured signal SAa(t) or SAb(t). The output of the correlation canceler 27 is a good primary signal approximation or secondary signal approximation In one embodiment, the approximation or is displayed on a display 28.

An adaptive noise canceler 30, an example of which is shown in block diagram form in Figure 5a, is employed as the correlation canceler 27, to remove either one of the erratic, secondary signal portions nAa(t) and nAb(t) from the first and second signals SA.(t) and SAb(t). The adaptive noise canceler 30 in Figure 5a has as one input a sample of the secondary reference which is correlated to the secondary signal portions nAa(t) and nAb(t). The secondary reference is determined from the two measured signals Sa(t) and SAb(t) by the processor 26 as described herein. A second input to the adaptive noise canceler, is a sample of either the first or second composite measured signals SAa(t) SAa(t) nAa(t) or SAb(t) sAb(t) nAb(t)- The adaptive noise canceler 30, in Figure 5b, may also be employed to remove either one of primary signal portions sAa(t) and sAb(t) from the first and second measured signals SA,(t) and SAb(t). The adaptive noise canceler 30 has as one input a sample of the primary reference which is correlated to the primary signal portions sAa(t) and sAb(t). The primary reference is determined from the two measured signals SAa(t) and SAb(t) by the processor 26 as described herein. A second input to the adaptive noise canceler 30 is a sample of either the first or second measured signals SAa(t) sAa(t) nAa(t) or SAb(t) sAb(t) nAb(t) The adaptive noise canceler 30 functions to remove frequencies common to both the reference n'(t) or and the measured signal SAa(t) or SAb(t). Since the reference signals are correlated to either the secondary signal portions nAa(t) and nAb(t) or the primary signal portions sAa(t) and sAb(t), the reference signals will be correspondingly erratic or well behaved. The adaptive noise canceler 30 acts in a manner which may be analogized to a dynamic multiple notch filter based on the spectral distribution of the reference signal or -13- Figure 5c illustrates an exemplary transfer function of a multiple notch filter. The notches, or dips in the amplitude of the transfer function, indicate frequencies which are attenuated or removed when a signal passes through the notch filter. The output of the notch filter is the composite signal having frequencies at which a notch is present removed. In the analogy to an adaptive noise canceler 30, the frequencies at which notches are present change continuously based upon the inputs to the adaptive noise canceler The adaptive noise canceler 30 (Figures 5a and 5b) produces an output signal, labeled herein as s"Aa(t), s"Ab(t), n"a(t) or n"Ab(t) which is fed back to an internal processor 32 within the adaptive noise canceler 30. The internal processor 32 automatically adjusts its own transfer function according to a predetermined algorithm such that the output of the internal processor 32 labeled bA(t) in Figure 5a and cA(t) in Figure 5b, closely resembles either the secondary signal portion nAa(t) or nAb(t) or the primary signal portion sAa(t) or sAb(t). The output bA(t) of the internal processor 32 in Figure 5a is subtracted from the measured signal, SAa(t) or SAb(t), yielding a signal output s"Aa(t) sAa() nAa(t) bAa(t) or a signal output s"Ab(t) sAb(t)+nAb(t)-bb(t). The internal processor optimizes sAa(t) or sAb(t) such that s"Aa(t) or s"Ab(t) is approximately equal to the primary signal sA(t) or sAb(t), respectively. The output cA(t) of the internal processor 32 in Figure 5b is subtracted from the measured signal, SAa(t) or SAb(t), yielding a signal output given by n"Aa(t) sAa(t) nAa(t) cAa(t) or a signal output given by n"Ab(t) sAb(t nAb(t) cAb(t). The internal processor optimizes n"Aa(t) or n"Ab(t) such that n"Aa(t) or n"Ab(t) is approximately equal to the secondary signal portion nAa(t) or nAb(t), respectively.

20 One algorithm which may be used for the adjustment of the transfer function of the internal processor 32 is a least-squares algorithm, as described in Chapter 6 and Chapter 12 of the book Adaptive Signal Processing by Bernard Widrow and Samuel Stearns, published by Prentice Hall, copyright 1985. This entire book, including Chapters 6 and 12, is hereby incorporated herein by reference.

Adaptive processors 30 in Figures 5a and 5b have been successfully applied to a number of 25 problems including antenna sidelobe canceling, pattern recognition, the elimination of periodic interference Sin general, and the elimination of echoes on long distance telephone transmission lines. However, considerable ingenuity is often required to find a suitable reference signal or since the portions nAa(t), nAb(t), sAa(t) and sAb(t) cannot easily be separated from the measured composite signals SAa(t) and If either the actual secondary portion nAa(t) or nAb(t) or the primary signal portion sAa(t) or sAb(t) were a priori available, techniques such as correlation cancellation would not be necessary.

GENERALIZED DETERMINATION OF PRIMARY AND SECONDARY REFERENCE

SIGNALS

An explanation which describes how the reference signals and may be determined follows.

A first signal is measured at, for example, a wavelength Aa, by a detector yielding a signal SAa(t): -14- SA(t) Aa(t) nAa(t) (1) where SAa(t) is the primary signal portion and nAa(t) is the secondary signal portion.

A similar measurement is taken simultaneously, or nearly simultaneously, at a different wavelength, Ab, yielding: SAb(t) Ab(t) nAb(t) (2) Note that as long as the measurements, SAa(t) and SAb(t), are taken substantially simultaneously, the secondary signal components, nAa(t) and nAb(t), are correlated because any random or erratic functions affect each measurement in nearly the same fashion. The substantially predictable primary signal components, sAa(t) and sAb(t), are also correlated to one another.

To obtain the reference signals and the measured signals SAa(t) and SAb(t) are transformed to eliminate, respectively, the primary or secondary signal components.

One way of doing this is to find proportionality constants, ra and ry, between the primary signal portions sAa(t) and sAb(t) and the secondary signal portions nAa(t) and nAb(t) such that the signals can be modeled as follows: SAa(t) ra Ab(t) (3) 20 nA,(t) r v nAb(t).

In accordance with the present signal model, these proportionality relationships can be satisfied in many measurements, including but not limited to absorption measurements and physiological measurements. Additionally, in accordance with the signal model, in most measurements, the proportionality constants ra and r v can be determined such that: 25 nAa(t) r nAbt) (4) sAa(t) r, sAb(t) Multiplying equation by r a and then subtracting equation from equation results in a single equation wherein the primary signal terms sAa(t) and sAb(t) cancel: SA(t) raSAb(t) nAa(t) ranb(t); a non-zero signal which is correlated to each secondary signal portion nAa(t) and nAb(t) and can be used as the secondary reference in a correlation canceler such as an adaptive noise canceler.

Multiplying equation by ry and then subtracting equation from equation results in a single equation wherein the secondary signal terms nAa(t) and nAb(t) cancel, leaving: SAat) r v SAb(t) Aa(t) rv sAb(t); a non-zero signal which is correlated to each of the primary signal portions sAa(t) and sAb(t) and can be used as the signal reference in a correlation canceler such as an adaptive noise canceler.

EXAMPLE OF DETERMINATION OF PRIMARY AND SECONDARY REFERENCE SIGNALS IN AN ABSORPTIVE SYSTEM Correlation canceling is particularly useful in a large number of measurements generally described as absorption measurements. An example of an absorption type monitor which can advantageously employ correlation canceling, such as adaptive noise canceling, based upon a reference or determined by a processor is one which determines the concentration of an energy absorbing constituent within an absorbing material when the material is subject to change. Such changes can be caused by forces about which information is desired or primary, or alternatively, by random or erratic secondary forces such as a mechanical force on the material. Random or erratic interference, such as motion, generates secondary components in the measured signal. These secondary components can be 20 removed or derived by the correlation canceler if a suitable secondary reference or primary reference is known.

A schematic N constituent absorbing material comprising a container 42 having N different absorbing constituents, labeled A 2

A

3 AN, is shown in Figure 6a. The constituents A, through AN in Figure 6a are arranged in a generally orderly, layered fashion within the container 42. An example of a particular type of absorptive system is one in which light energy passes through the container 42 and is absorbed according to the generalized Beer-Lambert Law of light absorption. For light of wavelength Aa, 9 this attenuation may be approximated by:

*O

I Ioexp(-j Ei,aCi) (6) i=1 -16- Initially transforming the signal by taking the natural logarithm of both sides and manipulating terms, the signal is transformed such that the signal components are combined by addition rather than multiplication, i.e.:

N

Sxa=ln( do EI; (7 i=1(7 where 1 0 is the incident light energy intensity; i is the transmitted light energy intensity; EiAa is the absorption coefficient of the i th constituent at the wavelength Aa; xi(t) is the optical path length of ith layer, the thickness of material of the i t h layer through which optical energy passes; and ci(t) is the concentration of the ith constituent in the volume associated with the thickness xi(t). The absorption coefficients e 1 through EN are known values which are constant at each wavelength. Most concentrations cl(t) through cN(t) are typically unknown, as are most of the optical path lengths xi(t) of each layer. The total optical path length is the sum of each of the individual optical path lengths xi(t) of each layer.

When the material is not subject to any forces which cause change in the thicknesses of the layers, the optical path length of each layer, xi(t), is generally constant. This results in generally constant attenuation of the optical energy and thus, a generally constant offset in the measured signal. Typically, 15 this offset portion of the signal is of little interest since knowledge about a force which perturbs the material is usually desired. Any signal portion outside of a known bandwidth of interest, including the constant undesired signal portion resulting from the generally constant absorption of the constituents when not subject to change, is removed. This is easily accomplished by traditional band pass filtering techniques.

However, when the material is subject to forces, each layer of constituents may be affected by the "20 perturbation differently than other layers. Some perturbations of the optical path lengths of each layer xi(t) may result in excursions in the measured signal which represent desired or primary information. Other perturbations of the optical path length of each layer xi(t) cause undesired or secondary excursions which mask primary information in the measured signal. Secondary signal components associated with secondary excursions must also be removed to obtain primary information from the measured signal. Similarly, the ability to compute secondary signal components caused by secondary excursions directly allows one to S"obtain primary signal components from the measured signal via simple subtraction, or correlation cancellation techniques.

The correlation canceler may selectively remove from the composite signal, measured after being transmitted through or reflected from the absorbing material, either the secondary or the primary signal -17components caused by forces which perturb or change the material differently from the forces which perturbed or changed the material to cause respectively, either the primary or secondary signal component.

For the purposes of illustration, it will be assumed that the portion of the measured signal which is deemed to be the primary signal sAa(t) is the attenuation term E 5 c 5 x 5 associated with a constituent of interest, namely A 5 and that the layer of constituent A 5 is affected by perturbations different than each of the layers of other constituents A, through A 4 and A 6 through AN. An example of such a situation is when layer A 5 is subject to forces about which information is deemed to be primary and, additionally, the entire material is subject to forces which affect each of the layers. In this case, since the total force affecting the layer of constituent A 5 is different than the total forces affecting each of the other layers and information is deemed to be primary about the forces and resultant perturbation of the layer of constituent

A

5 attenuation terms due to constituents A, through A 4 and A 6 through AN make up the secondary signal portion nA Even if the additional forces which affect the entire material cause the same perturbation in each layer, including the layer of A 5 the total forces on the layer of constituent A 5 cause it to have different total perturbation than each of the other layers of constituents A, through A 4 and A 6 through

AN.

It is often the case that the total perturbation affecting the layers associated with the secondary signal components is caused by random or erratic forces. This causes the thickness of layers to change erratically and the optical path length of each layer, xi(t), to change erratically, thereby producing a random or erratic secondary signal component nAa(t). However, regardless of whether or not the secondary signal 20 portion nAa(t) is erratic, the secondary signal component nAa(t) can be either removed or derived via a correlation canceler, such as an adaptive noise canceler, having as one input, respectively, a secondary reference or a primary reference as long as the perturbation on layers other than the layer of constituent A 5 is different than the perturbation on the layer of constituent A 5 The correlation canceler yields a good approximation to either the primary signal SAa(t) or the secondary signal nAa(t). In the event that an approximation to the primary signal is obtained, the concentration of the constituent of interest, c 5 can often be determined since in some physiological measurements, the thickness of the primary signal component, x 5 in this example, is known or can be determined.

The correlation canceler utilizes either the secondary reference or the primary reference s'(t) 30 determined from two substantially simultaneously measured signals SAW(t and SAb(t). Sa(t) is determined as above in equation SAb(t) is determined similarly at a different wavelength Ab. To find either the secondary reference or the primary reference attenuated transmitted energy is measured at the -18two different wavelengths A and A and transformed via logarithmic conversion. The signals SAW~t and SAP~) can then be written (logarithm converted) as: 4 N SAa(t)-E 5 ,Aac5x5(t) 1= Ei.,acixi E iaii(8) 1=-6 SA a(t) E5.Aac 5 x 5 nAa(t) (9) 4 N SAbWt E 5 ,Abc~x 5 'EiAbcixi FEicixi SAbct) E5, 4 bc 5 x 5 NOb~) 1 Further transformations of the signals are the proportionality relationships in accordance with the signal model of the present invention defining ra and rv, similar to equation which allows determination of a noise reference n't) and a primary reference These are: raE 5 ,Ab (1 2a) nAa rvnAb(2b where nAa d ra nAb 0 3a)

E

5 Aa dr 5 Ab- (13b) *It is often the case that both equations (12) and (13) can be simultaneously satisfied. Multiplying equation by ra and subtracting the result from equation yields a non-zero secondary reference which is a :20 linear sum of secondary signal components: n'(t0 SAaP) -raSAb(t) flAa(t) -ranAb(t) 0 4a) 4 N Eiacxit 1=6 ajx~) -19- 4

N

X ra'Ei~bcixi(t)+ E raci.Abcixi(t) (1 1i=6 .4 i cxi(t)[ EiA raEi4b

N

Y: Cixi(til EiA raE 1 (I 6a) i--6 Multiplying equation (11) by r. and subtracting the result from equation yields a primary reference which is a linear sum of primary signal components: sees 0S'(t) =SAP~) -rVSAb(t) SAaP) -rvsAb(t) (1 4b) 0 OS-c 5 x 5 (t)e 5 ,Aa rv c 5 x 5 (t)E5.b (1 0Se=c 5 x 5 (t)1E 5 .Aa ,rv E5,Ibl. (1 6b) S 15 A sample of either the secondary reference or the primary reference and a sample of 0@SSSS either measured signal SAP~) or SAbI, are input to a Correlation canceler 27, such as an adaptive noise 0 canceler 30, an example of which is shown in Figures 5a and 5b and a preferred example of which is 0 discussed herein under the heading PREFERRED CORRELATION CANCELER USING A JOINT PROCESS ESTIMATOR IMPLEMENTATION. The correlation canceler 27 removes either the secondary portion nAa(t) or nAb(t), or the primary portions, sAa(t) or SAP), of the measured signal yielding a good approximation to either the primary signals s"Aa(t) =E 5 .Aac 5 x 5 or s"Ab(t) =E 5 ,Abc5x5(t) or the secondary signals n "Aa(t) nia~t or n"Ab(t) =nAb(t). In the event that the primary signals are obtained, the concentration may then be determined from the approximation to the primary signal s Aa~t rsbt codn o c 5 SAa(t)lE ,AaX5(t) (17a) or cg(t) (17b) As discussed previously, the absorption coefficients are constant at each wavelength Aa and Ab and the thickness of the primary signal component, x 5 in this example, is often known or can be determined as a function of time, thereby allowing calculation of the concentration c 5 of constituent A 5 DETERMINATION OF CONCENTRATION OR SATURATION IN A VOLUME CONTAINING MORE THAN ONE CONSTITUENT Referring to Figure 6b, another material having N different constituents arranged in layers is shown.

In this material, two constituents A 5 and A 6 are found within one layer having thickness x 5 6

X

5 (t) x 6 located generally randomly within the layer. This is analogous to combining the layers of constituents A 5 and A 6 in Figure 6a. A combination of layers, such as the combination of layers of constituents A 5 and A 6 is feasible when the two layers are under the same total forces which result in the same change of the optical path lengths x 5 and x 6 of the layers.

Often it is desirable to find the concentration or the saturation, a percent concentration, of one constituent within a given thickness which contains more than one constituent and is subject to unique forces. A determination of the concentration or the saturation of a constituent within a given volume may be made with any number of constituents in the volume subject to the same total forces and therefore under the same perturbation or change. To determine the saturation of one constituent in a volume 20 comprising many constituents, as many measured signals as there are constituents which absorb incident light energy are necessary. It will be understood that constituents which do not absorb light energy are not consequential in the determination of saturation. To determine the concentration, as many signals as there are constituents which absorb incident light energy are necessary as well as information about the sum of concentrations.

25 It is often the case that a thickness under unique motion contains only two constituents. For example, it may be desirable to know the concentration or saturation of A 5 within a given volume which contains A 5 and A 6 In this case, the primary signals SA(t) and sAb(t) comprise terms related to both A and A 6 so that a determination of the concentration or saturation of A 5 or A 6 in the volume may be made.

A determination of saturation is discussed herein. It will be understood that the concentration of A 5 in 30 a volume containing both A 5 and A 6 could also be determined if it is known that A 5

+A

6 that there are no constituents in the volume which do not absorb incident light energy at the particular measurement wavelengths chosen. The measured signals SAa(t) and SAb(t) can be written (logarithm converted) as: -21- SA,(t) e5,Aac5X5,6(t) E6,Aa 56(t) nAa(t) (18a) sA(t) nAa(t) (18b) Sb(t) E5,Ab5X5,6(t) 6,AbC5,6(t) nb(t) (19a) Ab(t) nAb(t). (19b) It is also often the case that there may be two or more thicknesses within a medium each containing the same two constituents but each experiencing a separate motion as in Figure 6c. For example, it may be desirable to know the concentration or saturation of Ag within a given volume which contains A 5 and A 6 as well as the concentration or saturation of A 3 within a given volume which contains

A

3 and A 4

A

3 and A 4 having the same constituency as A 5 and A 6 respectively. In this case, the primary signals sAa(t) and sAb(t) again comprise terms related to both Ag and A 6 and portions of the secondary signals nA,(t) and nAb(t) comprise terms related to both A 3 and A 4 The layers, A 3 and A 4 do not enter into the primary equation because they are assumed to be perturbed by a different frequency, or random or erratic secondary forces which are uncorrelated with the primary force. Since constituents 3 and 5 as well as constituents 4 and 6 are taken to be the same, they have the same absorption coefficients E3Aa E5,a; E3,Ab E5,Ab; 4,Aa E6,Aa and E4,Ab e6,Ab Generally speaking, however, A 3 and 20 A 4 will have different concentrations than A 5 and A 6 and will therefore have a different saturation.

Consequently a single constituent within a medium may have one or more saturations associated with it.

The primary and secondary signals according to this model may be written as: sAa(t)

(E

5 ,Aac 5 E6a6 I x 5 6 nAa(t) [e 5 ,aC 3 6,Aac4 x 3 4 (t) 2 N EiAa ci xi(t)+ eiAa ci xi(t) i=1 i=7 t)=7 nAa(t) I5,Aa3 E6,,aC4l x 3 4 nAa(t) -22- SAb(t) [5,Abc5+ '6,AbC6] x5, 6 (21a) Ab(t) 5,AbC3 E6,Ab4 x 3 ,4(t) 2 N EiAb cixi(t)+ E i,Abc xi (21b) i=7 Ab(t) E5AbC3 6,AbC4l x3, 4 nAb(t) (21c) where signals nAa(t) and nAb(t) are similar to the secondary signals nAa(t) and nAb(t) except for the omission of the 3, 4 layer.

Any signal portions whether primary or secondary, outside of a known bandwidth of interest, including the constant undesired secondary signal portion resulting from the generally constant absorption of the constituents when not under perturbation, should be removed to determine an approximation to either the primary signal or the secondary signal within the bandwidth of interest. This is easily accomplished by traditional band pass filtering techniques. As in the previous example, it is often the case that the total perturbation or change affecting the layers associated with the secondary signal components is caused by ooO random or erratic forces, causing the thickness of each layer, or the optical path length of each layer, xi(t), to change erratically, producing a random or erratic secondary signal component nAa(t). Regardless of whether or not the secondary signal portion nAa(t) is erratic, the secondary signal component nAa(t) can be removed or derived via a correlation canceler, such as an adaptive noise canceler, having as one input a secondary reference or a primary reference s'(t) as long as the perturbation in layers other than the layer of constituents As and A 6 is different than the perturbation in the layer of constituents A 5 and A 6 Either the erratic secondary signal components nAa(t) and nb(t) or the primary components sAa(t) and sAb(t) may advantageously be removed from equations (18) and or alternatively equations (20) and by a correlation canceler. The correlation canceler, again, i requires a sample of either the primary reference or the secondary reference and a sample of either of the composite signals SAa(t) or SAb(t) of equations (18) and (19).

-23- DETERMINATION OF PRIMARY AND SECONDARY REFERENCE

SIGNALS

FOR SATURATION

MEASUREMENTS

One method for determining reference signals or from the measured signals SAa(t) and SAb(t) is what will be referred to as the constant saturation approach. In this approach, it is assumed that the saturation of Ag in the volume containing A 5 and A 6 and the saturation of A 3 in the volume containing A 3 and A 4 remains relatively constant over some period of time, i.e.: Saturation(A 5 cg(t) I [c 5 c 6 (t)1 (22a) Saturation(A 3 c 3 I [c 3 c 4 (t)1 (22b) Saturation(A 5 (1 [c 6 (t)1c 5 }1 (23a) Saturation(A 3 {1 (c 4 (t)1c 3 (23b) are substantially constant over many samples of the measured signals SAa and SAb. This assumption is accurate over many samples since saturation generally changes relatively slowly in physiological systems.

The constant saturation assumption is equivalent to assuming that: c..

5 c(t)lc 6 constant (24a) c 3 (t)c 4 constant 2 (24b) S 25 since the only other term in equations (23a) and (23b) is a constant, namely the numeral 1.

Using this assumption, the proportionality constants ra and r, which allow determination of the secondary reference signal and the primary reference signal in the constant saturation method are: 05,Aa c 5 x 5 6 E6,Aa C 6 x 5 6 .30 r a E5,Ab 5 x 5 6 6,Ab c 6 x 5 6 (t) sAa(t)IsAb(t) (26a) -24-

C

5 6Ac 'E6.Abc6 5 14 6 6 Aa (c 5 1c 6 6A S-Aa(tIs-Ab(t) constant3 where flAa(t) d ra(t)nAb(t) and

C

3

X

3 4 E6,Aa C 4

X

34 (t) E5,Abc3x3,4(t) IE6.AbC4x34(t)) (27a) (28a) (29a) (26b) 25 -nAa(t)InAb(t) 'E5.Aac3 'E6.Aac4

'E

5 ,Abc 3

'E

6 ,bc4 'E5.Aa(c3 1 c4) E6,Aa C5.Ab(c 3 c4) E6,Ab "a__n"bt constant 4 where SAaP) 6 rV(t)sAb(t).

(27b) (28b) (29b) It is often the case that both equations (26) and can be simultaneously satisfied to determine the proportionality constants r, and rv. Additionally, the absorption coefficients at each wavelength E5.,4a. C6.Aa' 65,Ab. and E6.Ab are constant and the central assumption of the constant saturation method is that C 5 (t)1C 6 and c 3 (t)1C 4 are constant over many sample periods. Thus, new proportionality constants r, and r, may be determined every few samples from new approximations to either the primary or secondary signal as output from the correlation canceler.

Thus, the approximations to either the primary signals sAa(t) and sAb(t) or the secondary signals nAa(t) and nAb(t), found by the correlation canceler for a substantially immediately preceding set of samples of the measured signals SAa(t) and SAb(t) are used in a processor for calculating the proportionality constants, ra and r for the next set of samples of the measured signals SAa(t) and SAb(t).

