GB2303453A - Digital MRI receiver with reduced data truncation effects - Google Patents

Description

TRANSIENT REDUCTION OF MRI SIGNALS IN A DIGITAL RECEIVER CROSS-REFERENCE TO RELATED APPLICATIONS This application is related to commonly-assigned patent application serial no. 08/260,789 filed on 16 June 1994 entitled "Synchronized Digital Signal Processor for MRI Reception" (attorney docket no. 89-192), the entire disclosure of which is incorporated herein by reference.

FIELD OF THE INVENTION This invention relates to nuclear magnetic resonance (NMR) imaging, and more particularly to RF receiver digital filtering techniques for use in magnetic resonance imaging (MRI) systems. Still more specifically, the present invention relates to transient reduction in a Magnetic Resonance Imaging digital RF receiver.

BACKGROUND AND SUMMARY OF THE INVENTION Nuclear magnetic resonance ("NMR") phenomena cause the human body (or other object of interest) to generate radio signals ("NMR signals") for pick-up by a magnetic resonance imaging ("MRI") system. The magnetic resonance imaging ("MRI") system has a radio frequency (RF) receiver which receives, amplifies and filters these NMR signals. The RF receiver1 5 output is processed by a computer to generate a displayed image of the body's internal structure.

To generate high quality images, it is important for the MRI RF receiver to accurately receive and process the weak NMR signals generated by the body. Unfortunately, various defects in RF receiver operation (e.g., internally generated noise, digital quantization errors, "aliasing" effects, quadrature channel imbalance) can introduce distortion and noise which degrade the "purity" of the received NMR signals -- and thus decrease the quality of the resulting images.

Signal filtering is one of the more important functions performed by an MRI receiver. Filtering is needed to extract the MRI signal from surrounding noise and signals -- and is also needed before analog-to-digital conversion to provide "anti-aliasing" as mentioned above. "Aliasing" occurs when the Nyquist rate (half the converter sampling rate) is less than the frequency of signal components presented to the converter input. Aliasing causes unwanted parts of the signal spectrum to "fold over" into the digitized sample stream representing the desired signal passband. These filters must provide tight frequency selectivity and other high performance.

Until very recently, analog receivers were used to receive the NMR signals in MR imaging systems. Because of the high performance requirements, suitable analog filters are expensive to design and implement while nevertheless suffering from certain performance deficiencies (e.g., frequency-dependent phase shifts, poor transient response, non-zero DC offset, drift, and imperfect gain and phase matching between pairs of filters used for "quadrature" channels).

So-called "digital receivers" have now begun to replace analog receivers in MRI systems. As digital signal processors (DSPs) and other "fast" digital hardware have become available, cost-effective and increasingly more capable, it has become possible to filter the received NMR signal in the digital domain instead of the analog domain in order to increase receiver performance in certain respects. For example, it is possible to construct, using modern digital signal processing components, a digital filter which exhibits a linear phase response throughout its passband. Digital filtering provides additional significant advantages including, for example, programmability, potential increases in dynamic range, and potential improvement in S/N.Similarly, "digital receivers" implemented using modern digital signal processing components have several well known advantages such as elimination of DC and low frequency noise, perfect matching of I and Q (quadrature) channels, high performance filters and finer quantization. Digital signal processing techniques can thus significantly improve noise and distortion performance (and hence image quality), and can provide additional advantages such as increased stability and flexibility. Co-pending commonly assigned U.S. patent application serial no. 08/260,789 filed 16 June 1994 discloses an example of a digital receiver for MRI use that provides these advantages and increased performance as compared to prior analog type MRI receivers.

Although MRI digital receivers with high performance digital filters are known, further improvements are possible.

Any filter (digital or analog) exhibits a "transient response" in response to changing input. The transient becomes smaller as time goes on, and eventually dies out to leave only a "steady state" response. Because the received MRI signal is intermittent, MRI receiver filtering inherently generates transient responses at the beginning and end of each MRI signal window.

These unavoidable transients can generate undesired artifacts on the displayed MR image unless care is taken to reduce their magnitude and effects.

The present invention provides improvements to MRI digital receiving techniques that reduce the effects of filter transients on an MR image.

Transient reduction in the preferred MRI digital receiver involves taking advantage of the particular properties of a sampled and digitally demodulated MRI signal with high dynamic range (e.g., 96db) that cause transients -namely, the aperiodic, specific time interval windowed nature of the data signal which must be low pass filtered and decimated to produce a predetermined data set size. The present invention provides techniques that: (i) eliminate or reduce the magnitude of filter transient response, and (ii) minimize degradation of the NMR data set due to unavoidable filter transients by designing the digital filter so that these unavoidable transients are placed such that they do the least harm to the MR image.

The present invention provides the following MRI digital receiver features for reducing MRI signal transients or reducing their effects: Data collected before the "sample gate" (beginning of the time window defining the "active" portion of the NMR received signal output) is used to initially "fill" the FIR digital low pass filter to reduce initial filter output transients. This data can be collected starting at the time the MRI receiver is enabled, when the signal is likely to be small and before the receiver needs to produce any output. Even though data received prior to "sample gate" is used to fill the filter, the first output data point nevertheless corresponds to the original data point coincident with the beginning of the time window.

