FR2695730A1 - Method and apparatus for processing an improved digital signal using a Fourier transform - Google Patents

Abstract

The method for determining the frequency of a time varying electronic signal comprises the steps of: (a) providing an unknown time varying electronic signal as an input signal; (b) dividing the input signal into a plurality of simultaneous signals; (c) converting each of the plurality of simultaneous signals into an encoded signal by performing analog-to-digital conversion, the sampling of each of the simultaneous signals being done at a different frequency; (d) performing a Discrete Fourier Transform (DFT) on each of said encoded signals using the encoded signals to request a decoding or storage device, the individual memory locations of that device having stored in them the value of the DFT corresponding to the binary representation of the address of the memory location; and (e) combining the results of the individual discrete Fourier transformations using the r-base representation to determine the frequency of the input signal.

Description

METHOD AND APPARATUS FOR PROCESSING IMPROVED DIGITAL SIGNAL

  USING A FOURIER TRANSFORMER

  FIELD OF THE INVENTION The present invention relates to the field of digital signal processing devices, and more specifically to a method and an apparatus for determining the frequency and phase of continuous or burst signals in real time by means of the Fourier Transformation

Discreet 5 DFT).

  2. This application refers to the

  application 07/833 338, filed February 10, 1992.

  Reliable detection and processing of time-varying electronic signals to determine

  their frequency and phase have a large number of applications

  In some special cases, the signal has a frequency which remains relatively constant during the signal interrogation time. In general, however, the frequency of the signals changes over time in such a time.

  In this case, it is desirable to monitor both the

  what the signal and the rate of change of thisfrequency So, in the general case, a measure of -2-

  instantaneous frequency is desired.

  The signal to be processed may be continuous or arrive at the detector in the form of signals in short bursts. For example, in radars, continuous signals and pulsed signals are used. In optical vibrators using interferometry, the signals are

  often continuous but change in proportional frequency

  the speed change of the vibrating element.

  When using the well-known Laser Doppler Velocimeter (VDL), the signals appear in the form of

  brief bursts, each signal having a unique frequency.

  Many applications require signals to be processed at a very high rate. Any signal processing means capable of handling

  signals at close to real-time

  In addition, the signals can be embedded in a background noise of a relatively high level.

  the signal-to-noise ratio (SNR) will be low (O d B or less).

  In such difficult conditions, the means of

  Signals should therefore be able to detect and

measure the signals.

  Many techniques have been developed for frequency measurement. Some of these techniques provide an almost instantaneous frequency measurement, the processing time being limited only by the duration of the signal being analyzed and a very short time for the transfer. Such techniques are primarily analog techniques, using either an analog-3-integrator for frequency-to-voltage conversion or a phase-locked loop (BPA) for frequency demodulation. Other techniques are usually based on counting the number of zero crossings in the signal over a specified period of time.

  The analog methods of the prior art

  provide a simple means of frequency measurement but suffer from a major drawback When the signal-to-noise ratio falls below 20 d B, the

  performance of these techniques deteriorate rapidly.

  This is caused by the additional zero crossings

  In addition, these processes do not provide

  no way to validate the measured frequency.

  In applications that require instantaneous frequency measurements when the SNR is as low as 0 d B or less, digital signal processing techniques are generally used. Several different algorithms for digital processing of these signals have been developed for analysis. Most of these methods are based on a variation of classical Fourier analysis. A general discussion of prior art methods for digital signal processing using Fourier analysis can be found in "Probability,

  Random Variables, and Stochastic Processes "of A.

  Papoulis, published by McGraw-Hill, New York, 1984 and "Spectral Analysis, A Modern Perspective," by S M Key and S.J R Marple published in Proc IEEE, Vol 69, No. 11, J = t, -4-

pages 1388-1419, November 1981.

  Although Fourier analysis provides optimal performance for both signal detection and frequency measurement, conventional Fourier transformation techniques suffer from several serious disadvantages.

  make them better than analogue

  only some of these techniques provide

  a reliable frequency measurement at a low SNR Second-

  However, they are inefficient in calculations when high resolution is required and, therefore, most of the prior art specific implementations of this method are rather complicated and slow. They are not suitable for processing.

  real-time signals even using the technology

  On the other hand, processes that provide fast processing do this at the expense of resolution and accuracy because they do not use

  that a limited number of data points in the trans-

training.

  U.S. Patent Application Serial No. 07 / 833,338, filed February 10, 1992, discloses another

  process and another device that are useful for detecting

  a time-varying coherent signal using Fourier analysis In the implementation of this method, the input signal is first sampled using an analog-to-digital converter (ADC)

  high speed or some other means The sample data-

  The parallel output of the shift register is then passed to a decoding means. These decoding circuits operate as a bitmap matching. N bits in M bits of the sampled signal (For this purpose, memory means such as ROM, RAM or EPROM can be used) In other words, the series of 1 and O of the sampled signal are used to solicit memory locations In each memory location, the DFT is calculated

  and the box TFD having the maximum power is stored.

  This box TFD corresponds to the whole part of the

  signal frequency rendered dimensionless with frequency

  sample rate, f, (integer part of Nf / fs, N

  being the number of boxes TFD) A second memory number

  in each memory location is the power of the DFT that had the maximum power (other means of

  validation may also be stored) Information

  signal strength can be used to validate the signal to determine whether or not the sampled

  coherent signal within the expected frequency range

  due. The procedure described above works very well for a limited number of samples in the signal

  but has the disadvantage of being limited to one sample-

  As a result, the frequency of the input signal can not be determined with a precision greater than a fraction of 1 / N of the sampling frequency. For example, 16 samples will allow estimation. frequency corresponding to a DFT of 16 points, and the frequency of the signal can be

  resolved at a fraction of 1/16 of the sampling frequency

  This requires a memory size of 216, which is a 64 K memory device. More sampling points would require more

  large memory devices, which are not available

  at present) In many cases this is inadequate The limited number of sampling points

  prevents the process from being used for many

  It is therefore desirable to have a method and apparatus that can determine the frequency of a

  signal with an arbitrary degree of precision.