Multiplying equation (19) by r a and subtracting the resulting equation from equation (18) yields a non-zero secondary reference signal: n'(t)-SAa(t) r aSAbt) n(t) n A (t (31a) Multiplying equation (19) by r, and subtracting the resulting equation from equation (18) yields a non-zero primary reference signal: SAa(t).rvSAb(t)- s (t).rvsAb(t). (31b) When using the constant saturation method in patient monitoring, initial proportionality coefficients can be determined as further explained below. It is not necessary for the patient to remain motionless even for an initialization period. With values for the proportionality coefficients r a and r, determined, a S 20 correlation canceler may be utilized with a secondary reference or a primary reference DETERMINATION OF SIGNAL COEFFICIENTS FOR PRIMARY AND SECONDARY REFERENCE SIGNALS USING THE CONSTANT SATURATION METHOD The reference processor 26 of Figures 4a and Figure 4b may be configured to multiply the second measured assumed signal 25 SAb(t)-Ab(t)+Ab(t) by each of a plurality of signal coefficients r 1 r 2 "r n and then subtract each result from the first measured signal SAa(t)-sAa(t)+nAa(t) to.obtain a plurality of reference signals t) SAa(t) r Ab(t) nAa(t) r nAb(t) (32) 30 for r r 1 r 2 rn as shown in Figure 7a. In other words, a plurality of signal coefficients are chosen to represent a cross section of possible signal coefficients.

In order to determine either the primary reference or the secondary reference from the above plurality of reference signals of equation signal coefficients ra and rv are determined from the -26plurality of assumed signal coefficients r 1 r 2 The coefficients ra and r, are selected such that they cause either the primary signal portions sA(t) and sAb(t) or the secondary signal portions nAa(t) and nAb(t) to cancel or nearly cancel when they are substituted into the reference function e. g.

SAa(t) raAb(t) (33a) nAa(t) r nAb(t) (33b) R'(ra, t) nAa(t) ranAb(t) (33c) t) sAa(t) rsAb(t). (33d) In other words, coefficients ra and r, are selected at values which reflect the minimum of correlation between the primary signal portions and the secondary signal portions. In practice, one does not usually have significant prior information about either the primary signal portions sAa(t) and sAb(t) or the secondary signal portions nAa(t) and nAb(t) of the measured signals SAa(t) and SAb(t). The lack of this information makes it difficult to determine which of the plurality of coefficients r 1 r 2 -rn correspond to the signal coefficients ra sAa(t)/sAb(t) and r, nAa(t)/nAb(t).

One approach to determine the signal coefficients ra and r. from the plurality of coefficients r 1 •o 20 r 2 r n employs the use of a correlation canceler 27, such as an adaptive noise canceler, which takes a first input which corresponds to one of the measured signals SAa(t) or SAb(t) and takes a second input which corresponds to successively each one of the plurality of reference signals R'(r 1 R'(r 2 t) as shown in Figure 7a. For each of the reference signals R'(r 1 R'(r 2 t, t) the corresponding output of the correlation canceler 27 is input to a "squares" operation 28 which squares the output of the correlation canceler 27. The output of the squares operation 28 is provided to an integrator29 for forming a cumulative output signal (a summation of the squares).. The cumulative output signal is subsequently input to an extremum detector 31. The purpose of the extremum detector 31 is to chose signal coefficients ra and r, from the set r 1 r 2 -rn by observing which provide a maximum in the cumulative output signal as in Figures 7b and 7c. In other words, coefficients which provide a maximum integrated S: 30 output, such as energy or power, from the correlation canceler 27 correspond to the signal coefficients ra and rv which relate to a minimum correlation between the primary signal portions and the secondary signal portions in accordance with the signal model. One could also configure a system -27geometry which would require one to locate the coefficients from the set r 1 r 2 -"rn which provide a minimum or inflection in the cumulative output signal to identify the signal coefficients r a and ry.

Use of a plurality of coefficients in the processor in conjunction with a correlation canceler 27 to determine the signal coefficients ra and rv may be demonstrated by using the properties of correlation cancellation. If x, y and z are taken to be any collection of three time varying signals, then the properties of some correlation cancelers C(x, y) may be defined as follows: Property C(x, y) 0 for x, y correlated (34a) Property C(x, y) x for x, y uncorrelated (34b) Property C(x y, z) C(x, z) C(y, z) (34c) With properties and it is easy to demonstrate that the energy or power output of a correlation canceler with a first input which corresponds to one of the measured signals SAa(t) or SAb(t) and a second input which corresponds to successively each one of a plurality of reference signals R'(r 1 R'(r 2 R(rn t) can determine the signal coefficients ra and rv needed to produce the primary reference and secondary reference If we take as a first input to the correlation canceler the measured signal SAa(t) and as a second input the plurality of reference signals R'(r 1 R'(r 2 ,R'(r t) then the outputs of the correlation canceler C(SAa(t), R'(rjt)) for j 1, 2, ,n may be written as S 20 C(sAa(t) nAa(t),sa(t)- rjsb(t) nAa(t)- rnAb(t)) :where j 1, 2, ,n and we have used the expressions 25 t) Sa(t) rSAb(t) (36) SAa(t)- sAa(t) nAa(t) (37a) SAb(t) sAb(t) nAb(t). (37b) 30 The use of property allows one to expand equation (35) into two terms C(SA C(sAa(t),sAa (t)-rsAb(t)+ nAa(t).rnAb(t)) -28- C(na(t),sAa(t)-rsAb(t)+ nAa(t)-rnAb(t)) (38) so that upon use of properties and the correlation canceler output is given by C(SAa(t), sAa(t)6(rj-ra) nAa(t) 6 (rjrv) (39) where 6(x) is the unit impulse function 6(x) 0 if x d 0 6(x) 1 if x 0.

The time variable, t, of the correlation canceler output C(SAa(t), R'(rj, may be eliminated by computing its energy or power. The energy of the correlation canceler output is given by EAa(r)- I C 2 (SAa(t),R'(rt)dt -6(r-ra I s2Aa(t)dt+6(r-r, J n a(t)dt. (41a) It should be understood that one could, equally well, have chosen the measured signal SAb(t) as the first input to the correlation canceler and the plurality of reference signals R'(r 1 R'(r 2 ,R'(rn, 20 t) as the second input. In this event, the correlation canceler energy output is EAb(r) C 2 SAb(t),R'(r,t)dt (41b) 6 (ri.ra) s2Ab(t)dt+ 6 (rj-rv) nAb(t)dt.

S25 It should also be understood that in practical situations the use of discrete time measurement signals may be employed as well as continuous time measurement signals. A system which performs a discrete transform a saturation transform in the present example) is described with reference to Figures 11-22. In the event that discrete time measurement signals are used,integration approximation methods such as the trapezoid rule, midpoint rule, Tick's rule, Simpson's C 30 approximation or other techniques may be used to compute the correlation canceler energy or power output.

In the discrete time measurement signal case, the energy output of the correlation canceler may be written, using the trapezoid rule, as -29n n 2t1) EAa(rj) 6(rj-ra)At s2Aa(t) 0.5(s 2 Aa(t) s 2 Aa(tn)) +6(rr)At n2A(t i=0 2 Aa(to)+ n2Aa(tn)) (42a) n EAb(r) 6(rj-r)At{ E s2Abti) 0.5(s 2 Ab(t) s2Ab(tn)) i=0 +6(rr, At{ n2bti)5(n2b(t n2 Ab(t)) (42b) i=0 where t i is the ith discrete time, to is the initial time, t n is the final time and At is the time between discrete time measurement samples.

10 The energy functions given above, and shown in Figure 7b, indicate that the correlation canceler output is usually zero due to correlation between the measured signal SAa(t) or SAb(t) and many of the plurality of reference signals R'(r 1 R'(r 2 However, the energy functions are non zero at values of r 1 which correspond to cancellation of either the primary signal portions sAa(t) and sAb(t) or the secondary signal portions nAa(t) and nAb(t) in the reference signal These values correspond to the 15 signal coefficients ra and r,.

It should be understood that there may be instances in time when either the primary signal portions s Aa(t) and sAb(t) or the secondary signal portions nAa(t) and nAb(t) are identically zero or nearly zero. In these cases, only one signal coefficient value will provide maximum energy or power output of the correlation canceler.

20 Since there may be more than one signal coefficient value which provides maximum correlation canceler energy or power output, an ambiguity may arise. It may not be immediately obvious which signal coefficient together with the reference function t) provides either the primary or secondary reference.

In such cases, it is necessary to consider the constraints of the physical system at hand. For example, in pulse oximetry, it is known that arterial blood, whose signature is the primary plethysmographic wave, has greater oxygen saturation than venous blood, whose signature is the secondary erratic or random signal.

Consequently, in pulse oximetry, the ratio of the primary signals due to arterial pulsation r a sAa(t)SAb(t) is the smaller of the two signal coefficient values while the ratio of the secondary signals due to mainly venous blood dynamics rv nAa(t)InAb(t) is the larger of the two signal coefficient values, assuming Aa 660 nm and Ab 910 nm.

It should also be understood that in practical implementations of the plurality of reference signals and cross correlator technique, the ideal features listed as properties and above will not be precisely satisfied but will be approximations thereof. Therefore, in practical implementations, the correlation canceler energy curves depicted in Figure 7b will not consist of infinitely narrow delta functions but will have finite width associated with them as depicted in Figure 7c.

It should also be understood that it is possible to have more than two signal coefficient values which produce maximum energy or power output from a correlation canceler. This situation arises when the measured signals each contain more than two components each of which are related by a ratio as follows: n SA(t) fAa,i(t) i=0 *(43) SAb(t)" fAbi( t i=0 where fAa,i(t)- ri fAb,i(t) i n i 0 rj.

-31- Thus, reference signal techniques together with a correlation cancellation, such as an adaptive noise canceler, can be employed to decompose a signal into two or more signal components each of which is related by a ratio.

PREFERRED CORRELATION CANCELER USING A JOINT PROCESS ESTIMATOR

IMPLEMENTATION

Once either the secondary reference or the primary reference is determined by the processor of the present invention, the correlation canceler can be implemented in either hardware or software. The preferred implementation of a correlation canceler is that of an adaptive noise canceler using a joint process estimator.

The least mean squares (LMS) implementation of the internal processor 32 described above in conjunction with the adaptive noise canceler of Figures 5a and Figure 5b is relatively easy to implement, but lacks the speed of adaptation desirable for most physiological monitoring applications. Thus, a faster approach for adaptive noise canceling, called a least-squares lattice joint process estimator model, is used in one embodiment. A joint process estimator 60 is shown diagrammatically in Figure 8 and is described in detail in Chapter 9 of Adaptive Filter Theory by Simon Haykin, published by Prentice-Hall, copyright 1986. This entire book, including Chapter 9, is hereby incorporated herein by reference.

The function of the joint process estimator is to remove either the secondary signal portions nAa(t) or nAb(t) or the primary signal portions sAa(t) or sAb(t) from the measured signals SAa(t) or SAb(t) 20 yielding either a primary signal approximation s"Aa(t) or s"Ab(t) or a secondary signal approximation n"Aa(t) or n"Ab(t). Thus, the joint process estimator estimates either the value of the primary signals SAa(t) or sAb(t) or the secondary signals nAa(t) or nAb(t). The inputs to the joint process estimator 60 are either the secondary reference or the primary reference and the composite measured signal SAa(t) or SAb(t). The output is a good approximation to the signal SA,(t) or SAb(t) with either the secondary signal 25 or the primary signal removed, i.e. a good approximation to either sAa(t), sAb(t), nAa(t) or nAb(t) The joint process estimator 60 of Figure 8 utilizes, in conjunction, a least square lattice predictor 70 and a regression filter 80. Either the secondary reference or the primary reference is input :i to the least square lattice predictor 70 while the measured signal SAa(t) or SAb(t) is input to the regression filter 80. For simplicity in the following description, SAa(t) will be the measured signal from S 30 which either the primary portion sAa(t) w the secondary portion nAa(t) will be estimated by the joint process estimator 60. However, it will be noted that SAb(t) could also be input to the regression filter and the primary portion sAb(t) or the secondary portion nAb(t) of this signal could be estimated.

-32- The joint process estimator 60 removes all frequencies that are present in both the reference n'(t) or and the measured signal The secondary signal portion nAa(t) usually comprises frequencies unrelated to those of the primary signal portion It is improbable that the secondary signal portion nAa(t) would be of exactly the same spectral content as the primary signal portion sAa(t). However, in the unlikely event that the spectral content of sAa(t) and nAa(t) are similar, this approach will not yield accurate results. Functionally, the joint process estimator 60 compares the reference input signal or which is correlated to either the secondary signal portion nAa(t) or the primary signal portion sAa(t), and input signal SAa(t) and removes all frequencies which are identical. Thus, the joint process estimator 60 acts as a dynamic multiple notch filter to remove those frequencies in the secondary signal component nAa(t) as they change erratically with the motion of the patient or those frequencies in the primary signal component sAa(t) as they change with the arterial pulsation of the patient. This yields a signal having substantially the same spectral content and amplitude as either the primary signal sAa(t) or the secondary signal nAa(t). Thus, the output s"Aa(t) or nAa(t) of the joint process estimator 60 is a very good approximation to either the primary signal sAa(t) or the secondary signal nAa(t).

The joint process estimator 60 can be divided into stages, beginning with a zero-stage and terminating in an mth-stage, as shown in Figure 8. Each stage, except for the zero-stage, is identical to every other stage. The zero-stage is an input stage for the joint process estimator 60. The first stage through the mth-stage work on the signal produced in the immediately previous stage, the (m-1)th-stage, such that a good primary signal approximation s"Aa(t) or secondary signal approximation n"Aa(t) is produced 20 as output from the m'h-stage.

The least-squares lattice predictor 70 comprises registers 90 and 92, summing elements 100 and **102, and delay elements 110. The registers 90 and 92 contain multiplicative values of a forward reflection coefficient rfm(t) and a backward reflection coefficient rb,m(t) which multiply the reference signal n'(t) or and signals derived from the reference signal or Each stage of the least-squares lattice 25 predictor outputs a forward prediction error fm(t) and a backward prediction error bm(t). The subscript m is indicative of the stage.

For each set of samples, i.e. one sample of the reference signal or derived substantially simultaneously with one sample of the measured signal the sample of the reference signal n'(t) or is input to the least-squares lattice predictor 70. The zero-stage forward prediction error fo(t) and 30 the zero-stage backward prediction error bg(t) are set equal to the reference signal or The backward prediction error bg(t) is delayed by one sample period by the delay element 110 in the first stage of the least-squares lattice predictor 70. Thus, the immediately previous value of the reference or s'(t) is used in calculations involving the first-stage delay element 110. The zero-stage forward prediction error -33is added to the negative of the delayed zero-stage backward prediction error b 0 multiplied by the forward reflection coefficient value f l(t) register 90 value, to produce a first-stage forward prediction error f Additionally, the zero-stage forward prediction error f 0 is multiplied by the backward reflection coefficient Fb,l(t) register 92 value and added to the delayed zero-stage backward prediction error b 0 (t-1) to produce a first-stage backward prediction error bl(t). In each subsequent stage, m, of the least square lattice predictor 70, the previous forward and backward prediction error values, f, 1 and bml(t.1), the backward prediction error being delayed by one sample period, are used to produce values of the forward and backward prediction errors for the present stage, fm(t) and bm(t).

The backward prediction error bm(t) is fed to the concurrent stage, m, of the regression filter There it is input to a register 96, which contains a multiplicative regression coefficient value K mA(t). For example, in the zero-stage of the regression filter 80, the zero-stage backward prediction error bo(t) is mul-.plied by the zero-stage regression coefficient KO~a(t) register 96 value and subtracted from the measured value of the signal SAa(t) at a summing element 106 to produce a first stage estimation error signal elAa(t). The first-stage estimation error signal elAa(t) is a first approximation to either the primary signal or the secondary signal. This first-stage estimation error signal el,A(t) is input to the first-stage of the regression filter 80. The first-stage backward prediction error bl(t), multiplied by the first-stage regression coefficient KIA(t) register 96 value is subtracted from the first-stage estimation error signal el,Aa(t) to produce the second-stage estimation error e,Aa(t). The second-stage estimation error signal e2,Aa(t) is a second, somewhat better approximation to either the primary signal sAa(t) or the secondary signal nAa(t).

The same processes are repeated in the least-squares lattice predictor 70 and the regression filter 80 for each stage until a good approximation ema(t), to either the primary signal sAa(t) or the secondary signal nAa(t) is determined. Each of the signals discussed above, including the forward prediction error fm(t), the backward prediction error bm(t), the estimation error signal em is necessary to calculate the forward reflection coefficient the backward reflection coefficient rb,m(t), and the regression coefficient K ma(t) register 90, 92, and 96 values in each stage, m. In addition to the forward prediction error fm(t), the backward prediction error bm(t), and the estimation error ema(t) signals, a number of intermediate variables, not shown in Figure 8 but based on the values labeled in Figure 8, are required to calculate the forward reflection coefficient fm(t), the backward reflection coefficient rb,m(t). and the S 30 regression coefficient KmA(t) register 90,92, and 96 values.

Intermediate variables include a weighted sum of the forward prediction error squares a weighted sum of the backward prediction error squares Bm(t), a scalar parameter Am(t), a conversion factor -34- Ym(t), and another scalar parameter pm.a(t). The weighted sum of the forward prediction errors 0m(t) is defined as: t Om(t) A t lf(i) 2; (44) 1=1 where A without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength and is typically less than or equal to one, A 1. The weighted sum of the backward prediction errors is defined as: t Bm(t) i t' i bm(i)1 2 i=1 where, again, A without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength and is typically less than or equal to one, A 1. These weighted sum intermediate error signals can be manipulated such that they are more easily solved for, as described in Chapter 9, 9.3 of 15 the Haykin book referenced above and defined hereinafter in equations (59) and DESCRIPTION OF THE JOINT PROCESS ESTIMATOR The operation of the joint process estimator 60 is as follows. When the joint process estimator is turned on, the initial values of intermediate variables and signals including the parameter the weighted sum of the forward prediction error signals the weighted sum of the backward prediction 20 error signals Bl(t), the parameter prAa(t), and the zero-stage estimation error eoAa(t) are initialized, some to zero and some to a small positive number 6: A. (0)O 0; (46) m-1 6; Bm(0)- 6; (48) mAa() 0; (49) eA(t) SAa(t) for t 0. After initialization, a simultaneous sample of the measured signal SAa(t) or SAb(t) and either the secondary reference or the primary reference are input to the joint process estimator 60, as shown in Figure 8. The forward and backward prediction error signals f 0 and b 0 and intermediate variables including the weighted sums of the forward and backward error signals O 0 and 9 0 and the conversion factor y 0 are calculated for the zero-stage according to: fg(t) bo(t) (51a) 0(t) B A 0 In'(t)1 2 (52a) y 0 1 (53a) if a secondary reference is used or according to: r f b 0 (51b) 0 p 0 A 0 Is'(t)1 2 (52b) 25 0 1 (53b) if a primary reference is used where, again, A without a wavelength identifier, a or b, is a constant multiplicative value unrelated to wavelength.

Forward reflection coefficient backward reflection coefficient rb,m(t), and regression 30 coefficient Ka(t) register 90, 92 and 96 values in each stage thereafter are set according to the output of the previous stage. The forward reflection coefficient rIf,(t), backward reflection coefficient b, l(t).

and regression coefficient K 1 Aa(t) register 90, 92 and 96 values in the first stage are thus set according to the algorithm using values in the zero-stage of the joint process estimator 60. In each stage, m>1, -36intermediate. values and register values including the parameter A, 1 the forward reflection coefficient rfm(t) register 90 value; the backward reflection coefficient rbm(t) register 92 value; the forward and backward error signals fm(t) and bmn(t); the weighted sum of squared forward prediction errors ~fmtas manipulated in 9.3 of the Haykin book; the weighted sum of squared backward prediction errors 8bsm(t), as manipulated in 9.3 of the Haykin book; the conversion factor Ym(t); the Parameter pma(t); the regression coefficient register 96 value; and the estimation error em+ 1Aait) value are set according to: Amlit) A Am.

1 {bm.i(t.1)fm~I(t)Iym.I(t1)) (54) Ffm(t) rbm(t) MI(t)Iam.it) (56) fmit) fm.

1 rFf~r(t)bgmI(ti1) (57) bm(t) balf(ti) Fbm(t)fm.1(t) (58) ~mt) -Ziwl(t) Am, A 1 1 2 1&m. (t.i)I (59) Vmt a M- (tI) {IAmiJ(t)1 2 !Om.(t)1 ~ym(t- 1 ym 1 Ibm.1(t-1)12I~ 1 gmJtII(1 Pm.,a(t) APm.Aa(t-1) (62) Kiii~a(t) -{.Pm.Aa(t)IllM(t)) (63) em.ql, 14 -Er.A'a(t) Km(t)bm(t) (64) where a ()denotes a complex conjugate.

These equations cause the error signals fm(t), bm(t), en~a(t) to be squared or tobe multiplied by one another, in effect squaring the errors, and creating new intermediate error values, such as .t) -37- The error signals and the intermediate error values are recursively tied together, as shown in the above equations (54) through They interact to minimize the error signals in the next stage.

After a good approximation to either the primary signal sAg(t) or the secondary signal nAe(t) has been determined by the joint process estimator 60, a next set of samples, including a sample of the measured signal SAa(t) and a sample of either the secondary reference or the primary reference are input to the joint process estimator 60. The re-initialization process does not re-occur, such that the forward and backward reflection coefficient rfm(t) and b,m(t) register 90, 92 values and the regression coefficient KmAa(t) register 96 value reflect the multiplicative values required to estimate either the primary signal portion sAa(t) or the secondary signal portion nAa(t) of the sample of SAa(t) input previously. Thus, information from previous samples is used to estimate either the primary or secondary signal portion of a present set of samples in each stage.

In a more numerically stable and preferred example of the above described joint process estimator, a normalized joint process estimator is used. This version of the joint process estimator normalizes several variables of the above-described joint process estimator such that the normalized variables fall between -1 and 1. The derivation of the normalized joint process estimator is motivated in the Haykin text as problem 12 on page 840 by redefining the variables defined according to the following conditions: m(OYm(t1) b PmOYm(b( A P t This transformation allows the conversion of Equations (54) (64) to the following normalized equations: -38m-AW AMAY-lt- )0 M_1m- 12]1111 _1 m-(t M 2]1+b b(O 0 1M_1 (0 12]1/21/ -[fM-(AM-i(Obmi(t-1)] S[1 -I Am 121112 [1 -Ibm 1 (tj1) j2I/2

P

M

(O I A m_.I10(2 Ip]fm1(t- 1) Ym(OYM-1(0[1 I bm~j(0) 12] Y rn(O Pr(tF1 I1/2pm m+1,10 e= mla(o) pm( bm(O Initialization of Normalized Joint Process Estimator Let N(t) be defined as the reference noise input at time index n and IJ(t) be defined as combined signal plus noise input at time index t the following equations apply (see Kaykin. p. 619): 1. To initialize the algorithm, at time t-0 set A M 0)= am(O)0= -39- Pm- =10- 6 Yo( 0 )=1 2 At each instant t-l, generate the various zeroth-order variables as follows: Yo(t-l)=1

P

0 o( P o(t-1) +N 2 (0 N(t 3. For regression filtering, initialize the algorithm by setting at time index t-0 Prn( 0 =0 4. At each instant t:l, generate the zeroth-order variable eo() U(t).

Accordingly, a normalized joint process estimator can be used for a more stable system.

In yet another embodiment, the correlation cancellation is performed with a QRD algorithm as shown diagrammatically in Figure 8a and as described in detail in Chapter 18 of Adaptive Filter Theory by Simon Haykin, published by Prentice-Hall, copyright 1986.

The following equations adapted from the Haykin book correspond to the QRD-LSL diagram of Figure 8a (also adapted from the Haykin book).

Comutations a. Predictions: For time t 1, 2. and prediction order m 1, 2, M where M is the final prediction order, compute: see.