The last stage of the multi-rate FIR filter is optimally designed so that the major transients occurring when data first enters the filter and when the last of the data is leaving the filter are discarded. This is possible because the number of filter outputs after decimation can be larger than the number required for the duration of the "sample gate" time window.

Unavoidable transients are placed at the end of the "sample gate" window. Because of the apparent "decay" of the signal amplitude due to the readout gradient and actual decay due to T2,signals occurring near the end of the window are smaller.

Since filter ringing amplitude is proportional to signal amplitude, the amplitude of the ringing is decreased or minimized by placing the ringing near the end of the "sample gate" window.

Filtering data as if it is wrapped around from the end of the acquisition to the beginning can give a transient response like that of a Fourier transform. This reduces transients for symmetric signals. The required data storage and processing is less than that required by a FT.

The transition band of the last multi-rate FIR low pass filter is optimized to reduce transients while at the same time providing a very sharp filter roll off so as to allow the maximum usable MR image field of view.

The "order" (number of coefficients or length) of the FIR low pass filter stages is as short as is consistent with reasonable performance, since the duration of the transient due to a digital filter is related to the order of the FIR filter.

A resulting preferred embodiment MRI digital receiver using these techniques and features provides an improved transient response and field of view as compared to prior analog MRI receivers.

BRIEF DESCRIPTION OF THE DRAWINGS These and other features and advantages provided by the present invention will become better and more completely understood by studying the following detailed description of presently preferred exemplary embodiments in conjunction with the drawings, of which: Figure 1 is a block schematic diagram of an example of an MRI system in which the present invention may be used; Figures 2A and 2B together are a detailed block diagram of a presently preferred example of an embodiment of an MRI digital receiver; Figure 3 is a schematic illustration of the convolution/decimation filtering operations performed by the preferred embodiment MRI digital receiver;; Figure 4 is a graphical illustration of the preferred embodiment input data stream applied to the FIR filters and, on another axis (not to scale), an example of a corresponding NMR signal envelope; Figures 5 & 5A-5D graphically illustrate convolution operations performed to provide FIR filtering; Figure 6 graphically illustrates an example of a convolution output envelope for the first (and subsequent but not last) digital filter; Figure 7 graphically illustrates an example of a convolution output envelope for the last digital filter; Figure 8 graphically illustrates an example of an advantageous last filter passband provided by the preferred embodiment; Figures 9(A)-9(F) illustrate performance characteristics of an example of a prior art analog Butterworth filter;; Figures 10(A)-10(F) illustrate performance characteristics of an example of a prior art analog Elliptic filter; Figures 11(A)- 1 1 (D) illustrate performance characteristics of an example of a first FIR digital filter provided by an example preferred embodiment of this invention; Figures 12(A)-12(D) illustrate performance characteristics of an example of a last FIR digital filter provided by an example preferred embodiment of this invention; Figures 13(A)-13(C) illustrate step response characteristics provided by an example of cascaded first and last FIR digital filters provided by an example preferred embodiment of this invention; and Figures 14A and ISA are photographs showing examples of imaging results provided by a system in accordance with the present invention as compared to examples of prior analog filter results shown in Figures 14B and 15B.

DETAILED DESCRIPTION OF PRESENTLY PREFERRED EXAMPLE EMBODIMENTS Providing some background regarding the type of overall system the present invention operates within, Figure 1 is a schematic block diagram of an example of a magnetic resonance imaging ("MRI") system 10 including a digital receiver 150. System 10 includes a computer 50, a sequencer 52, and an MRI subsystem 54. Subsystem 54 is controlled in real time by sequencer 52 to generate magnetic and radio frequency fields that stimulate nuclear magnetic resonance ("NMR") phenomena in an object 56 (e.g., a human body) to be imaged. A resulting image of body 56 on display 58 may show features and structures that cannot be seen using X-ray, ultrasound or other medical imaging techniques.

The basic techniques for magnetic resonance imaging are very well known and accordingly need not be explained here in detail. Very simply, MRI subsystem 54 includes a large static magnet 69 which applies a magnetic field to the object 56 (this field may be modified by "gradient" fields produced by gradient coils 68). This magnetic field aligns the spin axes of rotating nuclei (e.g., hydrogen atom protons) within the object 56. An RF transmitter 62 generates a radio frequency (RF) pulse of a particular radio frequency (called the "Larmor frequency"). This RF pulse is connected by a "transmit/receive" ("T/R") switch 64 to an RF coil 66 which applies a corresponding RF (electro) magnetic field to the body 56. The RF field temporarily stimulates the nuclei in object 56, causing the axes of their spins to be realigned.When the RF field is switched off, "relaxation phenomena" cause the nuclei to return to their non or less stimulated states. As the nuclei return to such non or less stimulated states, they generate their own RF magnetic field (the "NMR" signal).