  It is also known that the frequency resolution also depends on the sampling frequency A reduction in the sampling frequency results in a proportional improvement in the resolution of the frequency measurements Unfortunately, a reduction of the sampling frequency to less than two times the bandwidth of the signal will result in an ambiguity due to the aliasing of the spectrum The aliasing of the spectrum is the folding of information from one frequency band to another This occurs as a result of the sampling

  signal below the minimum sampling rate

  (In the prior art, the folding of the spectrum has been rigorously avoided because of this apparent ambiguity. On the other hand, the width of the spectrum of the input signal has been drastically signal band during the interrogation time of the signal is much lower than the highest frequency at

  As a result, the signal can be sample-

  born at a rate much lower than double the highest frequencies without losing the information associated with

  This spectrum, in turn, allows spectral analysis to be

  much higher signal (the resolution of the

  spectral lysis is inversely proportional to the sampling frequency) The present invention overcomes the problems associated with ambiguity in the

measuring the frequency of the signal.

  The present invention overcomes the limitations of the prior art by providing a method and apparatus for accurately determining the frequency and phase of a time-varying signal. With the present invention, the frequency of the signal can be

  measured with an arbitrary degree of precision the accuracy

  measurement increases exponentially, while the number of components in the device (and thus its

  complexity and cost) increases only linearly.

  The method for determining the frequency of a time-varying electronic signal consists of the steps of: (a) providing an unknown time-varying electronic signal as an input signal; (b) dividing the input signal into a plurality of simultaneous signals; (c) converting each of the plurality of these simultaneous signals into a coded signal, performing an analog / digital conversion, the sampling of each of the simultaneous signals being made at a different frequency; (d) performing a discrete Fourier transform (DFT) on each of said coded signals, using the coded signals to solicit a decoding or storage device, the individual memory locations of that device having stored therein the value of the TFD corresponding to the binary representation of the address of the memory location; and (e) combining the results of discrete discrete Fourier transformations to determine the 9 -

frequency of the input signal.

  Figure 1 is a flowchart illustrating the preferred embodiment of the method of the present invention. Fig. 2 is a general block diagram, illustrating the structure of the preferred embodiment of

the present invention.

  FIG. 3 is a diagram of the power spectrum for a discrete Fourier transform at N = 16 points in which each box of the plot represents the

  integer value of the frequency resolved to 1 / N.

  Figure 4 is a diagram showing how the frequency resolution increases when the frequency

  sampling is divided by r.

  Figure 5 illustrates an example of how

  whose resolution of the frequency measurement is increased

  at later stages, using the process of the

present invention.

  Figure 6 is a diagram showing how the case uncertainty of + / 1 at each stage propagates from stage to stage and is reduced even when the frequency

is folded.

  Fig. 7 is a simplified block diagram of a circuit that employs the present invention for

  detect the frequency of an input signal.

  Figure 8 illustrates a possible construction of a circuit for simultaneous real time measurement of

the phase of the signal.

  An apparatus and method for accurately detecting and measuring the frequency and phase of a time-varying signal in near real-time are

  described in the following description, for the purposes

  explanation, construction details, provisions

  and specific component descriptions are provided

  However, it will be appreciated by those skilled in the art that the present invention can be practiced without these specific details.

  places, components, structures and means of

  electronic devices have not been described for

  do not unnecessarily complicate this description.

  As mentioned previously, the continuous Fourier analysis method constitutes the theoretically optimum means of frequency measurement. In practical digital applications, Discrete Fourier Transformation (DFT) is used in place of the continuous method because the unknown signal is sampled using a high-speed analog-to-digital converter (ADC) The Discrete Fourier Transform (DFT) is a mathematical approximation of the

  process of continuous Fourier transformation The ex-

  The mathematical pressure of the DFT is well known to those skilled in the art and is given as a reference in the form: ## EQU1 ##

N N N

  where: O N <N In equation 1, F (n) is the value of the Fourier transform at the frequency (n / N) f 6 and N is the number

  discrete samples, x (k), obtained during the signal.

  (Note that F (n) is, in the general case, a complex number) When N increases to infinity, the accuracy of the DFT is close to that of the transformation of

Fourier continues.

  In the DFT method, the unknown input signal is compared to N sinusoidal waves having discrete frequencies ranging from -f 4/2 to f, / 2, fs being the sampling frequency When the frequency of the signal sampled and the frequency of sinusoidal waves are

  almost equal, the sum of the products, F (n), is

  aunt, which indicates a close degree of agreement This sine wave frequency is then taken as the

  signal frequency Noise, if present, contributes

  will be power-generating over a wide range of frequencies but will not show a single high peak, unless the noise is coherent (that is, unless it has a dominant frequency) The signal frequency is easily identifiable because the power in the frequency box will be much greater than the noise frequencies unless the SNR is too low. Figure 3 is a diagram of the power spectrum of a discrete Fourier transform at N = 16 points, in which each box of the plot represents the integer value of the frequency resolved to 1 / N. The phase of the unknown input signal can be calculated using the following expression: 2 * .ox (k) cos 2 irnk (= arctanl E l (2) M'.ox (k) sin 2 u Nk The DFT provides a good approximation of the continuous Fourier transformation but the process is not exact in itself The use of discrete samples leads to an unimportant but measurable error The performance of the DFT has been analyzed extensively The professionals of the technique know that, if we consider N discrete samples, the frequency difference, Var (f), is given by: Var (f) 12 fg 2 (3) 2 it SNR (N 2-1) N

  where f is the sampling frequency.