96600 0 9:066 -41- Pm-i (t-1 x pm-, (t-2) I ebml(t') I' Cbmi(t+l) Pm- 1 (t-1) Sbm-, Ebm-1 1/2 Pm-l(t-l) EfMOt b, (tFl Sb,m-i (t1 )bX'I fm-1 (t1) ITfm.0( =Cb,m_..(Fl),Xll 2 7tf~m_(tF) Sbm...1(t-1 )6fmi Xc7mi(tF1)+IEfm-l(o 1 2 Sfmi-t Em(t)Cfm.1()b..(l Sf r-i bX 1 7~m. tl -42- 7C* -Cm (x 1 2 t;m1(-1) +Sfm I _b'm1 (t1) b. Filtering: For order m 0, 1, and time 2, ,compute P m(O1P m(t 1) I Eb,m(O 1' Cb,m(O

M"(

P~M(0 SbAOm Eb~ Em+i (0 -Cbm(OEm(OSbm(OX 112 prn(t""i) Cb m(O X 1 2 p Sbm(t)Em(t Cbm(O Y M (0 em+i (0 =x m+1 (t)Em+i (0 -43- Initialization a. Auxiliary parameter initialization: for order m 1, 2, M, set =0 pm( 0 0 b. Soft constraint initialization: For order m 0, 1, M, set Pm(-1)=8 n(0 where 6 is a small positive constant.

c. Data initialization: For t 1, 2, compute E 0(0 =Ebo(0)

E

0 (0 =d(f Yo where p(t) is the input and d(t) is the desired response at time t.

FLOWCHART OF JOINT PROCESS ESTIMATOR In a signal processor, such as a physiological monitor incorporating a reference processor of the present invention to determine a reference or for input to a correlation canceler, a joint process estimator 60 type adaptive noise canceler is generally implemented via a software program having an iterative loop. One iteration of the loop is analogous to a single stage of the joint process estimator as -44shown in Figure 8. Thus, if a loop is iterated m times, it is equivalent to an m stage joint process estimator A flow chart of a subroutine to estimate the primary signal portion sA,(t) or the secondary signal portion nAa(t) of a measured composite signal, SAa(t) is shown in Figure 9. Tne flow chart illustrates the function of a reference processor for determining either the secondary reference or the primary reference The flowchart for the joint process estimator is implemented in software.

A one-time initialization is performed when the physiological monitor is powered-on, as indicated by an "INITIALIZE NOISE CANCELER" action block 120. The initialization sets all registers 90, 92, and 96 and delay element variables 110 to the values described above in equations (46) through Next, a set of simultaneous samples of the composite measured signals SAa(t) and SAb(t) is input to the subroutine represented by the flowchart in Figure 9. Then a time update of each of the delay element program variables occurs, as indicated in a "TIME UPDATE OF [Z 1 ELEMENTS" action block 130.

The value stored in each of the delay element variables 110 is set to the value at the input of the delay element variable 110. Thus, the zero-stage backward prediction error bo(t) is stored as the first-stage delay element variable, and the first-stage backward prediction error b 1 is stored as the second-stage delay element variable, and so on.

Then, using the set of measured signal samples SAa(t) and SAb(t), the reference signal is obtained using the ratiometric or the constant saturation methods described above. This is indicated by a "CALCULATE REFERENCE or s'(t)l FOR TWO MEASURED SIGNAL SAMPLES" action block 140.

A zero-stage order update is performed next as indicated in a "ZERO-STAGE UPDATE" action block 150. The zero-stage backward prediction error bo(t), and the zero-stage forward prediction error fo(t) are set equal to the value of the reference signal or Additionally, the weighted sum of the forward prediction errors and the weighted sum of backward prediction errors Bm(t) are set equal to the value defined in equations (47) and (48).

25 Next, a loop counter, m, is initialized as indicated in a action block 160. A maximum value of m, defining the total number of stages to be used by the subroutine corresponding to the flowchart in Figure 9, is also defined. Typically, the loop is constructed such that it stops iterating once a criterion for convergence upon a best approximation to either the primary signal or the secondary signal has been met by the joint process estimator 60. Additionally, a maximum number of loop iterations may be chosen at 30 which the loop stops iteration. In a preferred example of a physiological monitor a maximum number of iterations, m=6 to m=10, is advantageously chosen.

Within the loop, the forward and backward reflection coefficient rf,m(t) and Fbm(t) register and 92 values in the least-squares lattice filter are calculated first, as indicated by the "ORDER UPDATE MTH CELL OF LSL.LATTICE" action block 170 in Figure 9. This requires calculation of intermediate variable and signal values used in determining register 90, 92, and 96 values in the present stage, the next stage, and in the regression filter The calculation of regression filter register 96 value KmAi(t) is performed next, indicated by the "ORDER UPDATE MTH STAGE OF REGRESSION FILTER(S)" action block 180. The two order update action blocks 170 and 180 are performed in sequence m times, until m has reached its predetermined maximum (in the preferred embodiment, m-6 to m-10) or a solution has been converged upon, as indicated by a YES path from a "DONE" decision block 190. In a computer subroutine, convergence is determined by checking if the weighted sums of the forward and backward prediction errors Um(t) and Bm(t) are less than a small positive number. An output is calculated next, as indicated by a "CALCULATE OUTPUT" action block 200. The output is a good approximation to either the primary signal or secondary signal, as determined by the reference processor 26 and joint process estimator 60 subroutine corresponding to the flow chart of Figure 9. This is displayed (or used in a calculation in another subroutine), as indicated by a "TO DISPLAY" action block 210.

A new set of samples of the two measured signals SA(t) and SAb(t) is input to the processor and joint process estimator 60 adaptive noise canceler subroutine corresponding to the flowchart of Figure 9 and the process reiterates for these samples. Note, however, that the initialization process does not re-occur. New sets of measured signal samples SA(t) and SAb(t) are continuously input to the reference processor 26 and joint process estimator adaptive noise canceler subroutine. The output forms 20 a chain of samples which is representative of a continuous wave. This waveform is a good approximation to either the primary signal waveform sAa(t) or the secondary waveform nAa(t) at wavelength Aa. The waveform may also be a good approximation to either the primary signal waveform sAb(t) or the secondary waveform n"Ab(t) at wavelength Ab.

A corresponding flowchart for the QRD algorithm of Figure 8a is depicted in Figure 9a, with 25 reference numeral corresponding in number with an extension CALCULATION OF SATURATION FROM CORRELATION CANCELER OUTPUT Physiological monitors may use the approximation of the primary signals s"Aa(t or s"Ab(t) or the secondary signals or n"Ab(t) to calculate another quantity, such as the saturation of one constituent in a volume containing that constituent plus one or more other constituents. Generally, such calculations 30 require information about either a primary or secondary signal at two wavelengths. For example, the constant saturation method requires a good approximation of the primary signal portions SA,(t) and sAb(t) of both measured signals SAa(t) and SAb(t). The arterial saturation is determined from the approximations to both signals, i.e. s"Aa(t) and s"Ab(t). The constant saturation method also requires a good approximation -46of the secondary signal portions nAa(t) or nAb(t). An estimate of the venous saturation may be determined from the approximations to these signals i. n"Aa(t) and n"Ab(t).

A joint process estimator 60 having two regression filters 80a and 80b is shown in Figure A first regression filter 80a accepts a measured signal SAa(t). A second regression filter 80b accepts a measured signal SAb(t) for a use of the constant saturation method to determine the reference signal n'(t) or The first and second regression filters 80a and 80b are independent. The backward prediction error bmt) is input to each regression filter 80a and 80b, the input for the second regression filter bypassing the first regression filter The second regression filter 80b comprises registers 98, and summing elements 108 arranged similarly to those in the first regression filter 80a. The second regression filter 80b operates via an additional intermediate variable in conjunction with those defined by equations (54) through i.e-: PmAb(t) APmb(t1) {bm(t)em,Ab(t)lYm(t)}; and POAb( 0 0. (66) The second regression filter 80b has an error signal value defined similar to the first regression filter error signal values, em+ i.e.: em+,Ab(t) em,Ab(t) K mAb(t)bm(t); and (67) (68) eAb(t) SAb(t) for t 0. S The second regression filter has a regression coefficient KmAb(t) register 98 value defined similarly to the 25 first regression filter error signal values, i.e.: (69 KmAb(t) Pm.Ab(t)l(t}; or (691 These values are used in conjunction with those intermediate variable values, signal values, register and 30 register values defined in equations (46) through These signals are calculated in an order defined by placing the additional signals immediately adjacent a similar signal for the wavelength Aa.

For the constant saturation method, SAb(t) is input to the second regression filter 80b. The output is then a good approximation to the primary signal s"Ab(t) or secondary signal s"Ab(t).

-47- The addition of the second regression filter 80b does not substantially change the computer program subroutine represented by the flowchart of Figure 9. Instead of an order update of the mth stage of only one regression filter, an order update of the mth stage of both regression filters 80a and 80b is performed. This is characterized by the plural designation in the "ORDER UPDATE OF mth STAGE OF REGRESSION FILTER(S)" activity block 180 in Figure 9. Since the regression filters 80a and 80b operate independently, independent calculations can be performed in the reference processor and joint process estimator 60 adaptive noise canceler subroutine modeled by the flowchart of Figure 9.

An alternative diagram for the joint process estimator of Figure 10, using the ORD algorithm and having two regression filters is shown in Figure 10a. This type of joint process estimator would be used for correlation cancellation using the QRD algorithm described in the Haykin book.

CALCULATION OF SATURATION Once good approximations to the primary signal portions sAa(t) and s"Ab(t) or the secondary signal portion, n"Aa(t) and n"Ab(t), have been determined by the joint process estimator 60, the saturation of Ag in a volume containing

A

5 and Ag, for example, may be calculated according to various known methods.

Mathematically, the approximations to the primary signals can be written in terms of Aa and Ab, as: sAa(t) E5,Aac5x5,6(i 6,AaC6X5,6(t); and s"Ab(t) EAbC55,6(t) E6Abc6x5,6(t) (71) S Equations (70) and (71) are equivalent to two equations having three unknowns, namely c 5 c 6 and x 5 The saturation can be determined by acquiring approximations to the primary or secondary signal portions at two different, yet proximate times t, and t 2 over which the saturation of Ag in the volume containing A 5 and Ag and the saturation of A 3 in the volume containing A 3 and A 4 does not change 25 substantially. For example, for the primary signals estimated at times t 1 and t 2 (72) S"Aa(tl) E5,AaCSX5, (tl E6,AaC6X5,6(tl) S"Aa(t2) 5,Aac5X5,6(t2) 6Aa6X5,6(t2) (7 s"Ab(t2) E 5gbC5X5.6(2) E6,AbC -48- Then, difference signals may be determined which relate the signals of equations (72) through i.e.: AsAa S'Aa(tl).SAa(t2) 5 ,AaC 5 AX e6,Aac6Ax; and (76) AsAb SAb(tl)"Ab(t2) I 5,Abc 5 Ax .AbC 6 AX; (77) where Ax x5, 6 x 5 ,6(t 2 The average saturation at time t-(tl+t 2 )12 is: Saturation(t) C 5 (t)[C 5 c 6 (t)l (78) E6,AaE6,Ab(ASAaIASAb) (79) 6 6 ,Aa"5,Aa(E6Ab-5,Ab)(AsAa/lAAb) It will be understood that the Ax term drops out from the saturation calculation because of the division.

Thus, knowledge of the thickness of the primary constituents is not required to calculate saturation.

PULSE OXIMETRY MEASUREMENTS A specific example of a physiological monitor utilizing a processor to determine a secondary reference for input to a correlation canceler that removes erratic motion-induced 20 secondary signal portions is a pulse oximeter. Pulse oximetry may also be performed utilizing a processor to determine a primary signal reference which may be used for display purposes or for input to a correlation canceler to derive information about patient movement and venous blood oxygen saturation.

A pulse oximeter typically causes energy to propagate through a medium where blood flows close 25 to the surface for example, an ear lobe, or a digit such as a finger, a forehead or a fetus' scalp. An attenuated signal is measured after propagation through or reflected from the medium. The pulse oximeter estimates the saturation of oxygenated blood.

Freshly oxygenated blood is pumped at high pressure from the heart into the arteries for use by the body. The volume of blood in the arteries varies with the heartbeat, giving rise to a variation in 30 absorption of energy at the rate of the heartbeat, or the pulse.

Oxygen depleted, or deoxygenated, blood is returned to the heart by the veins along with unused oxygenated blood. The volume of blood in the veins varies with the rate of breathing, which is typically much slower than the heartbeat. Thus, when there is no motion induced variation in the thickness of the veins, venous blood causes a low frequency variation in absorption of energy. When there is motion -49induced variation in the thickness of the veins, the low frequency variation in absorption is coupled with the erratic variation in absorption due to motion artifact.

In absorption measurements using the transmission of energy through a medium, two light emitting diodes (LED's) are positioned on one side of a portion of the body where blood flows close to the surface, such as a finger, and a photodetector is positioned on the opposite side of the finger. Typically, in pulse oximetry measurements, one LED emits a visible wavelength, preferably red, and the other LED emits an infrared wavelength. However, one skilled in the art will realize that other wavelength combinations could be used. The finger comprises skin, tissue, muscle, both arterial blood and venous blood, fat, etc., each of which absorbs light energy differently due to different absorption coefficients, different concentrations, different thicknesses, and changing optical pathlengths. When the patient is not moving, absorption is substantially constant except for the flow of blood. The constant attenuation can be determined and subtracted from the signal via traditional filtering techniques. When the patient moves, this causes perturbation such as changing optical pathlength due to movement of background fluids venous blood having a different saturation than the arterial blood). Therefore, the measured signal becomes erratic.

Erratic motion induced noise typically cannot be predetermined andlor subtracted from the measured signal via traditional filtering techniques. Thus, determining the oxygen saturation of arterial blood and venous blood becomes more difficult.

A schematic of a physiological monitor for pulse oximetry is shown in Figures 11-13. Figure 11 depicts a general hardware block diagram of a pulse oximeter 299. A sensor 300 has two light emitters 20 301 and 302 such as LED's. One LED 301 emitting light of red wavelengths and another LED 302 emitting light of infrared wavelengths are placed adjacent a finger 310. A photodetector 320, which produces an electrical signal corresponding to the attenuated visible and infrared light energy signals is located opposite oe the LED's 301 and 302. The photodetector 320 is connected to front end analog signal conditioning circuity 330.

25 The front end analog signal conditioning circuitry 330 has outputs coupled to analog to digital conversion circuit 332. The analog to digital conversion circuitry 332 has outputs coupled to a digital signal processing system 334. The digital signal processing system 334 provides the desired parameters as outputs for a display 336. Outputs for display are, for example, blood oxygen saturation, heart rate, S and a clean plethysmographic waveform.

30 The signal processing system also provides an emitter current control output 337 to a digital-toanalog converter circuit 338 which provides control information for light emitter drivers 340. The light emitter drivers 340 couple to the light emitters 301, 302. The digital signal processing system 334 also provides a gain control output 342 for the front end analog signal conditioning circuitry 330.

Figure 1 la illustrates a preferred example for the combination of the emitter drivers 340 and the digital to analog conversion circuit 338. As depicted in Figure 11 a, the driver comprises first and second input latches 321, 322, a synchronizing latch 323, a voltage reference 324, a digital to analog conversion circuit 325, first and second switch banks 326, 327, first and second voltage to current converters 328, 329 and the LED emitters 301, 302 corresponding to the LED emitters 301, 302 of Figure 11.

The preferred driver depicted in Figure 1 la is advantageous in that the present inventors recognized that much of the noise in the oximeter 299 of Figure 11 is caused by the LED emitters 301, 302.

Therefore, the emitter driver circuit of Figure 11 a is designed to minimize the noise from the emitters 301, 302. The first and second input latches 321, 324 are connected directly to the DSP bus. Therefore, these latches significantly minimizes the bandwidth (resulting in noise) present on the DSP bus which passes through to the driver circuitry of Figure 11 a. The output of the first and second input latches only changes when these latched detect their address on the DSP bus. The first input latch receives the setting for the digital to analog converter circuit 325. The second input latch receives switching control data for the switch banks 326, 327. The synchronizing latch accepts the synchronizing pulses which maintain synchronization between the activation of emitters 301, 302 and the analog to digital conversion circuit 332.

The voltage reference is also chosen as a low noise DC voltage reference for the digital to analog conversion circuit 325. In addition, in the present embodiment, the voltage reference has an lowpass 20 output filter with a very low corner frequency 1Hz in the present embodiment). The digital to analog converter 325 also has a lowpass filter at its output witha very low corner frequency 1 Hz). The digital to analog converter provides signals for each of the emitters 301, 302.

""In the present embodiment, the output of the voltage to current converters 328, 329 are switched such that with the emitters 301, 302 connected in back-to-back configuration, only one emitter is active S 25 an any given time. In addition, the voltage to current converter for the inactive emitter is switched off at its input as well, such that it is completely deactivated. This reduces noise from the switching and voltage to current conversion circuitry. In the present embodiment, low noise voltage to current converters o: oare selected Op 27 Op Amps), and the feedback loop is configured to have a low pass filter to reduce noise. In the present embodiment, the low pass filtering function of the voltage to current converter 328, 30 329 has a corner frequency of just above 625 Hz, which is the switching speed for the emitters, as further discussed below. Accordingly, the preferred driver circuit of Figure 1 a, minimizes the noise of the emitters 301, 302.

-51- In general, the red and infrared light emitters 301, 302 each emits energy which is absorbed by the finger 310 and received by the photodetector 320. The photodetector 320 produces an electrical signal which corresponds to the intensity of the light energy striking the photodetector 320. The front end analog signal conditioning circuitry 330 receives the intensity signals and filters and conditions these signals as further described below for further processing. The resultant signals are provided to the analog-to-digital conversion circuitry 332 which converts the analog signals to digital signals for further processing by the digital signal processing system 334. The digital signal processing system 334 utilizes the two signals in order to provide a what will be called herein a "saturation transform." It should be understood, that for parameters other than blood saturation monitoring, the saturation transform could be better termed as a concentration transform, in-vivo transform, or the like, depending on the desired parameter. The term saturation transform is used to describe an operation which converts the sample data from time domain to saturation domain values as will be apparent from the discussion below. In the present example, the output of the digital signal processing system 334 provides clean plethysmographic waveforms of the detected signals and provides values for oxygen saturation and pulse rate to the display 336.

It should be understood that one or more of the outputs may be provided. The digital signal processing system 334 also provides control for driving the light emitters 301, 302 with an emitter current control signal on the emitter current control output 337.

This value is a digital value which is converted by the digital.to-analog conversion circuit 338 which provides a control signal to the emitter current drivers 340. The emitter current drivers 340 provide the 20 appropriate current drive for the red emitter 301 and the infrared emitter 302. Further detail of the operation of the physiological monitor for pulse oximetry is explained below. In the present case, the light emitters are driven via the emitter current driver 340 to provide light transmission with digital modulation at 625 Hz. The light emitters 301, 302 are driven at a power level which provides an acceptable intensity for detection by the detector and for conditioning by 25 the front end analog signal conditioning circuitry 330. Once this energy level is determined for a given patient by the digital signal processing system 334, the current level for the red and infrared emitters is maintained constant. It should be understood, however, that the current could be adjusted for changes in :I the ambient room light and other changes which would effect the voltage input to the front end analog signal conditioning circuitry 330. The red and infrared light emitters are modulated 30 as follows: for one complete 625 Hz red cycle, the red emitter 301 is activated for the first quarter cycle, and off for the remaining three-quarters cycle; for one complete 625 Hz infrared cycle, the infrared light emitter 302 is activated for one quarter cycle and is off for the remaining three-quarters cycle. In order -52to only receive one signal at a time, the emitters are cycled on and off alternatively, in sequence, with each only active for a quarter cycle per 625 Hz cycle and a quarter cycle separating the active times.

The light signal is attenuated (amplitude modulated) by the pumping of blood through the finger 310 (or other sample medium). The attenuated (amplitude modulated) signal is detected by the photodetector 320 at the 625 Hz carrier frequency for the red and infrared light. Because only a single photodetector is used, the photodetector 320 receives both the red and infrared signals to form a composite time division signal The composite time division signal is provided to the front analog signal conditioning circuitry 330.

Additional detail regarding the front end analog signal conditioning circuitry 330 and the analog to digital converter circuit 332 is illustrated in Figure 12. As depicted in Figure 12, the front end circuity 302 has a preamplifier 342, a high pass filter 344, an amplifier 346, a programmable gain amplifier 348, and a low pass filter 350. The preamplifier 342 is a transimpedance amplifier that converts the composite current signal from the photodetector 320 to a corresponding voltage signal, and amplifies the signal.

The preamplifier has a predetermined gain to boost the signal amplitude for ease of processing. The source voltages for the preamplifier 342 are -15 VDC and VDC. As will be understood, the attenuated signal contains a component representing ambient light as well as the component representing the infrared or the red light as the case may be in time. If there is light in the vicinity of the sensor 300 other than the red and infrared light, this ambient light is detected by the photodetector 320. Accordingly, the gain of the preamplifier is selected in order to prevent the ambient 20 light in the signal from saturating the preamplifier under normal and reasonable operating conditions.

•In the present case, the preamplifier 342 comprises an Analog Devices AD743JR OpAmp.

This transimpedance amplifier is particularly advantageous in that it exhibits several desired features for the system described, such as: low equivalent input voltage noise, low equivalent input current noise, low input bias current, high gain bandwidth product, low total harmonic distortion, high common mode rejection.

25 high open loop gain, and a high power supply rejection ratio.

The output of the preamplifier 342 couples as an input to the high pass filter 344. The output of the preamplifier also provides a first input 346 to the analog to digital conversion circuit 332. In the present embodiment, the high pass filter is a single.pole filter with a corner frequency of about 112 1 Hz.

0 However, the corner frequency is readily raised to about 90 Hz in one embodiment. As will be understood, S: 30 the 625 Hz carrier frequency of the red and infrared signals is well above a 90 Hz corner frequency. The high-pass filter 344 has an output coupled as an input to an amplifier 346. In the present embodiment, the amplifier 346 comprises a unity gain amplifier. However, the gain of the amplifier 346 is adjustable -53by the variation of a single resistor. The gain of the amplifier 346 would be increased if the gain of the preamplifier 342 is decreased to compensate for the effects of ambient light.

The output of the amplifier 346 provides an input to a programmable gain amplifier 348. The programmable gain amplifier 348 also accepts a programming input from the digital signal processing system 334 on a gain control signal line 343. The gain of the programmable gain amplifier 348 is digitally programmable. The gain is adjusted dynamically at initialization or sensor placement for changes in the medium under test from patient to patient. For example, the signal from different fingers differs somewhat.

Therefore, a dynamically adjustable amplifier is provided by the programmable gain amplifier 348 in order to obtain a signal suitable for processing.

The programmable gain amplifier is also advantageous in an alternative example in which the emitter drive current is held constant. The emitter drive current is adjusted for each patient in order to obtain the proper dynamic range at the input of the analog to digital conversion circuit 332. However, changing the emitter drive current can alter the emitter wavelength, which in turn affects the end result in oximetry calculations. Accordingly, it would be advantageous to fix the emitter drive current for all patients. In an alternative, the programmable gain amplifier can be adjusted by the DSP in order to obtain a signal at the input to the analog to digital conversion circuit which is properly within the dynamic range (+3v to -3v in the present case) of the analog to digital conversion circuit 332. In this manner, the emitter drive current could be fixed for all patients, eliminating the wavelength shift due to emitter current drive changes.

20 The output of the programmable gain amplifier 348 couples as an input to a low-pass filter 350.

Advantageously, the low pass filter 350 is a single-pole filter with a corner frequency of I Khz. This low pass filter provides anti-aliasing.

The output of the low-pass filter 350 provides a second input 352 to the analog-to-digital conversion circuit 332. Figure 12 also depicts additional defect of the analog-to-digital conversion circuit.