The NMR signal "echo" induces a voltage into RF coil 66. An electronic RF digital receiver 150 (which is connected by the "TIR" switch 64 to the RF coil 66 between RF pulse transmission) receives, amplifies, filters and detects the induced voltage to provide a pair of time-varying output signals. The digital receiver 150 includes an analog-to-digital conversion arrangement that converts these output signals into digital 2's complement representation. The digital receiver 150 samples the signal at fixed time intervals and outputs the sampled results as numerical digital data to the data acquisition and display computer 50.Sets or matrices of this numerical data so obtained are stored and analyzed by computer 50, which "reconstructs" (using complicated but conventional mathematical procedures) amplitude information corresponding to the concentration of nuclei within different volumes of the object. Such reconstructed amplitude information is used to generate a high quality image of the internal structure of the object 56, which can be displayed on a display screen 58, printed onto film for later viewing, etc.

Background About Digital Receiver 150 Figures 2A-2B together are a schematic diagram of an example of a digital receiver 150 provided in accordance with aspects of the present invention. Co-pending application serial no. 08/260,789 contains further details concerning the example of digital receiver 150. Briefly, digital receiver 150 includes an analog "front end" section 60 that selects a signal of a desired frequency and performs some filtering, and a digital section 188 that filters and processes in the digital domain.Digital receiver 150 receives an RF input from RF coil 66 via T/R switch 64 which also selectively couples the output of RF transmitter 62 to the RF coil when this coil is used to both transmit and receive (in this example, T/R switch 64 is controlled by a signal "Receiver Gate" generated by sequencer 52). It is also possible to transmit with one coil and receive with a second, in which case TIR switch 64 is replaced by decoupling of the TX and RX coil circuitry when appropriate. Digital receiver 150 couples this received input from T/R switch 64 to the input of an RF amplifier 100 to produce a signal that is heterodyned ("down converted") by a mixer 102 to a 2.0 WIz intermediate frequency, for example.This downconverted signal is provided to a first IF section 104 including an IF amplifier 136 and a bandpass filter 138. IF section 104 amplifies the down-converted signal with IF amplifier 136, and passes the amplified signal to bandpass filter 138 which acts as an anti-alias filter in addition to selecting the desired "difference" output of mixer 102. The example digital filter 150 uses a further mixer 106 to down-convert the output of first IF section 104 to a lower frequency band such as 125 Kilohertz for further filtering and amplification by a second IF section 108. Digital receiver second IF section 108 includes a 0-250 kHz bandpass filter 184 used to reject out-of-band signals in order to prevent aliasing.

The output of IF section 108 is sampled with a low distortion analog-to-digital converter ("ADC") 186 to produce a stream of periodic samples. In the example, ADC 186 has an amplitude resolution of 16 bits and thus produces a 16-bit 2's complement digital output for each sampling. In the example, the timing at which ADC 186 samples is determined by a sample timing signal S at frequency FO which is derived from master time base 127.

The RF transmit carrier frequency TX FREQ is determined by a frequency synthesizer 126 that is also derived from master time base 127. Common use of a master clocking signal derived from master time base 127 to generate the RF signal transmitted by transmitter 62 and to select the sampling times of ADC 186 ensures that there is a fixed relationship between the phase of the RF carrier (and thus of the NMR phenomena) and the ADC sampling times. This means that in the preferred embodiment the sampling times of ADC 186 are phase locked with the MRI phenomena occurring within the object being imaged. A fixed frequency divider 134 and a programmable frequency (divider) synthesizer 126 provide a known ratio between the sample rate of ADC 186 and the frequency of the received down-converted second IF version of the RF carrier (TX FREQ) produced by RF transmitter 62.

In the example, frequency synthesizer 126 creates TX FREQ and RX FREQ from 32 MHz supplied by Master Time Base 127. A TX FREQ of 15 MHz results from multiplying 32 MHz by the ratio 15/32 (or 120/256 which will be useful below). A RX FREQ of 13 MHz results from multiplying 32 MHz by the ratio 13/32 (or 104/256). Frequency converter 130 produces a 1.875 MHz LO (local oscillator) signal by multiplying 32 MHz by the ratio 15/256. Frequency divider 134 multiplies 32 MHz by the ratio 1/64 (or 4/256) to provide timing signal S at the sample rate Fs for ADC 186. The receiver amplifies the 15 MHz MR signal and converts it down to the second IF frequency at the ADC input.An example of the progression of frequencies to the input of the ADC is: MR sinal RX FREO 1.875 MHz LO ADC input 15 MHz - 13 MHz - 1.875 MHz = 0.125MHz In multiples of 32 MHz these are: 120/256 - 104/256 - 15/256 = 1/256 From these, the relation of the down converted MR signal frequency to the ADC sample rate Fs is (l/256)/(4/256) = 1/4. Depending on chosen frequencies, other ratios are possible. However, phase consistent samples require a ratio of integers.

The digitized signal output of ADC 186 is applied to a quadrature detector and floating point converter block 200. In the example, detector/converter 200 is a digital signal processor ("DSP") appropriately programmed to perform quadrature detection and floating point conversion.

DSP 200 generates two output channels (I and Q) in quadrature relationship.

Assuming that the ratio between ADC 186 sampling frequency and the carrier frequency of the second IF stage 108 is four-to-one as in the preferred embodiment, block 200 can perform quadrature detection by multiplexing with alternating sign inversions, i.e., by sending received samples alternately to the I and Q channels such that each channel receives every other sample. The signs of the samples are periodically reversed.