  As can be seen from Equation 3, the error

  in the measure of frequency is directly proportion-

  In this way, the frequency resolution can be considerably improved, simply in 14 -

  sampling at a lower sampling rate

  On the other hand, it is also well known that for a bandwidth limited band signal w, the signal should be sampled at a rate above the minimum sampling rate (ie, 2 w) for

  avoid the problem of aliasing.

  The method used in the present invention will now be described. Referring first to FIG. 1, a simplified block diagram of the preferred embodiment of the steps used in the method used to detect the frequency and phase of variant signals. in time is shown Initially, the input signal to be measured is provided in step 10, the signal

  input is divided into a plurality of simul-

  15, Sl, 52, SL The number of simultaneous signals may vary.

  that there are L different simultaneous signals 15.

  In step 20, each of the simultaneous signals is sampled and converted to a data stream Each of the simultaneous signals is sampled at a different frequency, and this produces a different set of coded data. Simultaneous signals

  are sampled at N different points, and N cor-

  corresponds to the value of N in equation 1 The coded data signals are indicated El, E 2, EL, at the

figure 1.

  In step 30, each of the signals of the streams of

  coded data is processed to determine the frequency

  The preferred embodiment utilizes Discrete Fourier Transformation (DFT). It will be appreciated by those skilled in the art that other frequency measurement systems can be used. In step 40, the results of the individual DFTs are combined with one another. new way to produce a measure

  very precise frequency of the input signal.

  Each of the steps used in the method of the present invention will now be described in more detail. Referring again to FIG. 1, in step 10, the input signal is divided into a plurality of simultaneous signals. preferred embodiment, the input signal is divided into 8 simultaneous signals, and L = 8 The preferred embodiment uses 8 simultaneous signals because 8 N has found that this number produces a definitive frequency measurement which is sufficiently accurate for most practical applications However, those skilled in the art will realize that the value chosen for L may be different and that a greater number or

  lower simultaneous signals can also be used.

  The simultaneous signals are then sampled

  at different frequencies in step 20 Frequency

  the first stage signal sampling, 51, is called fs In the preferred embodiment,

  each of the other signals is sampled at a frequency of

  which is half of the sampling frequency

  the previous stage: namely, 52 is sampled at fs / 2, 53 is sampled at fs / 4, 54 is sampled at fs / 8, etc. This system is easily implemented, and well-known to professionals of the technique Each of the simultaneous signals is sampled at the same number of points, N However, at each stage, the signal is sampled during the double of the time of the previous step, because of the reduction of the frequency

  This doubles the resolution of the sample

  during the previous stage, and is illustrated in

Figure 4.

  Sampling of the simultaneous signals in step 20 is carried out, in the preferred embodiment, by means of a digitizer. The digitizer produces a logic output of 1 when the signal level is greater than zero and logical O when the level This produces a single-bit data stream for each of the simultaneous signals. In the preferred embodiment, a 16-bit transformation is used and N = 16. The 16-bit coded signal of each of the coded signals. , El, is used in step 30

to calculate the DFT.

  Other variants of sampling methods

  can be used to encode the simultaneous signals.

  For example, it is possible to use another mode of

  realization that uses a four-bit sampling.

  Similarly, instead of locating the zero crossings, the coder / sampler could use a system that

  locates the maximum and the local minima of the signal.

  In step 30, the data from the simultaneous signals is processed using the discrete Fourier transform. In the present invention, the method 17 - which is used to calculate the DFT minimizes the volume of mathematical computations necessary to provide the

final frequency measurement.

  N-bit data points from coded data signals are stored and used

  as a data reading address in a large

  The memory device has 2 memory locations at the addresses represented by the N-bit binary representation of the numbers from 0 to 2 N-1 (remember that in the preferred embodiment, N = 16) each memory location or cell contains the value of the DFT for particular configurations of 1 and

  0, which constitute each memory address.

  memory may also contain the power of the DFT (or any other means of validation) for

  check that the DFT corresponds to a coherent signal.

  The DFT for each coded data stream

  can be calculated quickly, by soliciting simple

  the memory device. This process allows a deter-

  accurate frequency mination, while minimizing the number of components needed, and therefore the overall cost

and the complexity of the system.

  Although the present invention uses DFT to calculate the frequency of each of the encoded data streams, it will be appreciated by those skilled in the art that other methods of measuring frequency or

  The present invention may be used

  It uses DFT only because it has been considered the most reliable and efficient process in existence.

  for frequency determination.

  Finally, in step 40, the results of the individual DFTs are combined in a new way to produce a value of the frequency of the unknown input signal.

variant are described below.

  Referring next to FIG. 2, a general block diagram of a circuit which implements the method of the present invention is shown. In this embodiment, the input signal is first divided by a divider ( not shown in FIG. 2) and applied to L different sampling / coding units 200 This corresponds to step 10 of the method described above The function of each sampling / coding unit 200 is

  to generate a set of continuous or sample data

  This corresponds to step 20 of the method described above. In FIG. 2, the sampling / coding units can be implemented simply by sampling the input signal at a frequency of frequency fl, thus g 1 (f) can be written in the form: g 1 (f) = (f) (modf L) (4) The frequency of this signal is then measured using the processing element 210 The elements of processing measure the frequency of the outputs of each of the sampling / coding units As noted above, the DFT is used as an efficient method of 19 - measuring the frequency of the arithmetic unit, although other methods of frequency measurement, giving

  similar results can be used.

  The outputs 215 of the processing elements 210 are then combined in a new way to provide a definitive value of the frequency of the input signal f, f that can be written as a certain function G of gl (f), g 2 (f) ,, g (f) This

  corresponds to step 40 of the method described above.

  Thus, f = Glg 1 (f), g 2 (f), * * rg L (f) 1 (5) A feature of the present invention is to find the set of functions gl (f) ,, gt (f ) and the function

  G satisfying the relation given to equation 5.

  Two different groups of these functions are now going

to be described.