The analog-to-digital conversion circuit 332 comprises a first analog-to-digital converter 354 and a second analog-to-digital converter. 356. Advantageously, the first analog-to-digital converter 354 accepts input from the first input 346 to the analog-to-digital conversion circuit 332, and o Q o the second analog to digital converter 356 accepts input on the second input 352 to the analog-to-digital conversion circuitry 332.

In one advantageous example, the first analog-to-digital converter 354 is a diagnostic analog-to digital converter. The diagnostic task (performed by the digital signal processing system) is to read the output of the detector as amplified by the preamplifier 342 in order to determine if the signal is saturating the input to the high-pass filter 344. If the input to the high pass filter 344 -54becomes saturated, the front end analog signal conditioning circuits 330 provides a output.

Alternatively, the first analog-to-digital converter 354 remains unused.

The second analog-to-digital converter 352 accepts the conditioned composite analog signal from the front end signal conditioning circuitry 330 and converts the signal to digital form. The second analog to digital converter 356 comprises a single-channel, delta-sigma converter. A Crystal Semiconductor CS5317-KS delta-sigma analog to digital converter is used. Such a converter is advantageous in that it is low cost, and exhibits low noise characteristics. More specifically, a delta-sigma converter consists of two major portions, a noise modulator and a decimation filter. The selected converter uses a second order analog delta-sigma modulator to provide noise shaping.

Noise shaping refers to changing the noise spectrum from a flat response to a response where noise at the lower frequencies has been reduced by increasing noise at higher frequencies. The decimation fiter then cuts out the reshaped, higher frequency noise to provide 16-bit performance at a lower frequency. The present converter samples the data 128 times for every 16 bit data word that it produces. In this manner, the converter provides excellent noise rejection, dynamic range and low harmonic distortion, that help in critical measurement situations like low perfusion and electrocautery.

In addition, by using a single-channel converter, there is no need to tune two or more channels to each other. The delta-sigma converter is also advantageous in that it exhibits noise shaping, for improved noise control. An exemplary analog to digital converter is a Crystal Semiconductor CS5317.

The second analog to digital converter 356 samples the signal at a 20 Khz sample rate. The 20 output of the second analog to digital converter 356 provides data samples at 20 Khz to the digital signal processing system 334 (Figure 11).

The digital signal processing system 334 is illustrated in additional detail in Figure 13.

The digital signal processing system comprises a microcontroller 360, a digital signal processor 362, a program memory 364, a sample buffer 366, a data memory 368, a read only memory 25 370 and communication registers 372. The digital signal processor 362 is an Analog Devices AD 21020. The microcontroller 360 comprises a Motorola 68HC05, with built in program memory. The sample buffer 366 is a buffer which accepts the 20 Khz sample data from the analog to digital conversion circuit 332 for storage in the data memory 368. The data memory 368 comprises 32 KWords (words being 40 bits in the 30 present case) of static random access memory.

The microcontroller 360 is connected to the DSP 362 via a conventional JTAG Tap line. The microcontroller 360 transmits the boot loader for the DSP 362 to the program memory 364 via the Tap line, and then allows the DSP 362 to boot from the program memory 364. The boot loader in program memory 364 then causes the transfer of the operating instructions for the DSP 362 from the read only memory 370 to the program memory 364. Advantageously, the program memory 364 is a very high speed memory for the DSP 362.

The microcontroller 360 provides the emitter current control and gain control signals via the communications register 372.

Figures 14-20 depict functional block diagrams of the operations of the pulse oximeter 299 carried out by the digital signal processing system 334. The signal processing functions described below are carried out by the DSP 362 with the microcontroller 360 providing system management. The operation is software/firmware controlled. Figure 14 depicts a generalized functional block diagram for the operations performed on the 20 Khz sample data entering the digital signal processing system 334. As illustrated in Figure 14, a demodulation, as represented in a demodulation module 400, is first performed. Decimation, as represented in a decimation module 402 is then performed on the resulting data. Certain statistics are calculated, as represented in a statistics module 404 and a saturation transform is performed, as represented in a saturation transform module 406, on the data resulting from the decimation operation. The data subjected to the statistics operations and the data subjected to the saturation transform operations are forwarded to saturation operations, as represented by a saturation calculation module 408 and pulse rate operations, as represented in a pulse rate calculation module 410.

In general, the demodulation operation separates the red and infrared signals from the composite 20 signal and, removes the 625 Hz carrier frequency, leaving raw data points. The raw data points are :--"provided at 625 Hz intervals to the decimation operation which reduces the samples by an order of 10 to samples at 62.5 Hz. The decimation operation also provides some filtering on the samples. The resulting data is subjected to statistics and to the saturation transform operations in order to calculate a saturation value which is very tolerant to motion artifacts and other noise in the signal. The saturation value is S 25 ascertained in the saturation calculation module 408, and a pulse rate and a clean plethysmographic waveform is obtained through the pulse rate module 410. Additional detail regarding the various operations is provided in connection with Figures 15-21.

Figure 15 illustrates the operation of the demodulation module 400. The modulated signal format is depicted in Figure 15. One full 625 Hz cycle of the composite signal is depicted in Figure 15 with the S 30 first quarter cycle being the active red light plus ambient light signal, the second quarter cycle being an ambient light signal, the third quarter cycle being the active infrared plus ambient light signal, and the fourth quarter cycle being an ambient light signal. As depicted in Figure 15, with a 20 KHz sampling frequency, the single full cycle at 625 Hz described above comprises 32 samples of 20 KHz data, eight -56samples relating to red plus ambient light, eight samples relating to ambient light, eight samples relating to infrared plus ambient light, and finally eight samples related to ambient light.

Because the signal processing system 334 controls the activation of the light emitters 300, 302, the entire system is synchronous. The data is synchronousy divided (and thereby demodulated) into four 8-sample packets, with a time division demultiplexing operation as represented in a demultiplexing module 421. One eight-sample packet 422 represents the red plus ambient light signal; a second eight-sample packet 424 represents an ambient light signal; a third eight-sample packet 426 represents the attenuated infrared light plus ambient light signal; and a fourth eight-sample packet 428 represents the ambient light signal. A select signal synchronously controls the demultiplexing operation so as to divide the time-division multiplexed composite signal at the input of the demultiplexer 421 into its four subparts.

A sum of the last four samples from each packet is then calculated, as represented in the summing operations 430, 432, 434, 436 of Figure 15. The last four samples are used because a low pass filter in the analog to digital converter 356 has a setting time. Thus, collecting the last four samples from each 8-sample packet allows the previous signal to clear.

This summing operation provides an integration operation which enhances noise immunity. The sum of the respective ambient light samples is then subtracted from the sum of the red and infrared samples, as represented in the subtraction modules 438, 440. The subtraction operation provides some attenuation of the ambient light signal present in the data. It has been found that approximately 20 dB attenuation of the ambient light is provided by the operations of the subtraction 20 modules 438, 440. The resultant red and infrared sum values are divided by four, as represented in the divide by four modules 442, 444. Each resultant value provides one sample each of the red and infrared signals at 625 Hz.

~It should be understood that the 625 Hz carrier frequency has been removed by the demodulation operation 400. The 625 Hz sample data at the output of the demodulation operation 400 is sample data without the carrier frequency. In order to satisfy Nyquist sampling requirements, less than 20 Hz is needed (understanding that the human pulse is about 25 to 250 beats per minute, or about .4 Hz 4 Hz).

Accordingly, the 625 Hz resolution is reduced to 62.5 Hz in the decimation operation.

Figure 16 illustrates the operations of the decimation module 402. The red and infrared sample data is provided at 625 Hz to respective red and infrared buffer/filters 450, 452. The red and infrared buffer/filters are 519 samples deep. Advantageously, the buffer filters 450, 452 function as continuous first-in, first-out buffers. The 519 samples are subjected to low-pass filtering. Preferably, the low-pass filtering has a cutoff frequency of approximately 7.5 Hz. with attenuation of approximately -110 dB. The bufferlfilters 450, 452 form a Finite Impulse Response (FIR) filter with -57coefficients for 519 taps. In order to reduce the sample frequency by ten, the low-pass filter calculation is performed every ten samples, as represented in respective red and infrared decimation by 10 modules 454, 456. In other words, with the transfer of each new ten samples into the bufferlfilters 450, 452, a new low pass filter calculation is performed by multiplying the impulse response (coefficients) by the 519 filter taps. Each filter calculation provides one output sample for respective red and infrared output buffers 458, 460. The red and infrared output buffers 458, 460 are also continuous FIFO buffers that hold 570 samples of data. The 570 samples provide respective infrared and red samples or packets (also denoted "snapshot" herein) of samples. As depicted in Figure 14, the output buffers provide sample data for the statistics operation module 404, satulration transform module 406, and the pulse rate module 410.

Figure 17 illustrates additional functional operation details of the statistics module 404. In summary, the statistics module 404 provides first order oximetry calculations and RMS signal values for the red and infrared channels. The statistics module also provides a cross-correlation output which indicates a cross-correlation between the red and infrared signals.

As represented in Figure 17, the statistics operation accepts two packets of samples 570 samples at 62.5 Hz in the present embodiment) representing the attenuated infrared and red signals, with the carrier frequency removed. The respective packets for infraret! and red signals are normalized with a log function, as represented in the Log modules 480, 482. The normalization is followed by removal of the DC portion of the signals, as represented in the DC Removal modules 484, 486. The DC removal involves ascertaining the DC value of the first one of the samples (or the mean of the first several or the mean of an entire snapshot) from each of the respective red and infrared snapshots, and removing this DC value from all samples in the respective packets.

Once the DC signal is removed, the signals are subjected to bandpass filtering, as represented in red and infrared Bandpass Filter modules 488, 490. With 570 samples in each packet, the bandpass filters are configured with 301 taps to provide a FIR filter with a linear phase response and little or no distortion. The bandpass filter has a pass band from 34 beatslminute to 250 beatslminute. The 301 taps slide over the 570 samples in order to obtain 270 filtered samples representing the filtered red signal and 270 filtered samples representing the filtered infrared signal. In an ideal case, the bandpass filters 488, 490 remove the DC in the signal. However, 30 the DC removal operations 484, 486 assist in DC removal.

After filtering, the last 120 samples from each packet (of now 270 samples) are selected for further processing as represented in Select Last 120 Samples modules 492,494.

The last 120 samples are selected because the first 150 samples fall -58within the settling time for the Saturation Transfer module 406, which processes the same data packets, as further discussed below.

Conventional saturation equation calculations are performed on the red and infrared 120-sample packets. The conventional saturation calculations are performed in two different ways. For one calculation, the 120-sample packets are processed to obtain their overall RMS value, as represented in the first red and infrared RMS modules 496, 498. The resultant RMS values for red and infrared signals provide input values to a first RED RMSIIR RMS ratio operation 500, which provides the RMS red value to RMS infrared value ratio as an input to a saturation equation module 502. As well understood in the art, the ratio of the intensity of red to infrared attenuated light as detected for known red and infrared wavelengths (typically Ared 650 nm and AIR 910 nm) relates to the oxygen saturation of the patient. Accordingly, the saturation equation module 502 represents a conventional look-up table or the like which, for predetermined ratios, provides known saturation values at its output 504. The red and infrared RMS values are also provided as outputs of the statistics operations module 404.

In addition to the conventional saturation operation 502, the 120-sample packets are subjected to a cross-correlation operation as represented in a first cross.correlation module 506. The first cross correlation module 506 determines if good correlation exists between the infrared and red signals. This cross correlation is advantageous for detecting defective or otherwise malfunctioning detectors. The cross correlation is also advantageous in detecting when the signal model the model of Equations is satisfied. If correlation becomes too low between the two channels, the signal model is not met. In 20 order to determine this, the normalized cross correlation can be computed by the cross-correlation module 506 for each snapshot of data. One such correlation function is as follows: 2 t2.. a ub u If the cross correlation is too low, the oximeter 299 provides a warning audible, visual, etc.) to the operator. If a selected snapshot yields a normalized correlation of less *i 25 than 0.75, the snapshot does not qualify. Signals which satisfy the signal model will have a correlation greater than the threshold.

The red and infrared 120-sample packets are also subjected to a second saturation operation and cross correlation in the same manner as described above, except the 120 samples are divided into 5 equal bins of samples 5 bins of 24 samples each). The RMS, ratio, saturation, and cross correlation -59operations are performed on a bin-by-bin basis. These operations are represented in the Divide Into Five Equal Bins modules 510, 512, the second red and infrared RMS modules 514, 516, the second RED.

RMS/IR-RMS ratio module 518, the second saturation equation module 520 and the second cross correlation module 522 in Figure 17.

Figure 18 illustrates additional detail regarding the saturation transform module 406 depicted in Figure 14. As illustrated in Figure 18, the saturation transform module 406 comprises a reference processor 530, a correlation canceler 531, a master power curve module 554, and a bin power curve module 533. The saturation transform module 406 can be correlated to Figure 7a which has a reference processor 26 and a correlation canceler 27 and an integrator 29 to provide a power curve for separate signal coefficients as depicted in Figure 7c. The saturation transform module 406 obtains a saturation spectrum from the snapshots of data. In other words, the saturation transform 406 provides information of the saturation values present in the snapshots.

As depicted in Figure 18, the reference processor 530 for the saturation transform module 406 has a saturation equation module 532, a reference generator module 534, a DC removal module 536 and a bandpass filter module 538. The red and infrared 570-sample packets from the decimation operation are provided to the reference processor 530. In addition, a plurality of possible saturation values (the 'saturation axis scan") are provided as input to the saturation reference processor 530. In the present case, 117 saturation values are provided as the saturation axis scan. The 117 saturation values range uniformly from a blood oxygen saturation of 34.8 to 105.0. Accordingly, the 117 saturation values provide an axis scan for the reference processor 530 which generates a reference signal for use by the correlation canceler 531. In other words, the reference processor is provided with each of the saturation values, and a resultant reference signal is generated corresponding to the saturation value. The correlation canceler is formed by a joint process estimator 550 and a low pass filter 552.

It should be understood that the scan values could be chosen to provide higher or lower resolution than 117 scan values. The scan values could also be non-uniformly spaced.

As illustrated in Figure 18, the saturation equation module 532 accepts the saturation axis scan values as an input and provides a ratio "rn" as an output. In comparison to the general discussion of Figure 7a-7c, this ratio "rn" corresponds to the plurality of scan value discussed above in general. The 30 saturation equation simply provides a known ratio (redfinfrared) corresponding to the saturation value received as an input.

The ratio "rn" is provided as an input to the reference generator 534, as are the red and infrared sample packets. The reference generator 534 multiplies either the red or infrared samples by the ratio "rn and subtracts the value from the infrared or red samples, respectively. For instance, the reference generator 534 multiplies the red samples by the ratio "rn" and subtracts this value from the infrared samples. The resulting values become the output of the reference generator 534.

This operation is completed for each of the saturation scan values 117 possible values in the present embodiment). Accordingly, the resultant data can be described as 117 reference signal vectors of 570 data points each, hereinafter referred to as the reference signal vectors. This data can be stored in an array or the like.

In other words, assuming that the red and infrared sample packets represent the red Sred(t) and infrared SIR(t) measured signals which have primary s(t) and secondary n(t) signal portions, the output of the reference generator becomes the secondary reference signal which complies with the signal model defined above, as follows: Sir(t) r SrJ The reference signal vectors and the infrared signal are provided as input to the DC removal module 536 of the reference processor 530. The DC removal module 536, like the DC removal modules 484, 486 in the statistics module 404, ascertains the DC value of the first of the samples for the respective inputs (or mean of the first several or all samples in a packet) and subtracts the respective DC baseline from the sample values. The resulting sample values are subjected to a bandpass filter 538.

The bandpass filter 538 of the reference processor 530 performs the same type of filtering as the bandpass filters 488, 490 of the statistics module 404. Accordingly, each set of 570 samples subjected to bandpass filtering results in 270 remaining samples. The resulting data at a first output 542 of the bandpass filter 538 is one vector of 270 samples (representing the filtered infrared signal in the present embodiment). The resulting data at a second output 540 of the bandpass filter 538, therefore, is 117 reference signal vectors of 270 data points each, corresponding to each of the saturation axis scan values provided to the saturation reference processor 530.

25 It should be understood that the red and infrared sample packets may be switched in their use in the reference processor 530.. In addition, it should be understood that the DC removal module 536 and the bandpass filter module 538 can be executed prior to input of the data to the reference processor 530 because the calculations performed in the reference processor are linear. This results in a significant processing economy.

The outputs of the reference processor 530 provide first and second inputs to a joint process estimator 550 of the type described above with reference to Figure 8. The first input to the joint process -61estimator 550 is the 270-sample packet representing the infrared signal in the present embodiment. This signal contains primary and secondary signal portions. The second input to the joint process estimator is the 117 reference signal vectors of 270 samples each.

The joint process estimator also receives a lambda input 543, a minimum error input 544 and a number of cells configuration input 545. These parameters are well understood in the art. The lambda parameter is often called the "forgetting parameter" for a joint process estimator. The lambda input 543 provides control for the rate of cancellation for the joint process estimator. In the present embodiment, lambda is set to a low value such as 0.8. Because statistics of the signal are non-stationary, a low value improves tracking. The minimum error input 544 provides an initialization parameter (conventionally known as the "initialization value") for the joint process estimator 550. The minimum error value is 106. This initialization parameter prevents the joint process estimator 500 from dividing by zero upon initial calculations. The number of cells input 545 to the joint process estimator 550 configures the number of cells for the joint process estimator. The number of cells for the saturation transform operation 406 is six. As well understood in the art, for each sine wave, the joint process estimator requires two cells. If there are two sine waves in the 35 250 beatsminute range, six cells allows for the two heart beat sine waves and one noise sine wave.

The joint process estimator 550 subjects the first input vector on the first input 542 to a correlation cancellation based upon each of the plurality of reference signal vectors provided in the second input 540 to the correlation canceler 531 (all 117 reference vectors in sequence in the present embodiment). The correlation cancellation results in a single output vector for each of the 117 reference vectors. Each output vector represents the information that the first input vector and the corresponding reference signal vector do not have in common. The resulting output vectors are provided as an output oW o to the joint process estimator, and subjected to the low pass filter module 552. The low pass filter 552 comprises a FIR filter with 25 taps and with a comer frequency of 10 Hz with the sampling frequency of 62.5 Hz at the decimation frequency).

The joint process estimator 550 has a settling time of 150 data points.

Therefore, the last 120 data points from each 270 point output vector are used for further processing.

The output vectors are further processed together as a whole, and are divided into a plurality of bins of equal number of data points. As depicted in Figure 18, the output vectors are 30 provided to a master power curve module 554 and to a Divide into five Equal Bins module 556. The Divide into Five Equal Bins module 556 divides each of the output vectors into five bins of equal number of data points with 120 data points per vector, each bin has 24 data points). Each bin is then provided to the Bin Power Curves module 558.

-62- The Master Power Curve module 554 performs a saturation transform as follows: for each output vector, the sum of the squares of the data points is ascertained. This provides a sum of squares value corresponding to each output vector (each output vector corresponding to one of the saturation scan values). These values provide the basis for a master power curve 555, as further represented in Figure 22. The horizontal axis of the power curve represents the saturation axis scan values and the vertical axis represents the sum of squares value (or output energy) for each output vector. In other words, as depicted in Figure 22, each of the sum of squares could be plotted with the magnitude of the sum of squares value plotted on the vertical "energy output" axis at the point on the horizontal axis of the corresponding saturation scan value which generated that output vector. This results in a master power curve 558, an example of which is depicted in Figure 22. This provides a saturation transform in which the spectral content of the attenuated energy is examined by looking at every possible saturation value and examining the output value for the assumed saturation value. As will be understood, where the first and second inputs to the correlation canceler 531 are mostly correlated, the sum of squares for the corresponding output vector of the correlation canceler 531 will be very low. Conversely, where the correlation between the first and second inputs to the correlation canceler 531 are not significantly correlated, the sum of squares of the output vector will be high. Accordingly, where the spectral content of the reference signal and the first input to the correlation canceler are made up mostly of physiological movement of venous blood due to respiration) and non.physiological motion induced) noise, the output energy will be low. Where the spectral content of the reference signal and the first input to the correlation canceler 20 are not correlated, the output energy will be much higher.

A corresponding transform is completed by the Bin Power Curves module 558, except a saturation transform power curve is generated for each bin. The resulting power curves are provided as the outputs of the saturation transform module 406.

In general, in accordance with the signal model, there will be two peaks e' 25 in the power curves, as depicted in Figure 22. One peak corresponds to the arterial oxygen saturation of the blood, and one peak corresponds to the venous oxygen concentration of the blood. With reference to the signal model of the present invention, the peak corresponding to the highest saturation value (not Oeo 0necessarily the peak with the greatest magnitude) corresponds to the proportionality coefficient r. In other words, the proportionality coefficient r a corresponds to the redlinfrared ratio which will he measured for 30 the arterial saturation. Similarly, peak that corresponds to the lowest saturation value (not necessarily the peak with the lowest magnitude) will generally correspond to the venous oxygen saturation, which corresponds to the proportionality coefficient r v in the signal model of the present invention. Therefore, the proportionality coefficient rv will be a redlinfrared ratio corresponding to the venous oxygen saturation.

-63- In order to obtain arterial oxygen saturation, the peak in the power curves corresponding to the highest saturation value could be selected. However, to improve confidence in the value, further processing is completed. Figure 19 illustrates the operation of the saturation calculation module 408 based upon the output of the saturation transform module 406 and the output of the statistics module 404. As depicted in figure 19, the bin power curves and the bin statistics are provided to the saturation calculation module 408. In the present embodiment, the master power curves are not provided to the saturation module 408 but can be displayed for a visual check on system operation. The bin statistics contain the red and infrared RMS values, the seed saturation value, and a value representing the cross-correlation between the red and infrared signals from the statistics module 404.

The saturation calculation module 408 first determines a plurality of bin attributes as represented by the Compute Bin Attributes module 560. The Compute Bin Attributes module 560 collects a data bin from the information from the bin power curves and the information from the bin statistics. In the present embodiment, this operation involves placing the saturation value of the peak from each power curve corresponding to the highest saturation value in the data bin. In the present embodiment, the selection of the highest peak is performed by first computing the first derivative of the power curve in question by convolving the power curve with a smoothing differentiator filter function. In the present example, the smoothing differentiator filter function (using a FIR filter) has the following coefficients: 0.014964670230367 0.098294046682706 20 0.204468276324813 2.717182664241813 5.704485606695227 0.000000000000000 -5.704482606695227 25 -2.717182664241813 -0.204468276324813 -0.098294046682706 -i 0.014964670230367 This filter performs the differentiation and smoothing. Next, each point in the original power curve in 30 question is evaluated and determined to be a possible peak if the following conditions are met: the point is at least 2% of the maximum value in the power curve; the value of the first derivative changes from greater than zero to less than or equal to zero. For each point that is found to be a possible peak, the neighboring points are examined and the largest of the three points is considered to be the true peak.

-64- The peak width for these selected peaks is also calculated. The peak width of a power curve in question is computed by summing all the points in the power curve and subtracting the product of the minimum value in the power curve and the number of points in the power curve. The peak width calculation is applied to each of the bin power curves. The maximum value is selected as the peak width.

In addition, the infrared RMS value from the entire snapshot, the red RMS value, the seed saturation value far each bin, and the cross correlation between the red and infrared signals from the statistics module 404 are also placed in the data bin. The attributes are then used to determine whether the data bin consists of acceptable data, as represented in a Bin Qualifying Logic module 562.

If the correlation between the red and infrared signals is too low, the bin is discarded. If the saturation value of the selected peak for a given bin is lower than the seed saturation for the same bin, the peak is replaced with the seed saturation value. If either red or infrared RMS value is below a very small threshold, the bins are all discarded, and no saturation value is provided, because the measured signals are considered to be too small to obtain meaningful data. If no bins contain acceptable data, the exception handling module 563 provides a message to the display 336 that the data is erroneous.

if some bins qualify, those bins that qualify as having acceptable data are selected, and those that do not qualify are replaced with the average of the bins that are accepted. Each bin is given a time stamp in order to maintain the time sequence. A voter operation 565 examines each of the bins and selects the three highest saturation values. These values are forwarded to a clip and smooth operation 566.