In the example, the detector/converter block 200 also converts the 16-bit-wide digital samples provided by ADC 186 into (e.g., 32-bit wide) floating point format for more precise processing by following digital filtering blocks 300, 400. In the example, the digital filtering blocks 300, 400 may each include an Analog Devices Model ADSP21060 digital signal processor.

The digital filtering blocks 300, 400 digitally filter respective I,Q channels in floating point format, and may convert the resulting digitally filtered values back to 16-bit-wide fixed point precision representation suitable for further processing by computer 50.

Digital Filtering As explained in co-pending application serial no. 08/260,789 and shown in Figure 3, digital filtering is accomplished in the preferred embodiment using a multirate, multistage digital filter design. After sampling and quadrature detection the sampled data set x[n] (in each of the I and Q channels independently) is processed using a convolution transformation (block 302, 402) to provide a data set y[n] resulting from x[n] convolved with hl[n]. For this and all other filters described here, the number of coefficients in h[n] is even, so the filters are even ordered. In the example, the convolved data set y[n] is then decimated by block 304, 404 to provide a data set yd[m] resulting from decimation of y[n] by M1. This data set yd[m] with sampling rate F1 is the first digital filter output (see Figure 4). Note that the rate F1 of index "m" is a different (lower) rate than the sampling rate FO of "n," the index of input data set x[n]. The decimated set yd[m] is then convolved by further convolution block 306, 406 to provide a data set z[m] resulting from yd[m] convolved with h2[m]. This resulting convolved data set z[m] is decimated by a second decimation block 308, 408 to provide an output data set zd[s] resulting from the decimation of z[m] by decimation function M2. This output data set zd[s] with sampling rate F2 is the second digital filter output (see Figure 4). Note that the index "s" of this decimated output has sampling rate F2 which is a different (lower) rate than the rate Fl of index "m" of the first filter output.

This "multi-rate" filtering using two cascaded digital filters (blocks 302, 304 providing the first filter, blocks 306, 308 providing the second) provides certain advantages. In particular, oversampling of the input data x[n] at rate FO followed by a first convolution and decimation to provide a first output rate Fl, F 1 < F0, followed by a second convolution and associated decimation to provide a second output rate F2, F2 < F1, results in an implementation with significantly reduced overall computation, reduced storage, simplified filter design (i.e., wider normalized transition bands allowed at the first filter stage) and reduced finite-word-length effects (round off noise and coefficient sensitivity).See, for example, Chapter 5 entitled "Multistage Implementations of Sampling Rate Conversion" beginning at page 193 of Cochiere et al, Multirate Digital Signal Processing (Prentice-Hall 1983). Because of the multistage design shown in Figure 3, the early convolution filtering stage(s) 302, 402 operates with a relatively large sampling rate and associated large low pass filter transition width, thereby leading to relatively smaller required filter order (i.e., number of taps). For the last convolution stage 306, 406, the transition width becomes small, but so does the (decimated) sampling rate and the combination again leads to relatively smaller values of required filter order.

In the example, the first convolution 302, 402 has on the order of 320 taps, and the last convolution 306, 406 has on the order of 124 taps. The computation is kept low in each stage of the overall multistage structure leading to substantially reduced computational complexities compared to a single-stage digital filter.

Filter Input Data Set An FIR filter of the type shown in Figure 3 performs direct convolution of an impulse response h[ ] with the input data stream xt ]. For a data set sampled with a rectangular window (defined by the sequencer output "Sample Gate" in the preferred embodiment-see Figure 4), the input data stream x[ ] has a limited length -- and the question arises regarding what data is convolved with hl[ ] for the calculation ranges where h1 [ ] overlaps only part of the input stream xt ]. Figure 5 shows what is meant by the various "overlaps" (for example, hl[ ] and xt ]) while also illustrating the overall convolution process performed in the preferred embodiment.Figure 5 is a simplified example showing four FIR filter "taps" (hl, h2, h3, h4) that are to be convolved with an input data set x[ ] comprising eight elements xl-x8. The convolution process can be understood as a process of "sliding" the filter taps relative to the input data set, and calculating a sum of products for each different "slided position" of the filter taps (hl, h2, h3, h4) relative to the data set in order to arrive at a set of output values.

As can be seen in the first and last three examples shown in Figure 5, some of the h values have no corresponding x for those particular "slided positions." Similarly, no taps "line up" with input values for relative positions between filter taps and input values other than those shown in Figure 5 due to the finite length of the input data set shown. If no calculations are performed with respect to these taps that do not "line up" with input values, the taps do not contribute to the output for that particular "slided" position.This is the equivalent of "zero padding" the x[ ] data set at the beginning and end of the data set (i.e., forcing all input values before and after the finite Sample Gate window to be zero), and performing the calculations with respect to the zero values that have been "padded." Such calculations are shown in Figure 5A, but since multiplication of a filter tap value by a zero input value does not contribute to the filter's sum-of-products output for that "slided position," there is no need to actually perform the multiplication.