  In the present invention, measurements of

  frequency of high resolution are performed using

  a technique similar to that used for

  calculating the representation in base r of real numbers.

  The method of representation in base r is known to those skilled in the art, although it has not

  has been applied in the present context.

  general cepts of representation in base r go

  to be exposed as general information.

  the. In the representation in base r, A is a number -20 - real having the value O E A <r H The number A can be represented by using the representation in base r, in the form: A = M'L Ma> l (1 +, (6) For the calculation of the coefficients (ai), the number A is first divided by r ', M being determined by the maximum number to represent The division of A by r "normalizes this number to obtain A, with OAO <1 The value of the term (J + M) is an integer which determines the resolution with which the number A is represented, and M <J <Ao * In addition, r J + M is the number of steps of

  resolution in the representation of the number.

  In the first step, the coefficient a O is

  calculated by taking the integer part of the product r A 4.

  After the calculation of a 0, the number R O is calculated in sub-

  milking at O of the product r AO (in other words taking the fractional part of the number r A 0) For the second iteration, the coefficient a, is calculated by taking the integer part of the product r RO After the calculation of a ,, the number R 1 is calculated by taking the fractional part of A, and so on. This procedure can continue indefinitely if AO is an irrational number or a rational number of the form xiy, where x and y are integers and not being the form r 2 (z being a

whole number).

  To illustrate the preceding algorithm, the calculation of the base 2 (binary) representation of the number 21 - AO = 0.8 is given below by way of example: Ao = 0.8 r AO = 1.6 ao = 1 Ro = 0.6 A 1 = r RO = 1.2 a 1 = 1 R 1 = 0.2 A 2 = r R 1 = 0.4 a 2 = OR 2 = 0.4 A 3 = r R 2 = 0.8 to 3 = 0 R3 = 0.8 A 4 = r R 3 = 1.6 to 4 = 1 R 4 = 0.6 A 5 = r R 4 = 1.2 to 5 = 1 R 5 = 0.2 A 6 = r R 5 = 0.4 a 6 = OR 6 = 0.8 Thus 0.111110 gives the representation

binary (in base 2) of the number 0.8.

  As can be seen from this example, the calculation of the representation in base r of real numbers implies a way to multiply the rest of each

  iteration by the integer r and a means for calculating

  In addition, with each iteration, the precision of the representation of the

  number A is improved by a factor r.

  In the present invention, the measurement of frequency

  Quence based on individual DFTs is performed using a technique similar to that used for the computation of the base representation r To illustrate this application, consider the case where it is desired to measure the frequency f in a frequency range -fs / 2 to fs / 2, fs being the sampling frequency The normalized frequency (the frequency of the signal f with respect to this sampling frequency) is defined 22 by f / f The discrete frequency boxes of the DFT represent a given resolution by f / N The box TFD

will be the integer part of Nf / f 5.

  Using the DFT, the integer part of the number representing the frequency of the signal, f, can be calculated by determining the box TFD which has the maximum power. Other frequency estimation systems using sampled signals will also follow a configuration. similar To improve the accuracy with which the Nf / fs parameter and thus the frequency are measured, the iterative algorithm described above can be used. This iterative algorithm can be applied as follows Suppose the sampling frequency

  for the iteration i is f L * For this frequency of exchange

  the normalized frequency is given by fi = f / fai If N samples are used for the DFT, the integer part of Nfi then represents the box DFT having

  the maximum power For the iteration (i + 1), the multi-

  plication of Nfi by the factor r (r comes from the

  representation in base (r) may be carried out in samples

  signal at a rate f j / r For this f

  In addition, for each iteration i, the integer part of the product r Nfi for this iteration is calculated using the sampling frequency.

  determining the box TFD having the maximum power.

  In other words, for each iteration i + 1, the frequency

  standardized quence fi, 1 is equal to the normalized frequency

  for the iteration i multiplied by r (ie, fi +, = rf L).

  The integer part of the Nfi can then be calculated by determining the box TFD with the maximum power As can be seen from the above approach, in

  using these characteristics (obtained in sample-

  at different frequencies), a simple algorithm can be developed to provide a frequency measurement of

high resolution.

  An example could probably shed light on this procedure.

  Figure 5 illustrates the case where the real frequency ratio is Nf / fs = 5.1123, a DFT at N = 16

points being calculated.

  In the preferred embodiment of the present invention,

  In this invention, base 2 is used because mathematical

  binary ticks are well known in the art and

  easily implemented In the example of frequency

  quence 5, the frequency would be represented by the box TFD 5 with an unknown remainder of 0.123. In the next iteration, the sampling frequency is divided by 2 which amounts to multiplying the normalized frequency by 2 and the DFT is calculated. will be represented by the box TFD 10 with an unknown remainder of 0.246 At the next iteration, the sampling frequency is again divided by 2 so that the frequency calculated by the DFT should be 20.492 However, the frequency ratios exceeding 16 will be folded Thus, the folding frequency will be represented by 4,492 (20,492 16) so that it will fall in box 4 with an unknown remainder of 0,492 The fact that a folding has occurred can be determined by comparing the value of the Current Frequency Ratio with Result 24 - Previous This provides enough information to identify where folding occurs at each stage. The algorithm shows that the remainder after each iteration is increased by a factor of 2, but is' undefined until it exceeds 1 This integer value then contributes to the number in the box TFD, indicating that the remainder in the first iteration is then known as approximately 1/2 i At this moment of operations, the number of iterations is known, so that the information on the remainder at the first iteration can be better defined. This amounts to recognizing that the resolution is doubled. after each iteration Another way of formulating this is to say that at the first iteration, the frequency is known at + / 0.5 of the frequency box TFD, at the second it is known at +/- 0.25 of the box (referring to the initial bandwidth) and so on. Figure 6 illustrates how the present invention improves the accuracy of the

  frequency measurement at each iteration.