20 The clip and smooth operation 566 basically performs averaging with a low pass filter. The low V9606 pass filter provides adjustable smoothing as selected by a Select Smoothing Filter module 568. The Select 0S 0:0.i Smoothing Filter module 568 performs its operation based upon a confidence determination performed by a High Confidence Test module 570. The high confidence test is an examination of the peak width for the bin power curves. The width of the peaks provides some indication of motion by the patient wider peaks S 25 indicating motion. Therefore, if the peaks are wide, the smoothing filter is slowed down. If peaks are narrow, the smoothing filter speed is increased. Accordingly, the smoothing filter 566 is adjusted based an the confidence level. The output of the clip and smooth module 566 provides the oxygen saturation ":ee values.

0 In the presently preferred embodiment, the clip and smooth filter 566 takes each new saturation 30 value and compares it to the current saturation value. If the magnitude of the difference is less than 16 (percent oxygen saturation) then the value is pass. Otherwise, if the new saturation value is less than the filtered saturation value, the new saturation value is changed to 16 less than the filtered saturation value.

If the new saturation value is greater than the filtered saturation value, then the new saturation value is changed to 16 more than the filtered saturation value.

During high confidence (no motion), the smoothing filter is a simple one-pole or exponential smoothing filter which is computed as follows: y(n) 0.6 x(n) 0.4 y(n-1) where x(n) is the clipped new saturation value, and y(n) is the filtered saturation value.

During motion condition, a three-pole IIR (infinite impulse response) filter is used. Its characteristics are controlled by three time constants t a t b and t c with values of 0.985, 0.900, and 0.94 respectively.

The coefficients for a direct form I, IIR filter are computed from these time constants using the folowing relationships: a 0 0 a 1 tb (tc)(ta tb a2 (tb)(c)(ta tb a3 (tb) 2 (tc) 2 (ta) b0 1 tb- (tc)(ta (tc)(tb)) b 2 (tb)(tc)(ta 1) b 2 (tb)(tc)(t b (tb (t a) ta) 20 Figure 20 and 21 illustrate the pulse rate module 410 (Figure 14) in greater detail. As illustrated in Figure 20, the heart rate module 410 has a transient removal and bandpass filter module 578, a motion artifact suppression module 580, a saturation equation module 582, a motion status module 584, first and second spectral estimation modules 586, 588, a spectrum analysis module 590, a slew rate limiting module **592, an output filter 594, and an output filter coefficient module 596.

25 As further depicted in Figure 20, the heart rate module 410 accepts the infrared and red 570sample snapshots from the output of the decimation module 402. The heart rate module 410 further accepts the saturation value which is output from the saturation calculation module 408. In addition, the "maximum peak width as calculated by the confidence test module 570 (same as peak width calculation described above) is also provided as an input to the heart rate module 410. The infrared and red sample 30 packets, the saturation value and the output of the motion status module 584 are provided to the motion artifact suppression module 580.

-66- The average peak width value provides an input to a motion status module 584. If the peaks are wide, this is taken as an indication of motion. If motion is not detected, spectral estimation on the signals is carried out directly without motion artifact suppression.

In the case of motion, motion artifacts are suppressed using the motion artifact suppression module 580. The motion artifact suppression module 580 is nearly identical to the saturation transform module 406. The motion artifact suppression module 580 provides an output which connects as an input to the second spectral estimation module 588. The first and second spectral estimation modules 586, 588 have outputs which provide inputs to the spectrum analysis module 590. The spectrum analysis module 590 also receives an input which is the output of the motion status module 584. The output of the spectrum analysis module 590 is the initial heart rate determination of the heart rate module 410 and is provided as input to the slew rate limiting module 592. The slew rate limiting module 592 connects to the output filter 594. The output filter 594 also receives an input from the output filter coefficient module 596. The output filter 594 provides the filtered heart rate for the display 336 (Figure 11).

In the case of no motion, one of the signals (the infrared signal in the present embodiment) is subjected to DC removal and bandpass filtering as represented in the DC removal and bandpass filter module 578. The DC removal and bandpass filter module 578 provide the same filtering as the DC removal and bandpass filter modules 536, 538. During no motion conditions, the filtered infrared signal is provided to the first spectral estimation module 586.

S.The spectral estimation comprises a Chirp Z transform that provides i 20 a frequency spectrum of heart rate information. The Chirp Z transform is used rather than a conventional Fourier Transform because a frequency range for the desired output can be designated in a Chirp Z transform. Accordingly, a frequency spectrum of the heart rate is provided between 30 and 250 beats/minute. The frequency spectrum is provided to a spectrum analysis module 590 which selects the first harmonic from the spectrum as the pulse rate.

Usually, the first harmonic is the peak in the frequency spectrum that has the greatest magnitude and represents the pulse rate. However, in certain conditions, the second or third harmonic can exhibit the ooooo greater magnitude. With this understanding, in order to select the first harmonic, the first peak that has 0 an amplitude of at least 1/20th of the largest peak in the spectrum is selected). This minimizes the possibility of selecting as the heart rate a peak in the Chirp Z transform caused by noise.

S.i 30 In the case of motion, a motion artifact suppression is completed on the snapshot with the motion artifact suppression module 580. The motion artifact suppression module 580 is depicted in greater detail in Figure 21. As can be seen in Figure 21, the motion artifact suppression module 580 is nearly identical -67to the saturation transform module 406 (Figure 18). Accordingly, the motion artifact suppression module has a motion artifact reference processor 570 and a motion artifact correlation canceler 571.

The motion artifact reference processor 570 is the same as the reference processor 530 of the saturation transform module 406. However, the reference processor 570 utilizes the saturation value from the saturation module 408, rather than completing an entire saturation transform with the 117 saturation scan values. The reference processor 570, therefore, has a saturation equation module 581, a reference generator 582, a DC removal module 583, and a bandpass filter module 585. These modules are the same as corresponding modules in the saturation transform reference processor 530. The saturation equation module 581 receives the arterial saturation value from the saturation calculation module 408 rather than doing a saturation axis scan as in the saturation transform module 406. This is because the arterial saturation has been selected, and there is no need to perform an axis scan.

Accordingly, the output of the saturation equation module 581 corresponds to the proportionality constant ra (Lie., the expected red to infrared ratio for the arterial saturation value). Otherwise, the reference processor 570 performs the same function as the reference processor 530 of the saturation transform module 406.

The motion artifact correlation canceler 571 is also similar to the saturation transform correlation canceler 531 (Figure 18). However, the motion artifact suppression correlation canceler 571 uses a slightly different motion artifact joint process estimator 572. Accordingly, the motion artifact suppression correlation canceler 571 has a joint process estimator 572 and a low-pass filter 573. The motion artifact 20 joint process estimator 572 differs from the saturation transform joint process estimator 550 in that there are a different number of cells (between 6 and 10 in the present case), as selected by the Number of Cells input 574, in that the forgetting parameter differs (.98 in the present example), and in that oOooothe time delay due to adaptation differs. The low-pass filter 573 is the same as the low pass filter 552 of the saturation transform correlation canceler 531.

25 Because only one saturation value is provided to the reference processor, only one output vector of 270 samples results at the output of the motion artifact suppression correlation canceler 571 for each ooo input packet of 570 samples. Where the infrared wavelength is provided as oo ooa first input to the correlation canceler, the output of the correlation canceler 571 provides a clean infrared waveform. It should be understood that, as described above, the infrared and red wavelength signals could 30 be switched such that a clean red waveform is provided at the output of the motion artifact suppression correlation canceler 571. The output of the correbtion canceler 571 is a clean waveform because the actual saturation value of the patient is known which allows the reference processor 570 to generate a noise reference for inputting to the correlation canceler 571 as the reference signal. The clean waveform -68at the output of the motion artifact suppression module 580 is a clean plethysmograph waveform which can be forwarded to the display 336.

As described above, an alternative joint process estimator uses the QRD least squares lattice approach (Figure 8a, 9a and 10a). Accordingly, the joint process estimator 573 (as well as the joint process estimator 550) could be replaced with a joint process estimator executing the ORD least squares lattice operation.

Figure 21a depicts an alternative example of the motion artifact suppression module with a joint process estimator 572a replacing the joint process estimator 572. The joint process estimator 572a comprises a QRD least squares lattice system as in Figure 10a. In accordance with this example, different initialization parameters are used as necessary for the QRD algorithm.

The initialization parameters are referenced in Figure 21a as "Number of Cells," "Lambda," "MinSumErr," "Gamslnit," and "SumErrlnit." Number of Cells and Lambda correspond to like parameters in the joint process estimator 572. Gamslnit corresponds to the y initialization variable for all stages except the zero order stage, which as set forth in the QRD equations above is initialized to SummErrlnit provides the 6 initialization parameter referenced above in the QRD equations. In order to avoid overflow, the larger of the actual calculated denominator in each division in the QRD equations and MinSumErr is used. The preferred initialization parameters are as follows: Number of Cells 6 Lambda .8 20 MinSumErr 10- 20 Gamslnit 10- 2 •SumErrlnit 10 6 The clean waveform output from the motion artifact suppression module 580 also provides an input to the second spectral estimation module 588. The second spectral estimation module 588 performs the 25 same Chirp Z transform as the first spectral estimation module 586. In the case of no motion, the output from the first spectral estimation module 586 is provided to the spectrum analysis module 586; in the case of motion, the output from the second spectral estimation module 588 is provided to a spectrum analysis module 590. The spectrum analysis module 590 examines the frequency spectrum from the appropriate spectral estimation module to determine the pulse rate. In the case of motion, the spectrum analysis 30 module 590 selects the peak in the spectrum with the highest amplitude, because the motion artifact suppression module 580 attenuates all other frequencies to a value below the actual heart rate peak. In the case of no motion, the spectrum analysis module selects the first harmonic in the spectrum as the heart rate as described above.

-69- The output of the spectrum analysis module 590 provides the raw heart rate as an input to the slew rate limiting module 592, which provides an input to an output filter 594. The slew rate limiting module 592 prevents changes greater than 20 beats/minute per 2 second interval.

The output filter 594 comprises an exponential smoothing filter similar to the exponential smoothing filter described above with respect to the clip and smooth filter 566. The output filter is controlled via an output filter coefficient module 596. If motion is large, this filter is slowed down, if there is little or no motion, this filter can sample much faster and still maintain a clean value. The output from the output filter 594 is the pulse of the patient, which is advantageously provided to the display 336.

Alternative To Saturation Transform Module-Bank Of Filters An alternative to the saturation transform of the saturation transform module 406 can be implemented with a bank of filters as depicted in Figure 23. As seen in Figure 23, two banks of filters, a first filter bank 600 and a second filter bank 602 are provided. The first filter bank 600 receives a first measured signal SAb(t) (the infrared signal samples in the present embodiment) on a corresponding first filter bank input 604, and the second filter bank 602 receives a second measured signal SAa(t) (the red samples in the present embodiment) on a corresponding second filter bank input 606. The first and second filter banks utilize static recursive polyphase bandpass filters with fixed center frequencies and corner frequencies. Recursive polyphase filters are described in an article Harris, et. al.

"Digital Signal Processing With Efficient Polyphase Recursive All-Pass filters" attached hereto as Appendix 20 A. However, adaptive implementations are also possible. In the present implementation, the recursive polyphase bandpass filter elements are each designed to include a specific center frequency and bandwidth.

a a There are N filter elements in each filter bank. Each of the filter elements in the first filter bank 600 have a matching same center frequency and bandwidth) filter element in the second filter bank 602. The center frequencies and the corner frequencies of N elements are each designed to occupy N frequency ranges. 0 to F 1

F

1

F

2

F

2

F

3

F

3

F

4

FN.

1

F

N as shown in Figure 23.

It should be understood that the number of filter elements can range from 1 to infinity. However, There are approximately 120 separate filter elements with center frequencies spread evenly across a frequency range of 25 beatslminute 250 beatslminute.

30 The outputs of the filters contain information about the primary and secondary signals for the first and second measured signals (red and infrared in the present example) at the specified frequencies. The outputs for each pair of matching filters (one in the first filter bank 600 and one in the second filter bank 602) are provided to saturation determination modules 610. Figure 23 depicts only one saturation determination module 610 for ease of illustration. However, a saturation determination module can be provided for each matched pair of filter elements for parallel processing. Each saturation determination module has a ratio module 616 and a saturation equation module 618.

The ratio module 616 forms a ratio of the second output to the first output. For instance, in the present example, a ratio of each red RMS value to each corresponding infrared RMS value (Red/IR) is completed in the ratio module 616. The output of the ratio module 616 provides an input to the saturation equation module 618 which references a corresponding saturation value for the input ratio.

The output of the saturation equation modules 618 are collected (as represented in the histogram module 620) for each of the matched filter pairs. However, the data collected is initially a function of frequency and saturation. In order to form a saturation transform curve similar to the curve depicted in Figure 22, a histogram or the like is generated as in Figure 24. The horizontal axis represents the saturation value, and the vertical axis represents a summation of the number of points (outputs from the saturation equation modules 618) collected at each saturation value. In other words, if the output of the saturation equation module 618 for ten different matched filter pairs indicates a saturation value of 98%, then a point in the histogram of Figure 24 would reflect a value of 10 at 98% saturation. This results in a curve similar to the saturation transform curve of Figure 22. This operation is completed in the histogram module 620.

The results of the histogram provide a power curve similar to the power curve of Figure 22.

Accordingly, the arterial saturation can be calculated from the histogram by selecting the peak (greatest 20 number of occurrences in the area of interest) corresponding to the highest saturation value the peak in Figure peaks corresponding to the highest saturation value peak. Similarly, the venous or background saturation can be determined from the histogram by selecting the peak corresponding to the lowest saturation value the peak in Figure 24), in a manner similar to the processing in the saturation S calculation module 408.

It should be understood that as an alternative to the histogram, the output saturation (not necessarily a peak in the histogram) corresponding to the highest saturation value could be selected as the arterial saturation with the corresponding ratio representing r a Similarly, the output saturation corresponding to the lowest saturation value could be selected as the venous or background saturation with the corresponding ratio representing For example, the entry'a' in the histogram of Figure 24 would be chosen as the arterial saturation and the entry in the histogram with the lowest saturation value would be chosen as the venous or background saturation.

-71- ALTERNATIVE DETERMINATION OF COEFFICIENTS r, AND r As explained above, primary and secondary signal portions, particularly for pulse oximetry, can be modeled as follows: Srd s n 1 (red) (89) SIR s n 2 (infrared) sI ras 2 and n 1 r'v 2 (91) Substituting Equation (91) into Equation (89) provides the following: Sred ra 2 rn 2 (red) (92) Note that Sred and SIR are used in the model of equations (89) This is because the discussion below is particularly directed to blood oximetry. Sre d and SIR correspond to S 1 and S 2 in the preceding text, and the discussion that follows could be generalized for any measure signal S, and S 2 As explained above, determining r a and rv (which correspond to arterial and venous blood oxygen saturation via a saturation equation) can be accomplished using the saturation transform described above doing a scan of many possible coefficients. Another method to obtain ra and r, based on red and infrared data is to look for ra and r, which minimize the correlation between s k and nk, assuming sk is at least somewhat (and preferably substantially) uncorrelated with nk (where k 1 or These values can be found by minimizing the following statistical calculation function for k 2: Correlation(s,n) s2(SredS,,Rra, rv)n(S Sir where i represents time.

It should be understood that other correlation functions such as a normalized correlation could also .be used.

Minimizing this quantity often provides a unique pair of r a and r, if the noise component is 25 uncorrelated to the desired signal component. Minimizing this quantity can be accomplished by solving .Equations (90) and (92) for s 2 and n 2 and finding the minimum of the correlation for possible values of ra and r, Solving for s 2 and n 2 provides the following: inverting the two-by-two matrix provides: -72- Sred

SIR

(ra rv

S

1Lj 1 n2) (ra 1 ra rv (1 L~i Ta) Thus, S21 (1 -rV S r (n)2 ra-rv Ki ra) SRed) S2= 1~-r (Sred rv SIR) n. -1 (-red ra 1q) ra v Preferably, the correlation of equation (93) is enhanced with a user specified window function as follows:

N

Correlation(s., n 2 1E W~s 2 5 red? 5 IR, ra, rv) ri2(Sredl SIR, (93a) The Blackman Window is the presently preferred embodiment. It should be understood that there are many additional functions which minimize the correlation between signal and noise. The function above is simply one. Thus, -73- N

W.

Correlation (s 2 n 2 (S rdR)(S i=1 (r I N N N 2 -(Sred)2Wi+(ra+rv) SRiSred Wi+(SIR)2W (ra -r 1 1 i= 1 (93b) In order to implement the minimization on a plurality of discrete data points, the sum of the squares of the red sample points, the sum of the squares of the infrared sample points, and the sum of the product of the red times the infrared sample points are first calculated (including the window function, wj):

N

RR )E(Sr 2

W

i=1 (Sin )w, i=1 1=1

*N.

IRR (Sred)Wi i=1 S* These values are used in the correlation equation (93b). Thus, the correlation equation becomes an equation in terms of two variables, ra and ry. To obtain ra and an exhaustive scan is executed for a good cross-section of possible values for ra and r. 20-50 values each corresponding to saturation values ranging from 30 105). The minimum of the correlation function is then selected and the values of ra and r, which resulted in the minimum are chosen as ra and r v -74- Once r a and r, have been obtained, arterial oxygen saturation and venous oxygen saturation can be determined by provided ra and r, to a saturation equation, such as the saturation equation 502 of the statistics module 404 which provides an oxygen saturation value corresponding to the ratios ra and r.

In a further implementation to obtain ra and r the same signal model set forth above is again used. In order to determine ra and r, in accordance with this implementation, the energy in the signal s 2 is maximized under the constraint that s 2 is uncorrelated with n 2 Again, this implementation is based upon minimizing the correlation between s and n and on the signal model where the signal s relates to the arterial pulse and the signal n is the noise (containing information on the venous blood, as well as motion artifacts and other noise); ra is the ratio (RED/IR) related to arterial saturation and r, is the ratio (RED/IR) related to venous saturation. Accordingly, in this implementation, ra and rv are determined such that the energy of the signal S 2 is maximized where s2 and n 2 are uncorrelated. The energy of the signal s 2 is given by the following equation:

N

ENERGYs) 1E N ENERGY(s2) 2 (Sred

SIR)

2 (94) (r a-r) =1 N N (ra -rv) 2 i=1 =1 =1 **15 between the red and infrared signals.

(r [R-2r ,+r,2R2 (96) where R 1 is the energy of the red signal, R 2 is the energy of the infrared signal and R1, 2 is the correlation between the red and infrared signals.

The correlation between s 2 and n 2 is given by -R R1,2-rv r R2] (97) (ra-r) 2 1 N Correlation(s 2 ,n 2 -2 Z e (S -rvSr) S raSR) (ar) 2 ji=1 As explained above, the constraint is that s k and nk (k 2 for the present example) are uncorrelated. This "decorrelation constraint" is obtained by setting the correlation of Equation (97) to zero as follows:

R

12 rarR 2 0 (98) In other words, the goal is to maximize equation (94) under the constraint of equation (98).

In order to obtain the goal, a cost function is defined a Lagrangian optimization in the present embodiment) as follows: J(rarV,) r [R -2 rR 2 +rvR2 +(ra+rv)R a v) 2 (99) Programming, Addison-Wesley, 2d Ed., 1984.

Alonwhere p is the Lagrange multiplier. Findingf we assume that the value of if, r and that solve the cost functionst can betic, the functions R 1

R

2 and R12 defined above are time dependent. Accordingly, with two equations, two unknowns can be obtained by expressing the decorrelation constraint set forth in equation (98) at two 15 different times. The decorrelation constraint can be expressed at two different times, t 1 and t 2 as follows:

-R

1 (t 1 (ra+rv)R 12 rarvR 2 1) 0 (100) -76- -R(t 2 (ra+r)R12(t~ rarR 2 0 (101 1 Because equations (100) and (101) are non-linear in r, and rya change of variables allows the use of linear techniques to solve these two equations. Accordingly, with x ra rv; y rarv equations (100) and (101) become

R

12 (t)x

R

2 (t)y

R

l (tf) (102) R2()

R

2 R(t (103) These equation (102) and (103) can be solved for x and y. Then, solving for r a and r, from the changes of variables equations provides the following: v x r2 xr+Y 0 (104) rv :Solving equation (104) results in two values for rv. The r, value that results in xx 2 rvy 0 is selected. If both values of r, result in x2-rv y 0, the r, that maximizes the energy of s 2 10 (Energy(s 2 at t 2 is selected. r, is then substituted into the equations above to obtain r a Alternatively ra can be found directly in the same manner r, was determined.

Alternative To Saturation Transform-Complex FFT The blood oxygen saturation, pulse rate and a clean plethysmographic waveform of a patient can also be obtained using the signal model of the present invention using a complex FFT, as explained further 15 with reference to Figures 25A-25C. In general, by utilizing the signal model of equations with two measured signals, each with a first portion and a second portion, where the first portion represents a desired portion of the signal and the second portion represents the undesired portion of the signal, and where the measured signals can be correlated with coefficients r a and rv, a fast saturation transform on a discrete basis can be used on the sample points from the output of the decimation operation 402.

Figure 25A corresponds generally to Figure 14, with the fast saturation transform replacing the previously described saturation transform. In other words, the operations of Figure 25A can replace the operations of Figure 14. As depicted in Figure 25A, the fast saturation transform is represented in a fast -77saturation transformpulse rate calculation module 630. As in Figure 14, the outputs are arterial oxygen saturation, a clean plethysmographic waveform, and pulse rate. Figure 25B and 25C illustrate additional detail regarding the fast saturation transform/pulse rate calculation medule 630. As depicted in Figure the fast saturation transform module 630 has infrared log and red log modules 640, 642 to perform a log normalization as in the infrared and red log modules 480, 482 of Figure 17. Similarly, there are infrared DC removal and red DC removal modules 644, 646. In addition, there are infrared and red high-pass filter modules 645, 647, window function modules 648, 640, complex FFT modules 652, 654, select modules 653, 655, magnitude modules 656, 658, threshold modules 660, 662, a point-by-point ratio module 670, a saturation equation module 672, and a select saturation module 680. There are also phase modules 690, 692, a phase difference module 694, and a phase threshold module 696. The output of the select saturation module 680 provides the arterial saturation on an arterial saturation output line 682.

In this alternative, the snapshot for red and infrared signals is 562 samples from the decimation module 402. The infrared DC removal module 644 and the red DC removal module 646 are slightly different from the infrared and red DC removal modules 484, 486 of Figure 17. In the infrared and red DC removal modules 644, 646 of Figure 25B, the mean of all 563 sample points for each respective channel is calculated. This mean is then removed from each individual sample point in the respective snapshot in order to remove the baseline DC from each sample. The outputs of the infrared and red DC removal modules 644, 646 provide inputs to respective infrared high-pass filter module 645 and red high-pass filter module 647.

20 The high-pass filter modules 645, 647 comprise FIR filters with 51 taps for coefficients.

Preferably, the high-pass filters comprise Chebychev filters with a side-lobe level parameter of 30 and a oo corner frequency of .5 Hz 30 beatsminute). It will be understood that this filter could be varied for performance. With 562 sample points entering the high-pass filters, and with 51 taps for coefficients, there are 512 samples provided from these respective infrared and red snapshots at the output of the highpass filter modules. The output of the high-pass filter modules provides an input to the window function modules 648, 650 for each respective channel.

The window function modules 648, 650 perform a conventional windowing function. A Kaiser windowing function is used in the present embodiment. The functions throughout Figure 25B maintain a point-by-point analysis. In the present embodiment, the time bandwidth product for the Kaiser window function is 7. The output of the window function modules provides an input to the respective complex Fast Fourier Transform (FFT) modules 652, 654.