Assuming for purposes of this simplified illustration that values "before" the beginning and "after" the end of the input data set are "zero padded" as in Figures 5 and 5A so they don't contribute to the filter output, a sum-of-products is calculated for each of the eleven unique "positions" providing an output data set y[ ] consisting of eleven values yl - yell. At the relative "slided" position of the filter taps relative to the data set x[ ] shown at the top of Figure 5, the first filter tap hl is "aligned" with data set element xl to produce a product xl*hl. Since all other filter taps (h2, h3, h4) are "aligned" with 0 input data set values, these do not contribute to the results and the sum of products for this yl is simply: yl=xl*hl.

The next standard convolution filter output point y2 is calculated by "sliding" the filter taps hl-h4 one position to the left relative to the input data set x[ ], and calculating the resulting sum of the products defined by filter taps "aligned" with data set values. This yields the following results for data output point y2 y2=x 1*h2 + x2*hl.

This process continues for each different position of the FIR filter taps relative to non-zero values of the input data set to yield eleven different sum-of-product convolution output values for the digital filter.

Instead of zero padding the input data set, it is also possible to extend the first and last points outward to provide an input data set of, for example, the following: x8 x8 x8 x8 x8 x7 x6 x5 x4 x3 x2 xl xl xl xl xl xl In this case the response at the end of the sample window is more like an analog (causal) filter than is zero padding. Alternatively, the ends of the sample window can be "wrapped around" to provide an FIR filter response like a Fourier Transform (FT). This approach is described in more detail below.

One can also mix approaches, for example by zero padding the beginning of the data set and extending the final value out as far as needed. These different approaches have different consequences with regard to transients.

Digital Filter Transient Reduction As discussed above, filter transients in an MRI receiver can generate undesired artifacts on the displayed MR image unless care is taken to reduce their magnitude and effects. The preferred embodiment of the present invention provides several techniques for lessening the impact of transients on the output of an MRI digital receiver. Some of these techniques minimize the amplitude or duration of the transients, while other techniques change the point at which unavoidable transients occur in the output data stream in order to minimize their impact on the MR image. These techniques can be categorized as follows: i) prefilling the digital filter with non-zero data; ii) placing unavoidable transients at points in the output stream where they have the least adverse effect; iii) make the transient response be like that of a Fourier transform where the transient amplitude is proportional to the difference between the signal at the beginning and end of the data; iv) careful design of the digital filter transition bands; and v) careful design of the digital filter order (length).

I. Prefilline the Digital Filter Figures 5 & 5A show that if the initial input values xl, x2, x3, etc. of a time-windowed non-zero input data set are different from zero, the sum-of-products calculated by the FIR filter as these non-zero inputs are first presented to the FIR filter yield outputs that may be (and typically are) very different from the zero-valued filter outputs based on previous zero-valued inputs resulting from zero padding.Although FIR digital filters can be implemented to perform sum of product calculations in a sequence independent of the input data set time sequence, this process of presenting initial data set inputs to the filter and having the filter calculate corresponding sum-of-products convolution outputs yl, y2, etc. may be analogized to "filling" a pipeline -- since the filter cannot produce the "first" outputs yl, y2, y3, etc.

until it has performed the product and sum calculations for convolutions in which some of the products in the convolution output sum are based on zero values resulting from zero padding and other products in the sum are based on initial input values. The digital filter can be said to be completely "filled" when all filter taps of h "line up with" meaningful input values so that no outputs y have any contribution from zero values resulting from zero padding. Thus, looking at Figures 5 and SA, the filter shown has been "filled" at the y4-y8 calculations since each one of the filter taps hl, b2, h3, h4 is being multiplied by a true input value (e.g., x4, x3, x2, xl in the case of y4) and not by a zero value resulting from zero padding.

The bandwidth and pass band to stop band transition zone width govern the rate of decay and "ringing" frequency of the overshoot in the step response of FIR filters and, to a lesser extent, the amount of overshoot. The transition from zero padding to the DC signal component of a sample window is a step function with an associated transient at the output. The filling of symmetric (linear phase response) FIR filters also leads to similar transients. The filling transient is important when the data set is aperiodic; MRI signals present exactly such aperiodic input data sets.

In the preferred embodiment, for example, the first FIR filter might have a length of ORDER = 320 In accordance with one aspect provided by the present invention, an additional number of points (e.g., 20 - 50) from before the "Sample Gate" window is used to fill the filter and thereby increase the data set length. With most commonly used MRI sequences, the input NMR signal level is not zero at the time "Sample Gate" opens the digital receiver timing window. Rather, the NMR signal level typically has a lesser amplitude at some time prior to the opening of the digital receiver window at "Sample Gate" -- and then gradually increases to the NMR signal level existing at the time "Sample Gate" is asserted.If the digital filters start with all "zero" values when "Sample Gate" is asserted (i.e., if "zero padding" is used to supply input values outside of the "Sample Gate" window), a substantial transient may occur because the filter has not become conditioned to the non-zero NMR signal before producing outputs for analysis by computer 50.