  In practice, it has been found that when calculating the box TFD having the maximum power (for the calculation of the integer part of the ratio Nf / fi), there may be

  an uncertainty of + / 1 in the number of the box TFD.

  For example, if the Nf / fi ratio itself is equal to 1.5, then the TFD box with the maximum power could then be 1 or 2. Similarly, if the ratio itself is 0.5, the TFD box having the power The maximum could then be 0 or 1 This ambiguity propagates throughout the measurement as the sampling frequency decreases. The present invention overcomes this ambiguity by slightly modifying the formula

elementary in base r.

  The preferred embodiment therefore uses a representation of the numbers in base r modified for the number A of the form: A = i b 1 r <(7)

  o bi are integers such that -1 é bi <r.

* It should be noted that with this representation the number A would be represented with different sets of

  bi coefficients (in contrast to the case presented previously

  where there is a bijective correspondence between the number A and its representation in base 2 ie the coefficients ai) For example, with the representation in

  basis 2, the number A = 0,4 could be

  felt by the two following representations:

A O = 0.4

  r AO = 0.8 b O = 1 RO = -0.2 A 1 = r RO = -0.4 b 1 = OR 1 = -0.4 A 2 = r R 1 = -0.8 b 2 = -1 R 2 = 0.2 A 3 = r R 2 = 0.4 b 3 = OR 3 = 0.4 A 4 = r R 3 = 0.8 b 4 = 1 R 4 = -0.2 and

A O = 0.4

  26 - r AO = 0.8 b O = ORO = 0.8 A 1 = r RO = 1.6 b 1 = 1 R 1 = 0.6 A 2 = r R 1 = 1.2 b 2 = 1 R 2 = 0.2 A 3 = r R 2 = 0.4 b 3 = 0 R 3 = 0.4 A 4 = r R 3 = 0.8 b 4 = 0 R 4 = 0.8 A 5 = r R 4 = 1.6 b 5 = 1 R 5 = 0.6 Thus, the number A can be represented as (1.0, -1.0.1,0) or (0,1,1,0, 0.1)

  easily verify that the two representations cor-

  correspond to the same number A In addition, many other representations can be given for the same number A This representation variant is used to solve the uncertainty encountered in the calculation of the box DFT having the maximum power The uncertainty of

  TFD box of + / 1 at any stage changes the representation

  the final result, after a sufficient number of stages, will provide the same resolution

in the definition of the number.

  Referring again to Figure 1, the

  final frequency measurement at step 40 is performed

  killed, in the preferred embodiment, using the formula of equation 7 above The bi coefficients of equation 7 are simply the results of the individual DFTs The individual DFTs are summed, and the final sum is taken for the signal frequency

unknown entry.

  It should be noted that when calculating the frequency using the base r algorithm, the number of points used for the DFT is not necessarily limited to the 16 used in the preferred embodiment. number of points is, in some

  limits, preferable for the calculation of the DFT For example

  ple, the use of a greater number of points gives a better insensibility to the noise There is a practical limit of the number of points N which can be

  effectively used in processing For example,

  ple, increasing the number of sampling points

  increases the complexity, and therefore the overall cost, of

  Likewise, increasing the number of sample points beyond a certain parameter may not appreciably increase accuracy

  results of the frequency measurement.

  With N samples used for the DFT, the bi coefficients can be calculated using the following equation: bi = (di, + rdi) mod N (8) O: -N / 2 <a mod N e N / 2 and a = di ,, rdi The term di represents the frequency box TFD having the maximum power at the i-th step As an example, consider the case where the case uncertainty of + / la leads to that the box TFD let + 1 at the iteration 28 - i that is to say di = 10 when it should have been 9 In the iteration i + 1, the box TFD would be 18, which will fall back to box 2, (di, = 2) The introduction of these values in equation 8 gives: bi = (2 20) mod N = -2 This shows that the box TFD in the previous iteration was shifted by + 1 because of uncertainty of the measurement. If we go now to Figure 7, a diagram

  simplified principle of a circuit which uses the pre-

  The present invention for detecting the frequency of an input signal is shown. The input signal is provided at the input line 100. From there, the signal is divided into L different simultaneous signals. Each of the simultaneous components is directed to a stage. different spotted

  Stage 1, Stage 2, etc., to Stage L in Figure 7.

  In the preferred embodiment, as indicated above, there are a total of eight stages.

  eight stages give a definite frequency

  which is sufficiently precise for the majority of real-world applications It will be appreciated by those skilled in the art that the number of stages may vary, depending on the exact resolution

  is desired for a particular application.

  The simultaneous signals are each applied to a decoder 102. The decoder 102, as indicated above, is a digitizer which produces a 29 - bit sampled signal. Each of the simultaneous signals is

  sampled at a different frequency.

  The sampling frequency of the first stage is marked 104 and designated 51. Each of the signals in the following stages is sampled at a fixed divider.

  r the sampling frequency of the previous stage.

  The divisor r is the same as the value of r used in the modified r-base representation of equation 7. In the preferred embodiment, ra for value 2 and each stage is sampled at half the stage frequency. As previously shown, with the addition of each stage, the frequency resolution thus also increases by a factor of 2. The frequency resolution is then given by 1 / (N 2 L). Thus, with the addition At each stage, the frequency resolution is improved exponentially while the hardware implementation is increased

  linearly This is definitely a benefit

  that with this method, the high-resolution frequency measurement can be carried out using much less material than with conventional methods. The method described has the considerable advantage of allowing a cheap and reliable implementation of the measurement of high resolution frequency, using the method of

Fourier analysis.