The complex FFT modules 652, 654 perform complex FFTs on respective infrared and red channels on the data snapshots. The data from the complex FFTs is then analyzed in two paths, once which -78examines the magnitude and one which examines the phase from the complex FFT data points. However, prior to further processing, the data is provided to respective infrared and red select modules 653, 655 because the output of the FFT operation will provide repetitive information from 0-112 the sampling rate and from 112 the sampling rate to the sampling rate. The select modules select only samples from 0-1/2 the sampling rate 0-31.25 Hz in the present embodiment) and then select from those samples to cover a frequency range of the heart rate and one or more harmonics of the heart rate. Samples which fall in the frequency range of 20 beats per minute to 500 beats per minute are selected. This value can be varied in order to obtain harmonics of the heart rate as desired.

Accordingly, the output of the select modules results in less than 256 samples. The sample points 2-68 of the outputs of the FFTs are utilized for further processing.

In the first path of processing, the output from the select modules 653, 655 are provided to respective infrared and red magnitude modules 656, 658. The magnitude modules 656, 658 perform a magnitude function wherein the magnitude on a point-by-point basis of the complex FFT points is selected for each of the respective channels. The outputs of the magnitude modules 656, 658 provide an input to infrared and red threshold modules 660, 662.

The threshold modules 660, 662 examine the sample points, on a point-by-point basis, to select those points where the magnitude of an individual point is above a particular threshold which is set at a o percentage of the maximum magnitude detected among all the remaining points in the snapshots. In the present embodiment, the percentage for the threshold operation is selected as 1% of the maximum 20 magnitude.

0*00*After thresholding, the data points are forwarded to a point-by-point ratio module 670. The pointby-point ratio module takes the red over infrared ratio of the values on a point-by-point basis. However, a further test is performed to qualify the points for which a ratio is taken. As seen in Figure 25B, the sample points output from the select modules 653, 655 are also provided to infrared and red phase modules 690, 692. The phase modules 690, 692 select the phase value from the complex FFT points. The output of the phase modules 690, 692 is then presented to a phase difference module 694.

The phase difference module 694 calculates the difference in phase between the corresponding data points from the phase modules 690, 692. If the magnitude of the phase difference between any two I corresponding points is less than a particular threshold 0.1 radians) in the present embodiment), then m the sample points qualify. If the phase of two corresponding sample points is too far apart, then the sample points are not used. The output of the phase threshold module 696 provides an enable input to the REDIIR rate module 670. Accordingly, in order for the ratio of a particular pair of sample points to be taken, the three tests are executed: -79- 6. the red sample must pass the red threshold 660; 7. the infrared sample must pass the infrared threshold 662; and 8. the phase between the two points must be less than the predefined threshold as determined in the phase threshold 696.

For those sample points which qualify, a ratio is taken in the ratio module 670. For those points which do not qualify, the saturation is set to zero at the output of the saturation equation 672.

The resulting ratios are provided to a saturation equation module which is the same as the saturation equation modules 502, 520 in the statistics module 504. In other words, the saturation equation module 672 accepts the ratio on a point-by-point basis and provides as an output a corresponding saturation value corresponding to the discrete ratio points. The saturation points output from the saturation equation module 672 provide a series of saturation points which could be plotted as saturation with respect to frequency. The frequency reference was entered into the points at the complex FFT stage.

The arterial (and the venous) saturation can then be selected, as represented in the select arterial saturation module 680, in one of two methods. According to one method, the arterial saturation value can be selected simply as the point corresponding to the largest saturation value for all points output from the saturation equation module 672 for a packet. Alternatively, a histogram similar to the histogram of Figure 22 can be generated in which the number of saturation values at different frequencies (points) are summed to form a histogram of the number of occurrences for each particular saturation value. In either method, the arterial saturation can be obtained and provided as 20 an output to the select arterial saturation module on the arterial saturation output line 682. In order to obtain the venous saturation, the minimum arterial saturation value, of points that exhibit non-zero value, is selected rather than the maximum arterial saturation value. The saturation can be provided to the display 336.

The fast saturation transform information can also be used to provide the pulse rate and the clean plethysmographic wave form as further illustrated in Figure 25C. In order to obtain the pulse rate and a clean plethysmographic wave form, several additional functions are necessary. As seen in Figure 25C, the pulse rate and clean plethysmographic wave form are determined using a window function module 700, a spectrum analysis module 702 and an inverse window function module 704.

As depicted in Figure 25C, the input to the window function module 700 is obtained from the output of the complex FFT modules 652 or 654. In the present embodiment, only one measured signal is necessary. Another input to the window function module 700 is the arterial saturation obtained from the output of the select arterial saturation module 680.

The window function module performs a windowing function selected to pass those frequencies that significantly correlate to the frequencies which exhibited saturation values very close to the arterial saturation value. In the present embodiment, the following windowing function is selected: 1 sart- SA100 Tn1 (105) 100 where SAT n equals the saturation value corresponding to each particular frequency' for the sample points and SATart represents the arterial saturation as chosen at the output of the select arterial saturation module 680. This window function is applied to the window function input representing the complex FFT of either the red or the infrared signal. The output of the window function module 700 is a red or infrared signal represented with a frequency spectrum as determined by the FFT, with motion artifacts removed by the windowing function. It should be understood that many possible window functions can be provided.

In addition, with the window function described above, it should be understood that using a higher power will provide more noise suppression.

In order to obtain pulse rate, the output points from the window function module 700 are provided to a spectrum analysis module 702. The spectrum analysis module 702 is the same as the spectrum 15 analysis module 590 of Figure 20. In other words, the spectrum analysis module 702 determines the pulse rate by determining the first harmonic in the frequency spectrum represented by the output points of the windowing function 700. The output of spectrum analysis module 702 is the pulse rate.

In order to obtain a clean plethysmographic waveform, the output of the windowing function 700 is applied to an inverse window function module 704. The inverse window function module 704 completes 20 an inverse of the Kaiser window function of the window function module 648 or 650 of Figure 25B. In other words, the inverse window function 704 does a point-by-point inverse of the Kaiser function for points that are still defined. The output is a clean plethysmographic waveform.

Accordingly, by using a complex FFT and windowing functions, the noise can be suppressed from the plethysmographic waveform in order to obtain the arterial saturation, the pulse rate, and a clean 25 plethysmographic waveform. It should be understood that although the above description relates to operations primarily in the frequency domain, operations that obtain similar results could also be accomplished in the time domain.

-81- Relation to Generalized Equations The measurements described for pulse oximetry above are now related back to the more generalized discussion above. The signals (logarithm converted) transmitted through the finger 310 at each wavelength Aa and Ab are: SAa(t)-SArel(t) eHbO2,AacAHb02xA(t)+ EHbAa c A Hb xA (t) Hb02,AaC Hb02 xV +HbAacVHbxV(t) (105a) SAa(t)- Hb02AacAHb02xA(t)+ HbAaCAHbxA(t) nAa(t); (105b) SAa(t) sAa(t) nAa(t); (105c) SAb(t- SAred2(t) -Hb02,Abc

A

Hb02

A

EHbAb cA Hb xA (t) +EHb02,Abc Hb02 xV HbAbcHb xV (106a) SAb(t)-EH2b02A

A

Hb A(t) Hbb c A Hb xA (t nAb(t) (106b) 20006c) 20 SAb(t)- sAb(t) nAb(t) (106c) The variables above are best understood as correlated to Figure 6c as follows: assume the layer in figure 6c containing A 3 and A 4 represents venous blood in the test medium, with A 3 representing deoxygenated hemoglobin (Hb) and A 4 representing oxygenated hemoglobin (HB02) in the venous blood. Similarly, assume that the layer in Figure 6c containing Ag and A 6 represents arterial blood in the test medium, with Ag representing deoxygenated hemoglobin (Hb) and A 6 representing oxygenated hemoglobin (HB02) in the arterial blood. Accordingly, cVHb02 represents the concentration of oxygenated hemoglobin in the venous blood, cVHb represents the concentration of deoxygenated hemoglobin in the venous blood, x V represents the thickness of the venous blood the thickness the layer containing A 3 and A 4 Similarly, cAHb02 represents the concentration of oxygenated hemoglobin in the arterial blood, cAHb represents the concentration of deoxygenated hemoglobin in the arterial blood, and x A represents the thickness of the arterial blood the thickness of the layer containing A 5 and A 6 The wavelengths chosen are typically one in the visible red range, Aa, and one in the infrared range, Ab. Typical wavelength values chosen are Aa 660nm and Ab 910nm. In accordance with -82the constant saturation method, it is assumed that c AHbo 2 (t)Ic AHb(t) constant, and c V Hbo2(t)Ic VHb(t) constant2 The oxygen saturation of arterial and venous blood changes slowly, if .at all, with respect to the sample rate, making this a valid assumption. The proportionality coefficients for equations (105) and (106) can then be written as: EHbO2X;aC4bO2X(O +EHbjaCHbX(t) ra(z)

-ACA

EHbO2,;XbC4bO2X(Z) +E~bbb( (107) sAa(t) ra(t)sAb(t) nAa(t) d ra(t)nAb(t) nAa(t) rv(t)nAb(t) 0 08a) (109a) (1l08b) (1 ONb *000 .00* 0 *00* 0 In pulse oximetry, it is typically the case that both equations (108) and (109) can s mult ipoulyin equation (106) by ralt) and then subtracting equation (106) from eq .uation zero secondary reference signal is determined by: SAP~) -ra(t)SAb(t) 1 Oa) be satisf ied (105), a non- -'EHb02.Aac HbO2xV(t) +EHbacvHbXV(t) +nAa(t) .ra(t)[EHb02.AbCV lbO2xV(t) +'ibAbCVHbXV(t) +nAb(t)]- 0*0**0 0 0e 0 (l11 a) Multiplying equation (106) by rv(t) and then subtracting equation (106) from equation (105), a non-zero primary reference signal is determined by: 1Ob SAaP) rv(t)SAb(t) (11IGb) SAP~) -rv(t)sAb(t)(1ib -83- The constant saturation assumption does not cause the venous contribution to the absorption to be canceled along with the primary signal portions sA(t) and sAb(t). Thus, frequencies associated with both the low frequency modulated absorption due to venous absorption when the patient is still and the modulated absorption due to venous absorption when the patient is moving are represented in the secondary reference signal Thus, the correlation canceler or other methods described above remove or derive both erratically modulated absorption due to venous blood in the finger under motion and the constant low frequency cyclic absorption of venous blood.

To illustrate the operation of the oximeter of Figure 11 to obtain clean waveform, Figures 26 and 27 depict signals measured for input to a reference processor of the present invention which employs the constant saturation method, the signals SAa(t) Sred(t) and SAb(t) SAIR(t). A first segment 26a and 27a of each of the signals is relatively undisturbed by motion artifact, the patient did not move substantially during the time period in which these segments were measured. These segments 26a and 27a are thus generally representative of the primary plethysmographic waveform at each of the measured wavelengths. A second segment 26b and 27b of each of the signals is affected by motion artifact, i.e., the patient did move during the time period in which these segments were measured. Each of these segments 26b and 27b shows large motion induced excursions in the measured signal. A third segment 26c and 27c of each of the signals is again relatively unaffected by motion artifact and is thus generally representative of the primary plethysmographic waveform at each of the measured wavelengths.

Figure 28 shows the secondary reference signal nAa(t) ranAb(t), as determined by a 20 reference processor of the present invention. Again, the secondary reference signal is correlated to the secondary signal portions nAa and nAb. Thus, a first segment 28a of the secondary reference signal t- is generally flat, corresponding to the fact that there is very little motion induced noise in the first segments 26a and 27a of each signal. A second segment 28b of the secondary reference signal n'(t) exhibits large excursions, corresponding to the large motion induced excursions in each of the measured signals. A third segment 28c of the noise reference signal is generally flat, again corresponding to the lack of motion artifact in the third segments 26c and 27c of each measured signal.

It should also be understood that a reference processor could be utilized in order to obtain the primary reference signal sAa-rsAb(t). The primary reference signal would be generally indicative of the plethysmograph waveform.

Figures 29 and 30 show the approximations s"Aa(t) and s"Ab(t) to the primary signals sAa(t) and SAb(t) as estimated by a correlation canceler using a secondary reference signal Note that the scale of Figures 26 through 30 is not the same for each figure to better illustrate changes. in each signal.

Figures 29 and 30 illustrate the effect of correlation cancellation using the secondary reference signal n'(t) -84as determined by the reference processor. Segments 29b and 30b are not dominated by motion induced noise as were segments 26b and 27b of the measured signals. Additionally, segments 29a, 30a, 29c, and have not been substantially changed from the measured signal segments 26a, 27a, 26c, and 27c where there was no motion induced noise.

It should be understood that approximation n'Aa(t) and n"Ab(t) to the secondary signals nAa(t) and nAb(t) as estimated by a correlation canceler using a primary reference signal can also be determined.

METHOD FOR ESTIMATING PRIMARY AND SECONDARY SIGNAL PORTIONS OF MEASURED SIGNALS IN A PULSE OXIMETER Implementing the various examples of the correlation canceler described above in software is relatively straightforward given the equations set forth above, and the detailed description above. However, a copy of a computer program subroutine, written in the C programming language, which calculates a primary reference using the constant saturation method and, using a joint process estimator 572 which implements a joint process estimator using the equations (54) (64) is set forth in Appendix B. This joint process estimator estimates a good approximation to the primary signal portions of two measured signals, each having a primary portion which is correlated to the primary reference signal and a secondary portion which is correlated to the secondary reference signal This subroutine is another way to implement the steps illustrated in the flowchart of Figure 9 for a monitor particularly adapted for pulse oximetry. The two signals are measured at two different wavelengths Aa and Ab, where Aa is typically 20 in the visible region and Ab is typically in the infrared region. For example, tailored specifically to perform pulse oximetry using the constant saturation method, Aa 660nm and Ab 940nm.

The correspondence of the program variables to the variables defined in equations (54) (64) in the discussion of the joint process estimator is as follows:

S

Am(t) nc[ml.Delta rf,m(t) nc[ml.fref b,m(t) nc[m.bref f(t) nc[ml.ferr bm(t) nc[ml.berr Vm(t) nc[m].Fswsqr Bm(t) nc[m].Bswsqr Ym(t) nc[ml.Gamma pma(t) nc[m].Roh_a pm,Ab(t) nc[m].Roh_b ema(t) nc[m].err_a emAb(t) nc[mi.errb KmAa(t) nc[ml.Ka Km,Ab(t) nc[m].K_b A first portion of the program performs the initialization of the registers 90, 92, 96, and 98 and intermediate variable values as in the "INITIAUZED CORRELATION CANCELER" action block 120. A second portion of the program performs the time updates of the delay element variables 110 with the value at the input of each delay element variable 110 is stored in the delay element variable 110 as in the "TIME UPDATE OF LEFT (Z' 1 ELEMENTS" action block 130. The calculation of saturation is performed in a separate module. Various methods for calculation of the oxygen saturation are known to those skilled in the art. One such calculation is described in the articles by G.A. Mook, et al, and Michael R. Neuman cited above. Once the concentration of oxygenated hemoglobin and deoxygenated hemoglobin are determined, the value of the saturation is determined similarly to equations (72) through (79) wherein measurements at times t 1 and t 2 are made at different, yet proximate times over which the saturation is relatively constant. For pulse oximetry, the average saturation at time t (t +t 2 )12 is then determined by:

A

CHbo2(t SSat r te AA (112a) arteria A A CHbOA HbA aa 'E I Satvenous() V CH2( (113a CHbO c(t -86- SHb,1aE-Hb, fA _b (1 EHB,,.aEaHbO2,XAa(EHB,b EHbO2, n .a n) 13 A third portion of the subroutine calculates the primary reference or secondary reference, as in the "CALCULATE PRIMARY OR SECONDARY REFERENCE or FOR TWO MEASURED SIGNAL SAMPLES" action block 140 for the signals SAa(t) and SAb(t) using the proportionality constants ra(t) and determined by the constant saturation method as in equation The saturation is calculated in a separate subroutine and a value of ra(t) or is imported to the present subroutine for estimating either the primary portions sAa(t) and sAb(t) or the secondary portions nAa(t) and nAb(t) of the composite measured signals SAa(t) and SAb(t).

A fourth portion of the program performs Z-stage update as in the "ZERO STAGE UPDATE" action block 150 where the Z-stage forward prediction error Fo(t) and Z-stage backward prediction error bo(t) are set equal to the value of the reference signal or just calculated. Additionally zero-stage values of intermediate variables 9o and 6 0 (t)(nc[m.Fswsqr and nc[m].Bswsqr in the program) are calculated for use in setting registers 90, 92, 96, and 98 values in the least-squares lattice predictor 70 in the regression filters 80a and A fifth portion of the program is an iterative loop wherein the loop counter, M, is reset to zero 15 with a maximum of m-NC_CELLS, as in the action block 160 in Figure 9. NC_ CELLS is a predetermined maximum value of iterations for the loop. A typical value for NC_CELLS is between 6 and 10, for example. The conditions of the loop are set such that the loop iterates a minimum of five times o" and continues to iterate until a test for conversion is met or m-NC_ CELLS. The test for conversion is whether or not the sum of the weighted sum of four prediction errors plus the weighted sum of backward 20 prediction errors is less than a small number, typically 0.00001 0m(t)+Sm(t) 5 0.00001).

A sixth portion of the program calculates the forward and backward reflection coefficient rmf(t) and rm,b(t) register 90 and 92 values (nciml.fref and ncmmlbref in the program) as in the "ORDER UPDATE mth-STAGE OF LSL-PREDICTOR" action block 170. Then forward and backward prediction errors fm(t) and bm(t) (nc[ml.ferr and nc[mI.berr in the program) are calculated. Additionally, intermediate variables am(t), 25 Bm(t), and y(t) (nc[(m.Fswsqr, nc[m].Bswsqr, nc[m]. gamma in the program) are calculated. The first cycle of the loop uses the value for nc[l0.Fswsqr and nc[Ol.Bswsqr calculated in the ZERO STAGE UPDATE portion of the program.

A seventh portion of the program, still within the loop begun in the fifth portion of the program, calculates the regression coefficient register 96 and 98 values Kn.a(t) and KmAb(t) (nc[ml.K_a and -87nc[ml.K_b in the program) in both regression filters, as in the "ORDER UPDATE mth STAGE OF REGRESSION FILTER(S)" action block 180. Intermediate error signals and variables ema(t), emAb(t), PmAa(t), and PmAb(t) (ncfm].erra and nc[m].err b, nc[m].roh_a, and nc[ml.roh_b in the subroutine) are also calculated.

The loop iterates until the test for convergence is passed. The test for convergence of the joint process estimator is performed each time the loop iterates analogously to the "DONE" action block 190.

If the sum of the weighted sums of the forward and backward prediction errors 1m,(t) Bm(t) is less than or equal to 0.00001, the loop terminates. Otherwise, sixth and seventh portions of the program repeat.

The output of the present subroutine is a good approximation to the primary signals s"Aa(t) and s"Ab(t) or the secondary signals n"Aa(t) and n"Ab(t) for the set of samples SA(t) and SAb(t) input to the program. After approximations to the primary signal portions or the secondary signals portions of many sets of measured signal samples are estimated by the joint process estimator, a compilation of the outputs provides waves which are good approximations to the plethysmographic wave or motion artifact at each wavelength, Aa and Ab.

It should be understood that the subroutine of Appendix B is merely one embodiment which implements the equations (54) Although implementation of the normalized and QRD-LSL equations is also straightforward, a subroutine for the normalized equations is attached as Appendix C, and a subroutine for the QRD-LSL algorithm is attached as Appendix D.

While one example of a physiological monitor incorporating a processor 20 for determining a reference signal for use in a correlation canceler, such as an adaptive noise canceler, to remove or derive primary and secondary components from a physiological measurement has been described ooo in the form of a pulse oximeter, it will be obvious to one skilled in the art that other types of physiological monitors may also employ the above described techniques.

Furthermore, the signal processing techniques described may be used to compute the arterial and venous blood oxygen saturations of a physiological system on a continuous or nearly continuous time basis. These calculations may. be performed, regardless of whether or not the physiological system undergoes voluntary motion.

Furthermore, it will be understood that transformations of measured signals other than logarithmic S. conversion and determination of a proportionality factor which allows removal or derivation of the primary or secondary signal portions for determination of a reference signal are possible. Additionally, although the proportionality factor r has been described herein as a ratio of a portion of a first signal to a portion of a second signal, a similar proportionality constant determined as a ratio of a portion of a second signal to -88a portion of a first signal could equally well be utilized in the processor of the present invention. In the latter case, a secondary reference signal would generally resemble nAb(t) rnAa(t).

Furthermore, it will be understood that correlation cancellation techniques other than joint process estimation may be used together with the reference signals. These may include but are not limited to least mean square algorithms, wavelet transforms, spectral estimation techniques, neural networks, Weiner and Kalman filters among others.

One skilled in the art will realize that many different types of physiological monitors may employ the above teachings. Other types of physiological monitors include, but are in not limited to, electro cardiographs, blood pressure monitors, blood constituent monitors (other than oxygen saturation) monitors, capnographs, heart rate monitors, respiration monitors, or depth of anesthesia monitors.

Additionally, monitors which measure the pressure and quantity of a substance within the body such as a breathalizer, a drug monitor, a cholesterol monitor, a glucose monitor, a carbon dioxide monitor, a glucose monitor, or a carbon monoxide monitor may also employ the above described techniques.

Furthermore, one skilled in the art will realize that the above described techniques of primary or secondary signal removal or derivation from a composite signal including both primary and secondary components can also be performed on electrocardiography (ECG) signals which are derived from positions on the body which are close and highly correlated to each other. It should be understood that a tripolar Laplacian electrode sensor such as that depicted in Figure 31 which is a modification of a bipolar Laplacian electrode sensor discussed in the article "Body Surface Laplacian ECG Mapping" by Bin He and Richard J.

20 Cohen contained in the journal IEEE Transactions on Biomedical Engineering, Vol. 39, No. 11, November 1992 could be used as an ECG sensor. It must also be understood that there are a myriad of possible ECG oooo sensor geometry's that may be used to satisfy the requirements of the present invention. The same type of sensor could also be used for EEG and EMG measurements.

Furthermore, one skilled in the art will realize that the above described techniques can also be performed on signals made up of reflected energy, rather than transmitted energy. One skilled in the art will also realize that a primary or secondary portion of a measured signal of any type of energy, including but not limited to sound energy, X-ray energy, gamma ray energy, or light energy can be estimated by the techniques described above. Thus one skilled in the art will realize that the above techniques

S

can be applied in such monitors as those using ultrasound where a signal is transmitted through a portion of the body and reflected back from within the body back through this portion of the body. Additionally, monitors such as echo cardiographs may also utilize the above techniques since they too rely on transmission and reflection.

P.\OPER\DH\2125-99 nl.doc-210M6 O -89- While the present invention has been described in terms of a physiological monitor, one skilled in the art will realise that the signal processing techniques of the present invention can be applied in many areas, including but not limited to the processing of a physiological signal. The present invention may be applied in any situation where a signal processor comprising a detector receives a first signal which includes a first primary signal portion and a first secondary signal portion and a second signal which includes a second primary signal portion and a second secondary signal portion. Thus, the signal processor of the present invention is readily applicable to numerous signal processing areas.

Throughout this specification and the claims which follow, unless the context requires otherwise, the word "comprise", and variations such as "comprises" and "comprising", will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

The reference to any prior art in this specification is not, and should not be taken as, an acknowledgment or any form of suggestion that that prior art forms part of the common general knowledge in Australia.

0:00o: .0 APPENDIX A DIGITAL SIGNAL PROCESSING WITH EFFICIENT POLYPHASE RECURSIVE ALL-PASS

FILTERS

Fred Harris*, Maximilien d'Oreye de Lantremange*, and A.G.

Constantinides** Department of Electrical and Computer Engineering, San Diego State University, San Diego, California 92182-0190,

USA.