In accordance with this technique provided by the present invention, data is collected before "Sample Gate" (i.e., before the beginning of the time window defining the NMR signals of interest). This collected data is prepended to the input values collected during the sample window, and is used to initially fill the FIR digital low pass filter to reduce initial filter output transients (i.e., to ensure that the transient response is substantially "over" and the filter is exhibiting more nearly its steady state response by the time "Sample Gate" is asserted).

Figure 4 shows an example of how the preferred embodiment digital receiver structures the input stream applied to the first digital filter. The actual sampled NMR input signal of interest during the time window defined by "Sample Gate" is represented by input values x[sync], x[sync + 1], ., x[n].

Since the analog-to-digital converter 186 in the preferred embodiment is operating continually, it is a simple matter to also collect "p" samples pl, p2, pj that are generated between the time "Receiver Gate" turns the RF receiver on and the time "Sample Gate" opens the NMR sample window. The preferred embodiment prepends these initial samples p to the input data stream.

In the preferred embodiment, no samples representing any (recently) received signal phenomena can be gathered before "Receiver Gate" because the digital receiver RF and IF amplifiers are not active during that time - and accordingly, the corresponding values are zero padded in the preferred embodiment. Similarly, the input values occurring after "Sample Gate" is deasserted are also zero padded in the preferred embodiment.

Figure 4 shows, on another axis at the top of the figure, an example of a representative sampled received NMR signal envelope. The time scale for the depicted envelope is not as finely divided as the sample timing represented by individual samples x and p and is therefore not to scale, but nevertheless roughly illustrates an example of a received sampled NMR signal envelope output by the analog-to-digital converter 186 and demodulated by quadrature detector 200 with respect to the "Receiver Gate" and "Sample Gate" signals.

Since the digital receiver "front end" is off prior to "Receiver Gate" coming on, the sampled outputs of analog-to-digital converter 186 comprise a small random noise signal -- and the preferred embodiment digital receiver assumes they are zero and performs zero padding during this time. Turning "Receiver Gate" on is typically followed initially by noise and other transients generated by the digital receiver front end 60 due to switching transients, amplifier stabilization, residual energy from transmitted pulses, the DC component of the NMR signal and any spurious signal that demodulates to DC (any ADC input signal at exactly the second IF frequency will appear as DC at the digital filter inputs), etc.Once these receiver transients die down, the sampled output amplitude reduces to a relatively low value for most MRI sequences and then gradually increases as spin rephasing (and other effects, e.g., previous transmit pulse timing) causes the excited protons to generate their NMR signal. These values are all captured as "p" samples used to prefill the digital filter in the preferred embodiment.

The preferred embodiment system does not open the "Sample Gate" window much before the protons generate the desired NMR signal of interest in order to maximize received signal-to-noise ratio and reduce the amount of input data that needs to be processed. As can be seen in the Figure 4 plot, there is typically a relatively smooth transition between the relatively low signal amplitude existing during much of the time between "Receiver Gate" and "Sample Gate," and the higher signal amplitude occurring during the "Sample Gate" time window when the protons are producing the majority of the NMR signal - meaning that the prefill samples "p" are effective in conditioning the filter for the higher signal amplitudes that will exist during the "Sample Gate" time window.

As shown in Figure 4, during the "Sample Gate" time window the amplitude of the NMR signal grows and then decays to a lower signal amplitude. The "Sample Gate" time window is controlled to end at a point in time that will ensure capture of most of the NMR signal of interest while eliminating noise and other extraneous signals occurring after the NMR signal of interest has decayed. The preferred embodiment assumes that all input values occurring after the "Sample Gate" time window are zero, and uses zero padding during this time.

Presenting a filter with zero data before "Sample Gate" induces a strong step input to the filter. During the time before "Sample Gate" when "Receiver Gate" is on we expect that the signal will have grown from a smaller level.

Presenting the filter with this signal exposes it only to the usually smaller signal step when "Receiver Gate" comes on. This reduces the transient response at the "Sample Gate" time. The step also occurs earlier in time with the secondary advantage of being able to use the signal to prefill the filter.

During filling of the first half of the FIR filter, the output of the filter will reach about 50% of the steady state response to the input. The DC part of the input that comes on with the "Receiver Gate" acts like a step input. Due to the symmetry of the FIR filter's impulse response, the step response will reach half of the final value when half the filter is filled with samples 0 to N/2 - 1 (N is the number of filter taps). A few more samples (the number depending on the filter design) brings the output to within 4% of the final value. This is shown graphically in Figure 6. The preferred embodiment uses two or three filter stages. Figure 6 shows the synchronization typical of all but the last digital filter stage in a multiple filter stage system.As can be seen in Figure 6, as data reaches and then passes beyond h[N/2], the output rises to approximately 110% of the steady state output amplitude and then drops to within 4% of the steady state--indicated by the portion of the Figure 6 plot labeled "Major Transient." ks the data input progresses through the remainder of the filter, the output converges to the steady state (see the section of the Figure 6 plot between N/2 and N labeled "Minor Transient"). Steady state is maintained as long as the data input keeps the filter full (i.e., each filter coefficient aligns with a data point for the convolution). The time/magnitude variation of the output transient varies with the filter, but is always present in the step response to some extent.Nevertheless, it can be seen from Figures 4 and 6 that if it is possible to perform any prefill of the FIR filter stages their output transients will be reduced accordingly.