  In the preferred embodiment, 16 samples

  This is equivalent to a 16-point DFT in equation 1 above, N = 16. The output of each decoder 102 is then passed to a shift register. The output of the shift register is then applied to the decoding means 110. The decoding circuits act for a mapping of N bits into M bits. As described above, memory supports such as ROM, RAM and EPROM can be used for this task In this case, the output of the shift register can then be used as an address of the memory of M 2 N bits. In each memory cell, two numbers are stored. the box TFD having the maximum power (which corresponds to the integer part of the ratio Nf / fi with an uncertainty of + / 1) This number corresponds to the box TFD having the maximum power The second number stored in the memory cell the power of the box TFD which had the maximum power (other means of validation of the signal sampled could also be

used for the i-th stage).

  Signal strength information can be used to validate this signal to both give an indication of the presence of a signal and to validate the frequency measurements. The two numbers for the different stages are then applied.

to a decoding circuit 115.

  It is not necessary to have a different memory for the decoding circuit 110 in each of the stages. The reason for this is that the decoding circuit stores identical data regardless of

  the sampling frequency of the input signal.

  In other words, the output of the decoding circuit depends only on the output of the shift register 105. Each of the shift registers 105 can therefore be used to solicit a single memory circuit, regardless of the number of stages in the device. approach greatly reduces the total number of components and this

done, the cost of the system.

  The logic decoding circuits 115 accept the outputs of the decoding circuits 105 and combine each of the results of the individual DFTs according to the system presented above with respect to the equation 7. The individual bi coefficients are summed to produce a definite value of the frequency of the input signal.

  As can be seen from the description

  above, the processor, in the embodiment

  preferred, is able to provide f / 8 measurements per second.

  For a sampling frequency f, = 80 MHz, the processor provides 10 million frequency measurements per second using the Fourier analysis method even for the 16 real samples or 8 complexes that are used in the transformation of The present invention can be easily extended to

  transformations at 32, 64, 128, 256 sample points

  or more This exceeds by far the capacity of

  current processes using known technology.

  The process described above uses the repre-

  In the above method, it is desirable to sample the signal in the first stage at a rate greater than twice the maximum input frequency. This approach allows a correct frequency measurement over a maximum range. The following describes an alternative embodiment of the method for combining the outputs of the individual DFTs to provide the final frequency measurement. In this alternative embodiment, all stages can be sampled at a rate. which is far less than twice the frequency

maximum entry.

  For this variant embodiment, the final signal frequency is measured using the method of the mixed base representation With this approach, the coefficient of the representation of numbers is calculated using modular arithmetic. The calculation of the number from of its mixed base representation can be performed using the Chinese theorem

  from the rest or the formula of the mixed base.

  To apply this variant of the method to high resolution frequency measurements, the signal frequency, f, is sampled at different sampling frequencies f 1, fs 2 ,, f. The sampling frequencies are selected as follows: Suppose that

  Ni (O <i <n) represents the number of the frequency box

  TFD for step io the maximum power occurs As the sampling frequency of step i is equal to fi, the resolution step for i is therefore given by Si = fi / Ni. The sampling frequencies fali a * * tf are chosen so that the ratio Si / Sj (for O <i, j <N) is a rational number of the form Xi / Xj, Xi and Xj being prime numbers

relative (for O <i, j <n).

  For example, for N 1 = N 2 = 16, and assuming that f 1 = 16/13 M Hz and f 2 = 16/15 M Hz, then 51 = 13 and 52 = 15 and the ratio 51/52 = 13 / 15 corresponds to X 1 = 13 and

  X 2 = 15, 13 and 15 being relative prime numbers.

  With a signal of frequency f, the output TFD of step i is given by: di = int lf / Sil mod Ni = int lNif / f mod Ni di being the frequency box TFD (for step i) having

the maximum power.

  For example, if f = 3.4 M Hz, then with N 1 = N 2 = 16 and f 1 = 16/13 M Hz and f 2 = 16/15 M Hz, dl = int 1 (3.4 / 16 ) (13) (16) l mod 13 = 5 d 2 = int l (3,4 / 16) (15) (16) l mod 15 = 6 To recover the frequency f from the values of

  di, each di is first multiplied by the ratio Xi / Ni.

  The frequency is then calculated using either the Chinese theorem of the rest or the formula of the mixed base. As mentioned above for the mode of

  preferred embodiment, there may be an ambiguity of +/-

  1 in the determination of the box TFD having the maximum power Unlike the case of the representation in fixed base r, the penalty incurred with this ambiguity -34 - can lead to completely false results To solve this ambiguity, the sampling frequency is selected so that for any two frequencies f 1, f 2, (in the range in which the frequency is measured) if | di, di 2 | I1 O <i <n then the frequencies f 1 and f 2 satisfy I fi 1f 2 1 <If 0 <i <no the di, and di 2 are the representations TFD of f 1 and f 2 respectively This variant of mode of embodiment can be easily implemented by selecting and programming the logic decoding circuits correctly (element 220 of FIG. 2 and element 115 of FIG. 7). The implementation of this variant of embodiment will be easily apparent to the professionals.

of the technique.

  The present invention also comprises means for measuring the phase of the input signal. FIG. 8 illustrates a possible configuration for the implementation of

  phase measurement in real time.

  figuration can be implemented by means of

  analogue, digital or hybrid

  In a possible configuration, the measured frequency using the instantaneous frequency measuring circuits 152 is used to generate a sine wave and a cosine wave at a frequency equal to the input signal frequency 150. For this purpose, look-up tables, decoding circuits, or special analog circuits may be used The generated sine and cosine waves are then multiplied with the input signal by the multiplier. The multiplication may be performed using analog multipliers when the two signals (i.e. generated sinus and cosine waves and the

  input signal) are of analog form, or using

  numerical multipliers if the two signals are in digital form or by using a multiplication digital-to-analog converter (DAC) if a signal

  is of analogue form and the second of digital form

  Thus, the multiplier outputs are given by: sin (? O t + f) sin?, 0 t = 0.5 cosf 0.5 cos (2 &> o + t) (9) sin (? O t + f) cos & O t = 0, Ssini 0.5 sin (2? O + t) (10) Integrator 160 is then used to eliminate the second term from equations 9 and 10. Analog integrators can be used if analog multipliers are used or digital accumulators if digital multipliers are used Thus the accumulator outputs are given by 0.5 cos 4 and

  0.5 sin 4, and the phase can be calculated.