Signal Processing Section, Department of Electrical Engineering, Imperial College of Science, Technology and Medicine, Exhibition Road, London DW7-2BT, England.

ABSTRACT: Digital filters can be realized with remarkably small computational burden as polyphase recursive all-pass networks.

These networks are formed as a sum of M parallel all-pass subfilters with phase shifts selected to add constructively in the passband and destructively in the stopband. The design technique we present here 20 starts with prototype M-path recursive all-pass filters obtained by a new optimizing algorithm (described in detail elsewhere). These filters are operated with combinations of all-pass transformations, resampling, and cascading options. We demonstrate a number of designs using the new algorithm along with examples of filtering systems obtained by the techniques presented.

Presented at International Conference on Signal Processing Florence, Italy, Sept. 4-6, 1991 -91- 1. INTRODUCTION A standard finite impulse response (FIR) filter can be modeled, as indicated in Fig. 32, as the weighted summation of the contents of a tapped delay line. This summation is shown in and the transfer function of this filter is shown in M-1 y(n) h(m-n) x(m) (1) m=0 M-1 Y(Z) X(Z) h(n) Z" (2) n-0 We note the frequency selective characteristics of the filter output is due to the phase shift between successive samples in the 10 tapped delay line. This phaser summation is shown in Fig. 33 for two different frequencies.

Note that it is the phase shift, and not the weighing terms, which is responsible for the frequency dependent gain of the filter.

The weighing terms are used primarily to control passband width and stopband attenuation of the filter. An idea derived from spatial beamforming (known as beam spoiling) and from signal synthesis o* (peak-to-rms control) is to use structured phase shifts (with :i arbitrary amplitudes) to accomplish the same goal.

The class of filters we describe here replaces the weights of the FIR filter with all-pass subfilters which exhibit unity gain with frequency dependent phase shift. In anticipation of the polyphase -92structure, the all-pass subfilters are, as shown in and Fig. 34, first order polynomials in Z n where M is the number of taps in the structure. This composite form is indicated in Fig. 41a with a modified form reflecting a polyphase structure in 41b. The transfer function of this structure is shown in Figs. 44a and 44b show examples of equal ripple designs obtained from this new algorithm for a 2-path and for a 5-path filter with two and three all-pass stages per path respectively. Interacting constraints on the optimal design (described in the aforementioned paper) limit the possible number of stages per path for the 5-path filter to the sequences etc., so that the optimum 5-path filter uses three less stages than allocated to the design. Similarly the 2-path filter is limited to the sequences etc.

*.15 2. TWO PATH FILTERS We find a wealth of interesting properties and clever applications ,for this structure even if we limit our discussion to a 2-path filter. As designed, the 2-path filter is a half bandwidth filter with the 3-dB bank-width at 0.25 f If the zeros are restricted to the half sampling frequency, the filter identical to a half bandwidth Butterworth obtained by the standard arped bilinear transform. For this special case, the real parts of the root locations go to zero. If the zeros are optimized for equal ripple stop band behavior the filter becomes a constrained S. Elliptic filter. The constraints are related to a property of complementary all-pass filters. We define the all-pass sections for the 2-path filter at Ho(0) and H 1 and, as indicated in Fig. 35, the scaled -93by one-half sum and difference of these paths by A(Q) and the lowpass and highpass filters, respectively. We know that the all-pass sections satisfy from which we derive the power relationship between the Iowpass and. highpass filters shown in I HOW 1 2 jh 1 8) 1 2 1 IA(O9)1 2 +IB(O)1 2 10.5IH(6)+H,(9)] 1 2 I0.5[H 0 1 2 (6a) (6b) 5 I HOW 12+ jH 1 121 a. a.

a a a a a a a *a a a (6c) Now to interpret how this relationship impacts the 2-path filter.

10 For the complementary filters we define the minimum passband gain of by 1 -el, and the peak stopband gain by E 2 Substituting these gains in we obtain (1 -IE 1 2 2 2 =1 (7a) (1 -E 1 2 =1 (E 2 2 (7b) -94- 1 -2E, 2

-(E

2 2 For small El, we can ignore 2 which leads to 2 (7c) (8) Thus, if the stopband attenuation is selected to be 0.001 dB), the passband ripple is 0.000 000 5 (126.0 dB) or the passband minimum gain is 0.999 999 5 (-0.000 000 22 dB). As can be seen these filters have a remarkably flat passband. We conclude that the 2-path equal ripple stopband filters are elliptic filters with coupled passband and stopband ripple with -3.0 dB gain at 0.25 f. There are two significant differences between the 2-path and the standard implementation of the equivalent elliptic filter. The first is a four-toone savings in multiplications; a fifth order half bandwidth 2-path filter requires only two coefficients as opposed to the direct implementation which requires eight (scaling included). The second is that all-pass structures exhibit unity gain to internal states hence do not require extended precision registers to store internal states as do standard implementations.

As with any filter design, the transition bandwidth can be traded for out of band attenuation for a fixed order or transition bandwidth can be steepened for a fixed attenuation by increasing filter order.

While nomographs exist for the elliptic and Butterworth filters which can be implemented by the 2-path structure, a simple approximate relationship for the equal ripple filter is given in where A(dB) is attenuation in dB, If Af is transition bandwidth, and N is the total number of all-pass segments in the filter.

A(dB) (72Af+10)N (9) 2A. HILBERT TRANSFORM FILTERS The Hilbert Transform (HT) can be thought of as a particular type of half band filter. It is modelled and implemented by a wide band phase shifting network. The HT is often used in DSP applications to form the analytic signal a(n) as shown in a signal with spectra limited to the positive (or negative) frequency band.

a(n) x(n)+jx(n) We can cast the 2-path filter as a HT in a number of ways but a simple method, akin to the transformation performed on a half band FIR filter is a heterodyne of the half band filter to the quarter sample frequency. If the original filter response and transformer are denoted by h(n) and H(Z) respectively, then the heterodyned expressions can be easily seen to be those in (11).

1 1 a) -96- H(Z) H(ZeJi/2) (11 b) The transformation of a half band filter to an HT filter is accomplished by replacing each Z 1 of the transfer function with -jZ 1 Since the polynomials of the all-pass subfilters are second order, this transformation can be accomplished by changing the sign of the coefficient used in each all-pass sub filter and by associating a -j with the lower path delay. These operations are indicated in Fig. 36.

2B. INTERPOLATION AND DECIMATION FILTERS Any half bandwidth filter can be used to perform 2-to-1 resampling (up or down, popularly identified as interpolation and decimation). Finite impulse response (FIR) filters can be operated with a polyphase partition which does not process inserted zero input points (up-sampling) or compute the discarded output points (down sampling). While this option is not available for the general recursive filter, it is an option for the recursive all-pass M-path filter. The M- 5 path filter can be partitioned into polyphase segments because of the interaction of the internal delays of the M-th order subfilters and the delay line of each path. This relationship is particularly easy to see for the 2-path filter. An impulse applied at index no makes a contribution to the output at the same time via the upper path while an output is not available from the lower path till the next index due to its extra delay During that same next index, the upper path offers no contribution to the output because there is no Z' path associated with its Z 2 polynomial. Thus the filter delivers successive samples of its impulse response from alternate paths of the filter.

-97- Down sampling is accomplished by delivering alternate input samples to each path of the filter operating at the reduced input rate.

Since the delay of the second path is accomplished by the input commutation the physical delay element in that path is removed. The filtered and down sampled out-put is generated by the sum or difference of the two path responses. Note that the computation rate per input sample point is half that of the non resampled filter, thus if the 2-path filter of Fig. 44a is used for down sampling we would perform 3 multiplications per input point.

Up sampling is accomplished by reversing the down sampling process. This entails delivering the same input to the two paths and commutating between their outputs. Both forms of resampling are shown in Fig. 37. As in the previous example, when the 2-path filter of Fig. 44a is used for up sampling we would perform 3 15 multiplications per output point.

The cascade operation of down sampling and up sampling of the complementary outputs performs two band maximally decimated quadrature mirror filtering and reconstruction ****Cascading multiple stages of up sampling or down sampling S 20 filters can achieve high order sample rate change with remarkably small workload per data point. For instance, a 1-to-16 up sampler with 96 dB dynamic range for a signal with cutoff frequency of 0.4 f, requires 2-path filters with successively smaller number of all-pass stages of orders and This requires a total of 42 multiplications for 16 outputs, for an average workload of approximately 2.7 operations per output point.

-98- 2C. ITERATED POLYPHASE ALL-PASS FILTERS The all-pass networks described earlier are formed by polynomials in Z and specifically for the 2-path filters Z 2 A useful transformation is to replace each Z 2 with Z 2 k, to obtain higher order filters exhibiting K-fold spectral replication of the original filter. For Kthe half band filter centered at DC becomes a pair of quarter band filters centered at DC and An example of spectral replication for the iterated filter is shown in Fig. 38.

Note that this transformation scales the prototype filter's spectrum by 1 reducing both passband width and transition width.

Thus, very steep transition bandwidths and narrow filters can be realized by the use of low order polynomials of degree 2K obtained via delay elements. Energy in the replicated spectral regions can be removed by a sequence of filters incorporating various degrees of 5 resampling and iterated filters of reduced degree.

3. EFFICIENT ALL-PASS FILTER BANKS Efficient spectral partitioning can be obtained by cascading and resampling the outputs of iterated lowpass and HT filters. For instance, the spectra of a four-channel filter bank centered on the four 20 quadrants can be formed with a complementary half-band filter followed by a pair of resampled HT filters, as shown on the left side of Fig. 39. The workload for this 70 dB attenuation filter set is three multiplications per output channel.

A four-channel filter bank straddling the previous set centered on the four cardinal directions) can be formed with an iterated by two complementary half-band filter followed by both a -99complementary half band resampled filter and a resampled HT filter.

This spectra of this filter set is shown on the right side of Fig. 39.

The workload for this 70 dB attenuation filter set is two multiplications per output channel.

4. OTHER ALL-PASS

TRANSFORMATIONS

The prototype complementary all-pass filter set can also be transformed to filters of arbitrary bandwidth and of arbitrary center frequency by standard all-pass transformations The lowpass transformation for the half-band filter is shown in (12).

b+z 1 -tan(8o/2) (12) 1 +b 1 +tan(8 0 /2) This transformation warps the frequency variable of the filter so that the -3 dB point resides at frequency 80. When 8o is different from rr/2, the second-order polynomials of the all-pass subfilters acquire coefficients for the z' term. The resulting filter requires two 15 multiplications per pole zero pair, which is still half the workload of the traditional canonic forms. In addition, the pole at the origin (due to the delay of the second path) transforms to a first-order all-pass filter, thus converting an inactive pole to an active one requiring an additional first-order stage. Fig. 40 presents the frequency-warped S 20 version of the filter presented in Fig. 44a. Both this filter and its complement are available from the warped structure.

The bandpass transformation is presented in (13).

-100- Z-1

-Z-

1 C Z 1 cos(e 1 (13) 1 -c 1 This transformation warps the frequency variable of the filter so that the center frequency resides at frequency 81. If 81 is equal to 0.0, this transformation is equivalent to the iterated transformation described in 2.C. For any other frequency, this transformation converts the second-order all-pass filters to fourth-order all-pass structures. This requires four multiplications to form four pole-zero pairs of the resultant filter, which is still half the workload of the traditional canonic forms. In addition, the transformation converts the real pole (which is an image of the pole originally at the origin) to a pair of complex poles requiring a second-order all-pass stage. Fig. presents the frequency warped version of the filter presented in Fig.

45. As earlier, both this filter and its complement are available from the warped structure.

o* Other transformations and geometries can be used with the 15 digital all-pass structure, and the reader is directed to the bibliography of the listed papers for a profusion of options.

an Z M (3) H (Z

M

-101- M-1 Y(Z) X(Z) E H,(Z

M

(4) n=0 The roots of the M-th roots of and its reciprocal, are equally spaced about the origin as shown in Fig. 42 for the indicated degrees M. Note that we realize M poles and M zeros per multiplication in the all-pass stage. This means, for instance, that a two-path filter offers two poles and two zeros per multiplication as opposed to one pole (or zero) per multiplication for the standard (factored or unfactored) canonic forms.

As we go around the unit circle, we visualize that the all-pass subfilters exhibit rapid change in phase in the neighborhood of each pole-zero pair. By proper choice of the pole positions, the phase shift of each leg of the M path filter can be made to match or to differ by multiples of 2n/IM over selected spectral intervals. This is suggested in Figs. 43A-43D for M 2 and M 4. The coefficients of the all-pass 15 subfilters can be determined by standard algorithms [31 or by a new algorithm developed by Harris and d'Oreye and reported in a paper recently submitted for publication (Signal Processing).

5. CONCLUSIONS We have reviewed the form and utility of the all-pass polyphase 20 filter structure. We then presented a number of all-pass .i transformations which could be easily applied to M-path all-pass filter sets. The emphasis has been on two-path networks, but the material is easily extended to arbitrary M. We alluded to a new set of algorithms for designing M-path filters, which will be reported in an -102upcoming Signal Processing paper. We have demonstrated capabilities of this algorithm by using it to generate the examples presented in this paper.

The primary advantage of these structures is very low workload for a given filtering task. Other papers [8,9,10] have discussed the low sensitivity to finite arithmetic exhibited by these filters. The primary impediment to the use of these filters is their newness and the lack of availability design methods for computing filter weights.

This paper (along with excellent surveys listen in the bibliography) address the first problem, and a forthcoming paper addresses the second.

6. ACKNOWLEDGMENT This work was sponsored in part by the Industry/University Cooperative Research Center (I/UCRC) on Integrated Circuits and 15 Systems (ICAS) at San Diego State University (SDSU) and the University of California, San Diego (UCSD).

7. BIBLIOGRAPHY Private correspondence between F.J. Harris and Stan Acks of Hughes Aircraft, Radar Systems Group, El Segundo, CA, 1983.

M.R. Schroeder, "Number Theory in Science and Communications," Springer-Verlag, 1984, Chapter 28, Waveforms and Radiation Patterns, pp. 278-288.

R.A. Valenzuela and A.G. Constantinides, "Digital Signal Processing Schemes for Efficient Interpolation and Decimation," IEE Proceedings, Vol. 130, Pt. G, No. 6, Dec. 1983, pp. 225- 235.

-103- D. Elliot, "Handbook of Digital Signal Processing, Engineering Applications," Academic Press, 1987, Chapter 3, pp. 227-233.

Phillip A. Regalia, Sanjit K. Mitra, and P.P. Vaidyanathan, "The Digital All-Pass Filter: A Versatile Signal Processing Building Block," Proc. of IEEE, Vol. 76, No. 1, Jan. 1988, pp. 19-37.

A.G. Constantinides, "Spectral Transformations for Digital Filters," Proc. IEE, Vol. 117, No. 8, Aug. 1970, pp. 1585-1590.

S.K. Mitra, K. Hirano, S. Nishimura, and K. Sugahara, "Design of Digital Bandpass/Bandstop Filters with Independent Tuning Characteristics," FREQUENZ, 44(1990)3-4, pp. 117-121.

R. Ansari and B. Liu, "A Class of Low-Noise Computationally Efficient Recursive Digital Filters with Applications to Sampling Rate Alterations," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-33, No. 1, Feb. 1985, pp. 90-97.

15 H. Samueli, "A Low-Complexity Multiplierless Half-Band Recursive Digital Filter Design," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-37, No. 3, Mar. 1989, pp. 442- 444.

(10) P.P. Vaidyanathan and Zinnur Doganata, "The Role of Lossless Systems in Modern Digital Signal Processing: A Tutorial,"

IEEE

Trans. on Education, Vol. 32, No. 3, Aug. 1989, pp. 181-197.

-104- APPENDIX B LEAST SQUARE LATTICE NOISE CANCELING Example f or ratiometric approach to noise canceling /define LAMBDA 0.95 void OxiLSLNC( int reset, mnt passes, mnt *signal_1, int *signal_2, mnt *signal_3, int *target int *target_2) static static int.

int f loat i, ii, k, m, n, contraction; *sa, *sb, *sC, *out-a, *out c; Delta sqr, scale, noise-ref; *.3 if( reset TRUE) s_a signal_1; s b signal_-2; s-c signal_3; out-a target_1; out C target -2; factor scale 1.0 4160.0; noise canceller initialization at time t=0 nc[O) .berr nctO) .Gamma -0.0; 0; f or m<NCCELLS; nc~m].err-a 0.0; nc[rn).err-b =0.0; ncfm].Roh-a 0.0; nc~rn).Roh c 0.0; nc[m].Delta 0.0; ncl].Fswsqr 0.00001; nc~rn).Bswsqr 0.00001; -105- -END INITIALIZATION for (k0o; k<passes; contraction FALSE; for m< NC_-CELLS; Update delay elements nc (ml.berrl nc (ml .berr; nc [ml.Bswsqrl nc [in]Bswsqr; noise-ref nc[(0).err a nc[O).err-b =factor *log(l.0 *scale) Hs (sb) *scale); =log(i.0 b) *scale); =log(i.0 *scale); +s_a; b c; S. nc ferr nc[(0l berr nc 0 .Fswsqr nc[0) .Bswsqr noise ref noise ref LAMBDA nc[Ol.Fswsqr noise-ref noise ref; nc[0].Fswsqr; 25 Order Update for n NCCELLS (contraction FALSE); Adaptive Lattice Section mn n-1; ii= n-i; nc[m] .Delta nc[m] .Delta Delta_sqr

~=LAMBDA;

+=nctm) .berrl nc~m] .ferr =nc(m.Delta *nc[inl.Delta; nc[m] .Gamma; nc f ref nc bref =-nc~ml .Delta /nc~in].Bswsqri; =-nc~ml .Delta /nc[ml .Fswsqr; nc f err nc[ frr= nc f err nc f ref nc berrl; -106nc berr nc .Fswsqr nc [n Bswsqr nc mlberri nc .bref *nc .f err; nc~m] .Fswsqr Delta -sqr /nc[m] .Bswsqrl; nc[m] .Bswsqrl Delta sqr /nc[mn].Fswsqr; if( (nc[n] .Fswsqr nc[n] .Bswsqr) 0.00001 11 (n 5) nc~nI .Gamrna =nc[rn].Gamrna nc~rn).berrl nc~rn).berrl nc[nl .Bswsqrl; if(nc[n].Gamma 0.05) nc[n].Gamma 0.05; if(nc[n].Gamma >1.00) nc~n].Gamma 1.00; Joint Process Estimation Section 25 nc~n] .Roh a nc[rn].Roh a nc k-a nc[n] .err-a ncfm] .Roh c nc~rnl.Roh c nc[m].k c nc[nI.err-b

LAMBDA;

nc .berr *nc rm].err a nc Gamma -nc (in] Roh-a /nc (mn] Bswsqr; =nc[m].err a ncl).k-a nc[m] .berr;

SLAMDBA;

nc [mn] berr nc im] .err b nc [mn].Gamina -ncljm] .Roh-c nc[mn] .Bswsqr; nc~in].err b nc~inl.k-c nc[m] .berr;

C

else j contraction TRUE; for (i=ni; i'<NCCELLS; nclii].err-a 0.0; nc~i].Roh a 0.0; nc[i] .err-b 0.0; nc[i].Roh-c 0.0; nc[i).Delta 0.0; nc[i] .Fswsqr 0.00001; nc[i].Bswsqr 0.00001; nc[i].Bswsqrl 0.00001; *out (int) (-exp(nc~ii] .err_a) /scale); *outC++ (int) (-exp(nc~ii] err-b) /scale); ~Least Square Lattic 35 :40 7- APPENDIX C Normalized Adaptive Noise CAnceler #include <stdlib.h> #include <math.h> #define TRUE #define FALSE #define FLOAT32 #define I NT32 #define VOID #define FABSF #define SQRTF #define MAX(a,b) #define MIN(a,b) f loat long mnt void f abs sqrt (a) (a) (b) (b)

U

U.

#define MINVAL #define MAXDEL #define MINDEL #define MAXRHO #define MIN-RHO #define MINBSERR 0.01 0 .999999 -0.999999 25

U

U

typedef struct FLOAT32 berr; FLOAT32 berr_1; FLOAT32 delta; FLOAT32 err; FLOAT32 f err; FLOAT32 gamma; FLOAT32 gamma_1; FLOAT32 rho; FLOAT32 delta_1; FLOAT32 Bserr; FLOAT32 Bserr 1; 1 LANCCELLS;.

typedef struct 8- INT 32 FLOAT32 lan FLOAT32 mir

LANCCELLS

LANCContext;

CC;

rbda; -~error; *cells; number of cells put in value for lambda 1* parameter point to array of ANCCELLS number of cells lambda param min error extern LANCContext LANCInit( INT32 num cells, FLOAT32 lambda, FLOAT32 min-error); extern VOID LANCDone( LANCContext extern VOID LANCReset( LANCContext extern FLOAT32 LANCCalc( LANCContext FLOAT3 2 FLOAT3 2 anc) a a. a.

:25 anc, nps noise); input, context handle input, noise plus signal input, noise reference 1* The following macros provide efficient access to the lattice #define ANCCELLCIZE a a. a a.

a.

40 #def mne #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine xBERR 0 xBERR_1 xDELTA 2 xDELTA_1 xGAMMA 4 xGAMMA_1 xBSERR 6 xBSERR_1 xERR 8 xFERR 9 xRho 9- #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine berr P berr_1 P berr berr_1 Bserr Bserr_1 PBserr_1 P-delta delta delta_1 P-delta 1 xBERR)) xBERR_1 ANC_-CELL_-SIZE)) xBERR ANC-CELLSIZE)) xBERR_1)) xBSERR)) (p xBSERR_1)) xBSERR_1 ANCCELLSIZE)) xDELTA ANCCELLSIZE)) xDELTA)) (p xDELTA_1)) xDELTA_1 -ANC CELLSIZE) #define err #define N-err #define P ferr #define f err xERR)) xERR. ANCCELLSIZE)) ((p xFERR ANCCELLSIZE)) xFERR)) #def ine #def ine #def ine #def ine #def ine gamma P gamma N _gamma P-gamma -1 gamma 1 xGAMMA)) xGAI4MA ANCCELLSIZE)) xGAMMA ANCCELLSIZE)) xGAMMA_1 -ANC CELLSIZE)) (p xGAMMA_1)) 25 #define rho (p xRho)) Name: LANC mnit Abstract: Create an ANC context extern LANCContext LANCInit( INT32 FLOAT32 lambdE FLOAT32 mi ei 40 -iumc el :ror) is, 1* number of cells lambda param min error -110- LANCContext *anc; context anc (LANCTContext *)malloc(sizeof(LANCContext)); assert(anc

NULL);

anc->cc nuni cells; anc->lambda lambda; anc->min-error min-error; anc->cells (LANC CELLS *)malloc(sizeof(LANCCELLS) *(nurn-cells assert(anc->cells

NULL);

return(anc); Name: LANCReset Abstract: Reset an ANC context extern VOID LANCReset( LANCContext *anc){ FLOAT32 P 30 INT32

M

p (FLOAT32 *)anc->cells; for (mi 0; m ,=anc->cc; rho =0.0; err =0.0; ferr =0.0; berr =0.0; ge*:berr 1 =0.0; delta -0.0; :40 delta 1 =0.0; Bserr anc->min error; Bserr_1 =ancQ>tnin error; -111gamma gamma_1 p

MINVAL;

M MINVAL;

ANCCELLSIZE;

p (FLOAT32 *)anc-.>cells; gamma gamma_1 Cell 0 special case Name: LANCDone Abstract: Delete an ANC context extern VOID LANCDone( LANCContext *anc)( free (anc->cells); free (anc); a..

a a.

a a *aaa..

a a a. a.