The preferred embodiment technique of prefilling the filter with values sampled after "Receiver Gate" and prior to "Sample Gate" has the effect of placing the major transient as much as possible prior to the filter's first synchronized output (indicated as "Sync" in Figure 6) corresponding to the opening of the "Sample Gate" time window.

The transients in the output data set of a FIR filter have been checked in the case where the data set is much larger than the filter length ("ORDER").

The transient is quite large for the first ORDER/2 points, as has been previously observed. However, there is a very small transient effect from this point until the filter is completely full. To give a concrete example, assume an input comprising a single sine wave at f= F0/100 Hz in the x[1:2304] data set.

The convolution of x with hl for a 6875 Hz FIR filter results in a data set klt ]. The ORDER of hl is 320, so the first output point when hl is one more than half full includes x[ 160], which is near the end of the major transient in k1[]. Examining kl every 25 output points after 161 allows observation of the peaks and zero crossings of the sine wave in kl[ ]. The peaks occur every 50 points starting at 186 = 161 + 25::

index k1[ ] at Sine Wave Comment Peaks 161 0.151229 filter half full 186 0.991476 -0.61% (value should be 1.000000) 236 -1.00185 +0.43% (value should be -1.000000) 261 0.030189 286 0.999801 321 -0.611713 filter full 0.22% (Steady State Output from here on) 336 -0.997559 361 0.0313496 386 0.997559 421 -0.611713 436 -0.997559 461 0.0313496 486 0.997559 2286 0.997559 2304 filter not completely full, more than half full.

2336 -0.999856 +0.23% 2386 1.00164 +0.41% 2436 -0.990813 2464 filter less than half full (0.68%) 2486 0.0043484 The error due to transients is thus less than 1% at the peaks of the sine wave. Near zero the errors are less than 4% during the time the filter is between half full and full. This applies to data sets which are more nearly the size of the filter as well. In data sets smaller than the filter, zero padding is always present and the filter transient is thus always present.

In order to completely fill the first filter, "Receiver Gate" must come on a certain amount of time before "Sample Gate." For example, if ORDER of h1=384, "Receiver Gate" must come on 768 lls before "Sample Gate" is asserted. Otherwise, there will be some zero filling since x[i] = 0 t i < 0.

Similarly, if y[sync + N/2] is the first output used as the synchronized output, then there will have to be 384 ps of data before x[sync] and after x[sync + (512 * Ml)], or zero filling of the filter will result.

Since "Receiver Gate" is also available to the preferred embodiment digital receiver 150, it is this signal that-in this examples used to begin filter prefilling since this makes it possible to make use of all valid data without MR1 sequence changes. Although the preferred embodiment triggers filter prefilling on the occurrence of "Receiver Gate," it may be desirable to use some other event to cause the FIR filters to begin to fill. For example, it would be possible to turn on "Sample Gate" sooner.The DSP program can be parameterized to accept an offset between x0 and the beginning of "Sample Gate." If "Sample Gate" is turned on at the same time as "Receiver Gate," and the time and data differential is known by the filter program, then the maximum amount of x[n], n < 0 can be used to fill the FIR low pass filter stages. In one exemplary arrangement, the DSP demodulator 200 can read a register with one bit for "Sample Gate" and one bit for "Receiver Gate," with the corresponding data buffer being properly flagged for each event.

fl. Transient Placement As described above, the preferred embodiment digital receiver typically has first and second (last) cascaded digital filters. The second (last) FIR filter stage must also be prefilled with points prior to "Sample Gate" to avoid potential ringing if x[0] + 0. However, all x[n], n < 0 are not valid data, since the receiver in an MRI system is gated on at a specific point in time. The small random noise signal existing prior to "Receiver Gate" can be considered to be zero for the input to the second digital filter, eliminating the need to compute outputs y[n], n < < 0 0 which are only dependent on data before the Receiver Gate.

Most transients due to filling the first half of the second (last) filter stage can be avoided by computing the first output point zd[0] with the data point having index "syncl" aligned with coefficient h[ORDER/2] of the second (last) FIR filter stage. This placement of the data point with index "syncl" prefills the filter with at least ORDER/2 + 1 data points. Figure 7 shows the synchronization typical of the last filter stage. For the two stage filter of the preferred embodiment, Figures 6 and 7 correspond respectively to the first and second filters shown in Figure 3.

As an example, assume the second FIR filter is ORDER=124 with decimation M2 = 2, with a data set yd[ ] length of 512 plus some points, (e.g., 32 = syncl) based on first filter outputs yd[ ] responsive to data points p[ ] collected before the "Sample Gate." Assume that the number of outputs of the second filter is 256. There are then (124/2 - syncl)/2 = (62 - syncl)/2 = 15 points output with the < 4% transient resulting from the filter going from more than half full to full. There are another (512 + syncl - 124)/2 = (388 + syncl)/2 = 210 output points while the filter is full (i.e., in steady state). Then there are a remaining set of points while the filter is going from full to half full which lasts 256-15-210 = 31 output points.Depending on the value of synci, there are possibly some points output after the filter is half empty -- but it is desirable for most of these points to be discarded (i.e., not calculated). In any case, the major transient effect is here limited to the end of the output data set, as desired. Due to the refocusing followed by apparent "decay" of the MRI signal amplitude due to the read-out gradient and actual decay due to T2, it is particularly desirable to minimize transients resulting from digital low pass filtering near the beginning of the time window -- since those transients may introduce noise or spectral artifacts into the most important parts of the acquired filtered data set used to generate an image - and to move unavoidable transients to near the end of the "sample gate" window where the MRI signal has decayed in amplitude.