  The phase difference between two signals can then be obtained by calculating the phase of each signal (relative to a common reference) and then

  taking the phase difference between these two signals.

  Since the above methods utilize 36-Fourier analysis for frequency measurement, the techniques provide reliable frequency measurement even at a RSB.

  In addition, it has been found that the processes provided

  It is also an effective means of signal detection. This allows the present invention to be used for the treatment of

  signals in bursts as continuous signals.

  Other means of validation can be provided when comparing the frequency measured at each stage

with that of the previous stage.

  When the present invention is used to process burst signals, a time domain burst detector may also be included to prevent false detection and processing of coherent background signals. This will also prevent triggering of the detector by a background signal. The time domain burst detector, in combination with the frequency domain detector, is therefore considered part of an alternative embodiment of the present invention. The time domain burst detector uses a level control. threshold that any potential signal voltage must exceed in order to validate the burst detector circuit Several approaches are possible for this system, including the requirement that the high-pass filtered signal exceed both a positive voltage level and a positive voltage level. a negative voltage level and also processes that start by straightening and squaring the ten signal then use the signal strength to trigger the circuit. 37 - As a result, a new process and a new

  apparatus for the digital signal processing used

  the discrete Fourier transformation have been

  described This description has been made with reference to

  specific examples of embodiments thereof. Those skilled in the art will appreciate, however, that various changes and modifications can be made without departing from the overall spirit of the field of use of the invention. The specification and accompanying diagrams should therefore be considered as

  illustrative rather than restrictive. The field of use

  complete description of the present invention is limited only by

by the following claims.

38 -

Claims (29)