Name: LANCCaic Abstract: Calculate 35 40 FLOAT3 2 LANCCalc( LANCContext FLOAT3 2 FLOAT3 2 I NT32 FLOAT32 FLOAT32 B, FLOAT32 qc anc, nps noise) input, context handle input, noise plus signal input, noise reference F, B2, F2; 12, qd3 -112- INT32 output cell; Update time delay elements in cell structurep (FLOAT32 *)anc->cells; for (m 0; m anc-cc; gamma_1 gamma; berr_1 berr; Bserr_1 Bserr; delta_1 delta; p ANCCELLSIZE; Handle Cell p (FLOAT32 *)anc->cells; Bserr anc->lambda Bserr_1 noise noise; Bserr MAX (Bserr, MINBSERR); ferr noise SQRTF(Bserr); ferr MAX(ferr, MINDEL); ferr MIN(ferr, MAXDEL); berr ferr; rho anc->lambda SQRTF(Bserr2. Bserr) *rho +berr* nps;' N-err =nps rho berr; output_cell anc->cc Assume last cell for starter for (m 1; m anc->cc; p

AWCCELLSIZE;

35 B =SQRTF(1.0 P-berr_1 *P-berr_1); B2 *SF =SQRTF (1.O0 Pf ferr *P ferr )-F2 :40 P-delta P-deltal F B P-berr 1 *P ferr; P-delta MAX(P-delta,

MINDEL);

P-delta MIN(P-delta,

MAXDEL);

-113- 1.0 Pdelta P-delta; 1.0 /SQRTF(qd3); qd3 qd2 f err f err f err berr be rr berr gamma gamma gamma Bser~t Bser2 rho rho rho rho N-er~ (P-ferr -P -delta P berr_1) qd2 *B2; MAX(ferr, MINDEL); MIN(ferr, MAXDEL); (P-berr_-1 -P -delta P ferr *a2 F2; MAX(berr, MINDEL); MIN(berr, MAXDEL); Pgamma (1.0 P berr P berr); MAX(gamma, MIN_-VAL); MIN(gamma, MAXDEL); P-Bserrl1 qd3; MAX(Bserr, MINBSERR); anc- >lambda SQRTF ((Bserr_1 Bserr) *(gamma /gamma_1) berr err; MAX(rho, MINRHO); MIN(rho, MAXRHO); err rho berr; 25

S.

5550 p (FLOAT32 (anc..>cells [output_cell 1* *ANC CELLSIZE*/; return (N-err);

S

S

*5 S OS -114- APPENDIX D

QRD

#include <stdlib.h> #include <math.h> #define TRUE 1 #define FALSE 0 #define FLOAT32 #define I1NT32 #define VOID #define FABSF #define SQRTF f loat long int void f abs sqrt typedef struct{ INT3 2

}LQRDJPEFCONTEXT;

dummy; typedef LQRDJPEFCONTEXT LQRDJPEFHandle; 25 0@ 0000 extern LQRDJPEFHandle LQRDJPEFInit( INT32 N' FLOAT32 Lambda, FLOAT32 SumErr) FLOAT32 Gamslni FLOAT32 MinSumi aimCells, :nit, OS@Oee

S

0 eOSeSe 0 0O 0 00

S.

extern VOID LQRDJPEFDone( LQRDJPEFHandle hJPE); extern VOID #define Reset( LQRDJPEFHandle hJPE); extern FLOAT32 LQRDJPEFCalc( LQRDJPEFHandle hJPE, 40 handle -115- FLOAT3 2 FLOAT3 2 nps noise) noise plus signal noise reference #def ine MAX b) #define MIN(a,b) #definle LQRDJPEFCELL

SIZE

typedef struct 0 FLOAT32 sinf ,sinf_1 FLOAT32 sinb ,sinb 1 (a) (a) FLOAT32 cosf ,cosf_1 FLOAT32 cosb ,cosb_1 FLOAT32 epsf; FLOAT32 epsb ,epsb~l FLOAT32 pief ,pief 2.1 FLOAT32 pieb ,piebi1 FLOAT32 Fserr, Fserr_-1, SQRTF_Fserr, sQRTF-Fserr_1; FLOAT32 Bserr_1, Bserr_2, SQRTFBserr_1, SQRTF-Bserr_2; FLOAT32 p_1, p_2; FLOAT32 gamsl1; FLOAT32 epsil1; .0.0.

0

LQRDJPEFCELL;

struct INT 32 FLOAT3 2 FLOAT3 2 FLOAT3 2 FLOAT3 2 Bserr FLOAT3 2 FLOAT3 2 SumErrlnit NumCells; Lambda; SumErrlnit; Gamslflit; MinSumErr; number of cells Lambda Initial value for Fserr, Bserr Initial value for gains Minimum for Fserr, SQRTFLambda; square root of Lambda SWRTF SumErrInit; square root -116- LQRDJPEFCELL *cells; LQRDJPEF Context; point to array of JPE CELLS The following macros provide efficient access to the lattice Define variables offsets within structure #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine xSINF xSINF_1 xSINB xSINB_1 xCOSF xCOSF_1 xCOSB xCOSB_1 xEPS F xEPSB xEPSB_1 #def ine #def ine #def ine #def ine e in.

#def ine #def ine #def ine xPIEF 11 xPIEF_1 xPIEB 13 xPIEB_1 xFSERR xFSERR_1 xSQRTFFSERR xSQRTFFSERR_1 xBSERR_1 xBSERR_2 xSQRTFBSERR_1 xSQRTFBSERR_2 #def ine #def ine #def ine #def ine #def ine #def ine xpl xp_2 FLOAT32 epsb epsb_1 FLOAT32 pief pief_1 -117- FLOAT32 pieb pieb_1 FLOAT32 Fserr, Fserr_-1, SQRTFFserr,-SQRTFFserr_1; FLOAT32 Bserr_1, Bserr 2, SQRTF Bserr_1, SQRTFBserr_2; FLOAT32 p_1, p_2; FLOAT32 gains_1; FLOAT32 epsi_1; LQRDJPEF CELL: typedef struct INT3 2 FLOAT32 FLOAT 32 Bserr NumCells; Lambda; SumErrlnit; 1* number of cells Lambda Initial value for Fserr, FLOAT32 FLOAT 32 FLOAT3 2 FLOAT3 2 LQRDJPEF CELL Gainslnit; 1 MinSumErr; SQRTFLambda; SQRTFSumErrlnit; *cells; 1 Initial value for gains Minimum for Fserr, Bserr square root of Lambda square roof of SuinErrlnit point to array of JPECELLS 9 LQRDJPEFContext; The following macros provide efficient access to the lattice Define variable offsets within structure #def ine #def ine #def mne #def ine #def ine #def ine #def ine #def ine xSINF xSINF_1 xSINB xSINB_1 xCOSF xCOSF_1 xCOSB xCOSB_1 #define xEPSF -118- #define xEPSB #define xEPSB_1 #define xPIEF #define xPIEF_1 #define xPIEB #define xPIEB_1 #def ine #def ine #def ine #def ine #def ine #def ine #def ire, #def ine xFSERR xFSERR_1 xSQRTFFSERR xSQRTFFSERR 1 xBSERR 1 xBSERR_2 xSQRTFBSERR_1 xSQRTFBSERR_2 #define xp-l #definie xp_2 *3 0 3 5 #def ine #def ine #def ine #def ine #def ine #def ine #tdef ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine xGAMSQ_1 xEPSI_1 sin (ptr xSINF)) sinf_-1 (*(ptr xSINF_1)) P-sinf ((ptr xSINF LQRDJPEFICELL_-SIZE)) P.sinf_1 (ptr xSINF_1 LQRDJPEFCELLSIZE)) sinb ((ptr xSINB) sinbi (*(ptr xSINB_-1)) P-sinb (*(ptr xSINB LQRDJPEF_-CELL_-SIZE)) P-sinb_1 (*(ptr xSINB_1 LQRDJPEFCELL-SIZE)) cosf ((ptr xCOSF) cosf_-1 (*(ptr xCOSF_-1)) P-cosf (*(ptr xCOSF LQRDJPEF_-CELL_-SIZE)) P-cosf_1 (*(ptr xCOSF_1 LQRDJPEFCELLSIZE)) cosb xCOSB)) cosb_-1 (*(ptr xCOSB_-1) P cosb (*(ptr xCOSB LQRDJPEFCELLSIZE) -119- #define P-cosb_1 C*(ptr xCOSB_1 LQRDJPEFCELLSIZE)) #define epsf #define Pepsf (ptr xEPSF)) (*(ptr xEPSF

LQRDJPEFCELLSIZE))

#def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine #def ine ffdef ine #def ine epsb (ptr xEPSB) epsb-l ((pt r XEPSB_1)) P-epsb (*(ptr xEPSB -LQRDJPEFICELL_-SIZE)) Pepsbl1 (*(ptr xEPSB_1 LQRDJPEFCELLSIZE)) pief (*(ptr xPIEF)) pief 1 ((ptr xPIEF_1)) P-pief (*(ptr xPIEF LQRDJPEFCELLSIZE)) Pypief 1 (*(ptr xPIEF_1 LQRDJPEFCELLSIZE)) pieb ((ptr xPIEB)) piebil ((ptr xPIEB_-1)) P-pieb (*(ptr xPIEB LQRDJPEFICELL_-SIZE)) Ppiebl1 (*(ptr xPIEB_1 LQRDJPEFCELLSIZE)) #4def ine #def ine #def ine #def ine #def ine #def ine #def ine Fserr Fserr_1 PFserr PFserr-

SQRTFFE

SQRTFFE

SQRTFP-

(*ptr xFSERR)) (*(ptr xFSERR_1)) (*(ptr xFSERR LQRDJPEFCELLSIZE)) 1 (*(ptr xFSERR_1 LQRDJPEFCELLSIZE)) ;err (*(ptr xSQRTF_FSERR)) ~err 1(*(ptr xSQRTFFSERR_1)) Fserr (*(ptr xSQRTFFSERR

LQRDJPEFCELLSIZE))

-Fserr 1 (*(ptr xSQRTFFSERR_1

LQRDJPEFCELLSIZE))

#define SQRTFP #def ine #def ine #def ine #def ine, #def ine #def ine #def ine Bserr_1 Bserr_2 PBserr_1 P_-Bserr_2 SQRTFBserr_2 SQRTFBserr_2 SQRTFPBseri ((ptr xBSERR_1) ((ptr xBSERR_2) (*(ptr xBSERR_1 LQRDJPEFCELLSIZE) (*(ptr xBSERR_2 LQRDJPEFCELLSIZE) (*(ptr xSQRTFBSERR_1)) (*(ptr xSQRTFBSERR_2)) (*(ptr xSQRTFBSERR_1

LQRDJPEFCELLSIZE))

-2 (*(ptr xSQRTFBSERR_2 LQRDJPEF CELLSIZE)) #define SQRTFPBseri -120- #define p_1 #define p_2 #define Pp~l #define Pp_2 (*(ptr xpl1)) (*(ptr xp_2)) (*(ptr xpl1 (*(ptr xp_2

LQRDJPEFCELLSIZE))

LQRDJPEFCELLSIZE))

#define gains_1 (*(ptr xGAIISQ_1)) #define Pgamsl1 (*(ptr xGAMSQ2. LQRDJPEFCELLSIZE)) #define epsil1 ((ptr xEPSI_1)) #define P-epsi_3. (*(ptr xEPSI_1 LQRDJPEFCELLSIZE)) static FLOAT32

RSQRTF(

FLOAT32 x){ return 1.OF SQRTF(x); Name Abstract LQRDJPEF-Init Create a JPE context 25 a.

35 40 extern LQRDJPEFHandle LQRDJPEFInit( INT32 NurnCells, FLOAT32 Lambda, FLOAT32 SurnErrlnit, FLOAT32 Gainslnit, FLOAT32 MinSumErr) LQRDJPEFContext *jpe; jpe malloc (sizeof (LQRflJPEFContext)) assert(jpe !=NULL); jpe->NumCells NuinCells; jpe->Lanbda Lambda; jpe->SuinErrlnit SumErrlnit; jpe->Gamslnit =Gaislnit; jpe->MinSumErr =MinSumErr; -121jpe->SQRTF_-Lambda SQRTF(jpe->Lambda); jpe->SQRTFSumErrflit SQRTF(jpe->SumErrInit); jpe->cells malloc (sizeof (LQRJPEFCELL) (NumCells assert(jpe->cells 1=NULL); LQRDJPEF_-Reset ((LQRDJPEFHandle) jpe); return ((LQRDJPEF-handle)jpe); Name LQRDJPEFInit Abstract Create a JPE context 1 5- extern

VOID

LQRDJPEF Done( LQRDJPEFHandle hJPE)( LQRDJPEFContext *jpe =(LQRDJPEF_Context *)hJPE; free(jpe->cel)S free(jpe); Name LQRDJPEF_Reset Abstract Reset a JPE extern VOID LQRDJPEFReset( LQRDJPEFHandle hJPE) LQRDJPEFContext *jpe =(LQRDJPEFContext *hJPE; FLOAT32 *ptr; INT32

M;

ptr =(FLOAT32 *)jpe->cells; -122for (m m jpe->NumCells; sinf O.OF; sinb, O.OF; cosf 0.OF; cosb 0.OF; epsf 0.OF; epsb 0.QF; pief 0.OF; pieb 0.OF; p_1 =O.OF; Fserr jpe->SumErrlnit; Bserr_1 jpe->SumErrlnit; gamsl1 jpe->Gamslnit; SQRTF_-Fserr jpe->SQRTF_SumErrflit; SQRTFBfserr_1 jpe->SQRTF _SumErrlnit; ptr LQRDJPEFCELLSIZ'E; ptr (FLOAT32 *)jpe->cells; Cell #0 special case gamsl1 1.OF; 3 4. 0 Name Abs tract :LQRDJPEFCalc extern FLOAT32 LQRDJPEFCalc( LQRDJPEFHandle FLOAT32 nps, FLOAT32 noise){ LQRDJPEFContext INT32

M

FLOAT32 *ptr; FLOAT32 tMP; Time update section hJPE, noise plus signal noise reference *jpe (LQRDJPEFContext *)hJPE; -12 3ptr =(FLOAT32 *)jpe..)cells; for (mn 0; mn jpe->NumCells; /some of following delay elements are not needed sinf_1 sinb_1 Cosf_-1 cosb_1 epsb_1 pief_1 pieb_1 FSerr_1 Bserr_2 p_2 sinf; sinb; cosf; cosb; =epsb; pief; pieb; Fserr; Bserr 1; P-1; SQRTFBserr_-2 -SQRTF_-Bserr_-1; SQRTFFserr_1 SQRTFFserr; ptr LQRDJPEF_CELLSIZE;

I

1* Order update section 1* Handle Cell 0 ptr.= (FLOAT32 (jpe->cells) point to cell 0 epsf noise; epsb noise; epsi_1 nps; rest of cells for (m 1; mn jpe->NumCells; rn++) ptr LQRDJPEFCELLSIZE; access next cell Prediction section PBserr_1 jpe->Lambda PBserr_2 Pepsb-l P-epsbl; PBserr_1 IAX(PBserrl1, jpe->MinSunErr); -124- SQRTF_-P_-Bserr_-1 SQRTF(PBserr_-1);' tmp RSQRTF(PBserr_1); this comes free on DSP P-cosb_1 jpe->SQRTF_Lambda SQRTF_P_Bserr9 tmp; P sinb 1 =P-epsbl1 tmp; tmp jpe->SQRTF_Lambda Pypief_1; P-cosb_1 P-epsf P-sinb_1 tmp; P-pief P-cosb_1 tmp P-sinbi1 P-epsf; gamsl1 P-cosbi1 Pgamsl; pFserr jpe->Lambda PFserr_1 P_epsf Pepsf; PFserr MAX(PFserr, jpe->MinSumErr); SQRTF_P+Fserr SQRTF(P_Fserr); tmp, RSQRTF(PFserr) 1* this comes free on DSP P-cosf jpe->SQRTF_Lambda SQRTF_P_Fserr 1 tmp; P sinf P-epsf tmp; 0025 tmp, jpe->SQRTF_-Lambda Pypieb_1; epsb P-cosf P_epsb-l P-sinf tmp; :0.0.0P-pieb P-cosf tmp Psinf P_epsb_1; 0:*0:30 Joint Process Estimation section tmp jpe->SQRTF_-Lambda Pp2; epsi_1 =P-cosb_1 P-epsil1 P-sinb_1 tmp; 5P-pj P-cosb_1 tmp P-sinb_1 P-epsil1; ptr LQRDJPEFCELLSIZE; 1* access next cell Do minimum work for JPE of very last cell only four equations are required for prediction section -125- PBserr_1 jpe->Lambda PBserr_2 P-epsb_1 P_epsb_1; PBserr_1 MAX(PBserrl1, jpe->MinSumErr); 5 SQRTFPBserr_1 SQRTF(PBserr_1); tmp RSQRTF (PBserr_1); 1* this comes free on DSP P-cosb_1 jpe->SQRTFLambda SQRTF_PBserr 2 trnp; P-sinb_1 P-epsbl1 tmp; Joint Process Estimation for last cell tmp jpe->SQRTF_-Lambda P_2; epsi_1 P-cosb_1 Pepsi 1 P-sinb_1 tmp; P-Pl =Pcosbl1 tmp +Psinb-l P-epsil1; gamsl1 Pcosbl1* P-gamsl1; return(gams_1 *epsi_1);

Claims (22)

1. A method for the improvement of the determination of a physiological parameter having a predetermined range of possible values based upon physiological signals, said method comprising the steps of: sensing first and second physiological signals, each of said physiological signals having a desired portion and an undesired portion; based upon said physiological signals, determining at least two possible values of said physiological parameter based on at least two alternative calculation methods for said physiological parameter; and determining a resulting value for the physiological parameter from the at least two possible values.

2. The method of claim 1, wherein at least one of the at least two alternative methods comprises a calculation based upon a scan of values potentially indicative of said physiological parameter.

3. The method of claim 1, wherein determining a resulting value comprises calculating an energy value for each of the possible values and selecting value based upon the energy value.

4. The method of claim 3, wherein said selecting comprises selecting a possible value with the energy value that is a minimum.

5. The method of claim 3, wherein said selecting comprises selecting a possible value with the energy value that is a maximum.

6. The method of claim 1, wherein said physiological parameter is blood oxygen saturation.

7. The method of claim 1, wherein said physiological parameter is pulse rate.

8. The method of claim 4, wherein determining the resulting value comprises the step of selecting at least one of the values based on a determination of confidence for the values.

9. The method of claim 1, wherein said physiological parameter is respiration. The method of claim 1, wherein at least one of the at least two alternative methods comprises a calculation based on the physiological signals after they have been effected P p:\OPER\DF358282 spaI.do-I120203 -127- by an adaptive algorithm.

11. The method of claim 10, wherein said physiological parameter comprises a plethysmographic waveform.

12. The method of claim 10, wherein said physiological parameter comprises oxygen saturation.

13. The method of claim 10, wherein said adaptive algorithm comprises adaptively filtering selected frequencies from said signals.

14. The method of claim 10, wherein said adaptive algorithm comprises filtering said signals with a Kalman filter.

15. The method of claim 10, wherein said adaptive algorithm comprises filtering said signals with an adaptive noise canceler.

16. The method of claim 13, wherein said physiological parameter comprises blood oxygen saturation.

17. The method of claim 13, wherein said physiological parameter comprises heart rate.

18. The method of claim 1, wherein at least one of the at least two alternative methods comprises the step of selecting at least one of the at least two values based on characteristics of the physiological signal indicative of the quality of the physiological signal.

19. The method of claim 1, wherein determining the resulting value comprises averaging the resulting value over time, said averaging dependent upon characteristics of the physiological signal indicative of the quality of the physiological signal. The method of claim 19, wherein the averaging is based on confidence in the quality of the physiological signals.

21. The method of claim 20, wherein the confidence is determined by analysing whether there is significant motion noise present in the physiological signals.

22. The method of claim 19, wherein said step of averaging comprises averaging over a time S indow, wherein said window is increased with indications of said physiological parameter which have a lower confidence of accuracy and decreased with indications of said PIPOPER\DH\358282 spa!.d-122I03

128- physiological parameter which have a higher confidence of accuracy. 23. The method of claim 10, wherein said physiological parameter is blood oxygen saturation and wherein said step of determining further comprises a calculation based on a conventional red over infrared ratio. 24. The method of claim 1, wherein said physiological parameter is blood oxygen saturation and wherein one of said at least two alternative calculation methods are a calculation based upon a scan of possible values for said physiological parameter, and a calculation based on a conventional red over infrared ratio. The method of claim 1, wherein the step of determining a resulting value comprises selecting from the at least two values at least one value that is a maximum among the at least two values. 26. The method of claim 1, wherein the step of determining a resulting value comprises averaging at least some of the at least two values. 27. The method of claim 1, wherein one of the alternative methods comprises at least one calculation in the frequency domain. 28. The method of claim 27, wherein the calculation in the frequency domain comprises performing a Fourier Transform on the physiological signals. 29. The method of claim 1, wherein at least one of the at least two alternative methods comprises a calculation based on a ratio of a normalised representation of the physiological signal resulting from the first wavelength to a normalised representation of the physiological signal resulting from the second wavelength. A method of improving the determination of a physiological parameter based upon physiological signals, said method comprising the steps of: sensing a physiological signal indicative of the physiological parameter, said physiological parameter having a predetermined range of possible values; providing at least two possible calculation methods for calculating said physiological parameter; and utilising at least one of the first and the second methods to determine a resulting value for the physiological parameter. S31. The method of claim 30, wherein determining the resulting value comprises calculating a P:\OPER\DH\;58282 spal.doc-12/02/03 -129- power value for said possible values and selecting as the resulting value at least one of the possible values with a power value that is a minimum. 32. The method of claim 30, wherein said physiological parameter is blood oxygen saturation. 33. The method of claim 30, wherein said physiological parameter is pulse rate. 34. The method of claim 32, wherein determining the resulting value comprises selecting at least one of the possible values based on a determination of confidence in the accuracy of at least some of said possible values. The method of claim 34, wherein selecting at least one of the possible values comprises averaging the possible values with said confidence in the accuracy in a range that indicates that the possible value is likely valid. 36. The method of claim 35, wherein said step of averaging comprises averaging over a time window, wherein said window is increased for possible values of said physiological parameter having a lower confidence of accuracy and decreased for possible values of said physiological parameter having a higher confidence of accuracy. 37. The method of claim 30, wherein determining the resulting value comprises selecting from at least two values at least one value that is a maximum among the at least two values. 38. The method of claim 30, wherein determining the resulting value comprises averaging at least some of at least two values. 39. The method of claim 30, wherein one of the alternative methods comprises at least one calculation in the frequency domain. The method of claim 39, wherein the calculation in the frequency domain comprises performing a Fourier Transform on the physiological signal. 41. The method of claim 30, wherein at least one of the at least two alternative methods comprises a calculation based on a ratio of a normalised representation of the physiological signal resulting from a first wavelength to a normalised representation of the physiological signal resulting from a second wavelength. 42. The method of claim 30, wherein at least one of the at least two alternative methods Scomprises selecting at least one of at least two values based on characteristics of the '4 l P:OPER\DH\2358282 spal.doc.-120203

130- physiological signal indicative of the quality of the physiological signal. 43. The method of claim 30, further comprising averaging the resulting value over time, said averaging dependent upon characteristics of the physiological signal indicative of the quality of the physiological signal. 44. The method of claim 43, wherein the averaging is based on confidence in the quality of the physiological signal. The method of claim 44, wherein the confidence is determined by analysing whether there is a significant motion noise present in the physiological signal. 46. The method of claim 30, wherein at least one of the at least two alternative methods comprises a calculation based on the physiological signal after they have been effected by an adaptive algorithm. 47. The method of claim 46, wherein at least one of the at least two alternative methods comprises a calculation based upon a scan of values potentially indicative of said physiological parameter. 48. A method for the improvement of the determination of a physiological parameter, substantially as hereinbefore described with reference to the drawings. DATED this 12th day of February, 2003 MASIMO CORPORATION By DAVIES COLLISON CAVE Patent Attorneys for the applicant