  A method for determining the frequency of a time-varying signal, comprising the steps of: (a) providing an input signal;   (b) dividing said input signal into a plural   simultaneous signals; (c) sampling at the same time of said simultaneous signals, each of said signals being sampled at   a different frequency so as to generate a   coded signals; (d) matching each of said encoded signals with a known representation of a signal, said known representation of signals having precalculated values indicative of a frequency of the encoded signals; (e) use of said known representations   for calculating said frequency of said input signal.   The process according to claim 1, wherein There are 8 simultaneous signals.   The method of claim 1, wherein each of said simultaneous signals is sampled on a bit using a digitizer.   The method of claim 1, wherein each of said simultaneous signals is sampled in   using multi-bit sampling.   The method of claim 1, wherein each of said simultaneous signals is sampled at 16 different points.   The method of claim 1, wherein a first of said simultaneous signals is sampled at a frequency of fst and each of said subsequent signals   is sampled at a multiple of f.   The method of claim 6, wherein f. is twice a maximum frequency of said input signal to measure.   The method of claim 6, wherein   said multiple has a value less than one.   The method of claim 6, wherein   said multiple is equal to one half.   The method of claim 1, further comprising the step of determining a phase of said input signal. The method of claim 1, wherein said step of using calculates said frequency of said input signal according to the base representation r of numbers, so as to produce a measurement of said   frequency of said signal varying in time.   The method of claim 1, wherein said utilizing step calculates said frequency of said input signal according to the mixed base representation of numbers, so as to produce a measurement of said   frequency of said signal varying in time.   A method for determining the frequency of a time-varying electronic signal, comprising the steps of: (a) providing said time-varying electronic signal as an input signal; - (b) dividing said input signal into a number L of simultaneous signals;   (c) division of each of said L simul-   taned to a coded signal by performing an analog / digital conversion using one-bit sampling; (d) performing discrete Fourier transform (DFT) on each of said encoded signals;   (e) use of the results of those trans-   discrete Fourier formations for determining the frequency of said time varying electronic signal. The method of claim 13, wherein There are 8 simultaneous signals.   The method of claim 13, wherein said step of converting said input signal into a   coded signal includes the taking of 16 samples of said input signal.   The method of claim 13, wherein said DFT is accomplished using said encoded signals as an address of a memory location containing a value of said DFT corresponding to said encoded signals. A method for determining the frequency of a time-varying electronic signal, comprising the steps of: (a) providing said time-varying electronic signal as an input signal; (b) dividing said input signal into a series 41 - of a number L of simultaneous signals;   (c) converting each of said L simul-   taned into a coded signal by performing an analog / digital conversion using one-bit sampling, whereby each of said simultaneous signals is sampled at a frequency which is half the   sampling frequency of the previous simultaneous   tooth, and a total of N different points are sampled   for each simultaneous signal; (d) storing each of the encoded signals in a shift register; (e) using each of said coded signals to access memory means, said means for   memory having 2 N memory addresses, each of   said storage addresses containing at least one   value of a discrete Fourier transform corresponding to   to a binary representation of said storage address; and (e) calculating the frequency F (x) of said input signal according to the following formula: F (x) = 2 q -bjr (i bi being equal to the box TFD having the maximum power for each stage i.   The method of claim 17 comprising in   additionally, after said calculation step, the determining step   nation of a phase of said input signal.   Apparatus for determining the frequency of a time-varying electronic signal, comprising: input means for accepting said time-varying signal as an input signal, said input means providing means for dividing said input signal; signal   input into a plurality of different simultaneous signals   ent; at least one sampling / coding means coupled to said input means for sampling each of said simultaneous signals at a different frequency so as to generate a plurality of coded signals; at least one processing means for determining a frequency transformation of each of said coded signals; a logic circuit coupled to said processing means for combining said frequency transformations to determine the frequency of said frequency signal varying in time.   Apparatus according to claim 19, wherein each of said simultaneous signals is sampled by said sampling / coding means at a frequency different.   Apparatus according to claim 19, wherein said processing means performs a transformation of   Discrete Fourier on each of said coded signals.   Apparatus according to claim 19, further comprising phase determining means coupled to said logic circuit for determining a phase of said signal varying in time.   Apparatus according to claim 22, wherein said phase determining means comprises: input means for receiving an output from said logic circuit; a generator for creating sine and cosine waves having a frequency equal to said frequency of said time varying signal; multiplier means coupled to said input means and said generator; integrator / accumulator means coupled to said audit average multiplier.   Apparatus for measuring the frequency of a time-varying electronic signal, comprising: input means for receiving said time-varying signal as an input signal, said input means dividing said L-input signal different simultaneous signals; a number L of sampling / coding units coupled in parallel to said input means, said sampling / coding units sampling each of said simultaneous signals at a different frequency at N different points so as to generate L different coded signals;   a treatment element coupled to each of   said sampling / coding units for performing a discrete Fourier transform on each of said coded signals; a logic circuit coupled to each of said processing elements for combining said   Discrete Fourier transformation according to the representation   basing said number of numbers to produce a measure of said frequency of said time varying signal. Device according to claim 24, wherein L = 8 26 Device according to claim 24, wherein N = 16   Apparatus according to claim 24, wherein each of said sampling / coding units comprises a digitizer which produces a digital output of "1" when said simultaneous signal has a level greater than zero   and a digital output of "0" when said simulated signal   tane has a level below zero.   Device according to claim 24, wherein   r = 2, and each of said sample units   swimming / coding samples its corresponding simultaneous signal   laying at a frequency that is half the frequency previous sampling.   Apparatus according to claim 24, wherein said logic circuit means calculates the frequency, F (x), of said input signal according to the following formula: F (x) = 2 l Db Ir -   bi being equal to the box of the Fourier transformation   discrete having maximum power for each stage i.   A device for measuring the frequency of a time-varying electronic signal, comprising: input means for receiving said time-varying signal as an input signal, said input means dividing said input signal into an input signal; a plurality of different simultaneous signals; a one-bit decoder coupled to each of said simultaneous signals, each of said one-bit decoders sampling said simultaneous signals at a different frequency at N different points; an N-parallel parallel serial-output shift register coupled to each of said decoders; at least one M-bit N-bit decoding circuit, said decoding circuit being coupled to each of said shift registers, and receiving   g an output of said shift register, in   deriving a value corresponding to a discrete Fourier transform of said N-bit pattern from said shift registers; each of said decoding circuits being coupled   to a single logical decoding means, said means for decoding   logic coding combining said discrete Fourier transformations according to the representation of numbers in base r so as to give a definitive measurement of   said frequency of said input signal.   Apparatus according to claim 30, wherein said logic circuit means calculates the frequency, F (x), of said input signal according to the following formula: F (x) = fir (i 1 bi being equal to the box of the Fourier transformation   discrete having maximum power for each stage i.   Apparatus according to claim 30, wherein -46 -   said decoding circuit comprises memory means.   Apparatus according to claim 30, wherein said decoding circuit further produces an enable signal corresponding to said discrete Fourier transform. Apparatus according to claim 30, wherein there is a single decoding circuit, each of said shift registers being coupled to said decoder circuit. single decoding.   Apparatus according to claim 30, wherein there are a plurality of decoder circuits, each of said shift registers being coupled to a driver circuit. separate decoding.   A device for measuring the frequency of a time-varying electronic signal, comprising: input means for receiving said time-varying signal as an input signal, said input means dividing said input signal into an input signal; a plurality of different simultaneous signals; a one-bit decoder coupled to each of said simultaneous signals, each of said one-bit decoders   sampling said simultaneous signals at a frequency of   different in N different points; an N-parallel parallel serial-output offset shift register coupled to each of said decoders; an N-bit decoding circuit in M bits coupled to each of said shift registers, said circuits   decoding device receiving an output from said decoder register.   calibration and producing a value that corresponds to a 47 -   discrete Fourier transformation of said configuration   N bits from said shift registers; each of said decoding circuits being coupled   to a single logical decoding means, said decoding means   logic combining said discrete Fourier transformations according to the representation of mixed base numbers so as to produce a definitive measurement of   said frequency of said input signal.   A device for measuring the frequency of a time-varying electronic signal, comprising: input means for receiving said time-varying signal as an input signal, said input means dividing said L-input signal different simultaneous signals; a number L of sampling / coding units coupled to said input means, each of said sampling / coding units having an output, each of said outputs being a sampled or continuous signal having a frequency which is a function of the frequency   said input signal, thereby allowing the frequency   said input signal being represented as a vector of L components;   a treatment element coupled to each of   so-called sampling units / coding for measuring said   frequency of said outputs of said sample units   Stroke / encoding; a logic circuit coupled to each of said processing elements for combining said frequencies to calculate said frequency of said input signal 48 -   from said vector of L components.   Apparatus according to claim 37, wherein said sampled signal frequency is equal to   said input frequency as a function of the sampling frequency   pling. Apparatus according to claim 37, wherein said processing elements use Discrete Fourier Transformation to measure the frequency output of said units. sampling / coding.   Apparatus according to claim 37, wherein said processing elements use zero crossing techniques to measure said frequency of   outputs of said sampling / coding units.   Apparatus according to claim 19, further comprising a frequency domain burst detecting means coupled to said logic circuit means;   validation means for determining the validity   An apparatus according to claim 41, wherein said frequency domain burst detecting means calculates a Discrete Fourier Transform of said sampled signal at different sampling frequencies; determines a signal-to-noise ratio   said sampled signals and compares said   signal / noise ports to a predetermined value.   Apparatus according to claim 41, further comprising signal power detecting means for preventing false detection of coherent background signals. Apparatus according to claim 41, wherein said frequency domain burst detecting means measures a frequency of said input signal according to an adaptive number of samples, said number of samples being adapted according to the length of bursts. said input signal.