In accordance with this technique provided by the present invention, the second (or last) stage of the multi-rate FIR filter is optimally designed so that the major transients occurring when data first enters the filter and when the last of the data is leaving the filter are discarded, which is possible since the number of filter outputs is larger than the number required for MR imaging.

m. Fourier Transform Like Transient Response The amplitudes of the transients at the beginning and end of the sample window with the FIR filters described so far are proportional to the steps from zero to data at the beginning and from data back to zero at the end. A Fourier transform has equal amplitude transients at the beginning and end of the transformed data. The amplitude of these transients is proportional to the difference in data levels at the beginning and end of the transformed data.

Thus data where the NMR signal and noise are the same at the beginning and end would have no transient with a FT versus a transient at each end with an FIR filter. Alternatively, if the NMR signal and noise are opposite at the beginning and end, the FT has transients proportional to twice the beginning (or ending) level while the FIR filter transients are still proportional to each level.

A spin echo's NMR signal contains a mixture of signals that are the same at both ends and opposite at both ends. The mixture depends on the phase of the signal relative to the demodulators and the symmetry of the object. A "properly" phased symmetric object will have a signal that is real (zero imaginary component) and (neglecting T2 decay) symmetric about its center. It approaches equal amplitude at both ends depending on the timing of the sample window. An anti-symmetric object (not naturally occurring since half of it must produce negative signal) will have a signal that is imaginary (zero real component) and anti-symmetric about its center. It approaches opposite amplitudes at both ends. Actual objects are combinations of both, the anti-symmetric part subtracting or adding to the symmetric part to represent an asymmetric object.To the extent that objects are symmetric, the imaginary part is small and the real part approaches equality at both ends. The random noise part of the data is unpredictable and the DC offset is constant. With these signal properties, the transient response of a Fourier Transform ("FT") has potential advantages.

To provide a FT like response, the input data set can be formed by "wrapping around" the ends of the sample window when it is presented to the FIR filter. This may result, for example, in an input data set such as, for example: x3 x2 xl x8 x7 x6 xS x4 x3 x2 xl x8 x7 x6 as is shown in Figure 5B. This structures the data like a Fourier series where the same data is repeated periodically forever.

FT filtering based on a "wrapped around" input data set can implement a "brick wall" filter that is non-causal and has in principle an infinite roll-off.

Very steep slopes on the passband provide sharp filtering. However, they can also cause problems in certain MRI applications because: (a) discontinuities cause transients; and (b) the transients spread over a significant part of the sample window. In addition, FT filtering can be computationally intensive, and it is best to have the entire data set before filtering begins. For these reasons, such FT type filters may not be preferred for some MRI applications.

On the other hand, there may be some MRI applications in which FT type filtering can be used to advantage. For example, the signal growth and decay during "Sample Gate" as described above is normal for a spin echo or "gradient echo," but a free induction decay (FID) as commonly elicited in chemical spectroscopy appears within microseconds following a "hard" RF excitation pulse. Such a signal provides no opportunity for prefilling a FIR filter. An FID is amenable to "wrapping" the end of the FID around to the beginning as a way to have a FT type transient response. If one has a spin echo signal and wants to process the later half of the echo like a FID, one could activate "Sample Gate" at the middle of the echo. In this scheme, some of the first half of the spin echo can be received with the "Receiver Gate" on.

Prefilling the filter with this data can eliminate any transient at the center of the echo. The other half of the echo then provides an FID like signal but without a transient at the beginning. Prefilling may also be effective with an FT like response if the end of the sample window is wrapped around to the beginning of the prefill data.

Figure 5B shows that at the beginning and end of the data the filter coefficients hl - h4 are convolved with the same inputs. This results in the following equalities in this example: yl = y9, y2 = y10, y3 = yll.

There are eleven outputs based on the eight inputs. An FT would have only eight inputs and outputs. With the three identical values there are only eight unique outputs. Figure 5B thus shows that when data is wrapped around, the number of repeated data points needed to produce a set of unique convolution outputs is one less than the number of filter taps. It follows that when the number of filter taps is less than or equal to the number of data points, the data is repeated less than one time. When the number of taps is one more than the number of data points, exactly one repetition is needed. Using larger numbers of taps requires more repeated data.

Since yl = y9, y2 = y10, y3 = yll in the Figure 5B example, there are several different possibilities for producing a set of unique convolution outputs, such as: yl to y8 y2 to y9 y3 to ylO y4 to y11 yl-y2, y4-y8 & yll yl, y4 to y8, yl0 & yl 1 etc.

Figures 5C and 5D show two of these different possibilities.

Figure 5C shows a calculation of yl to y8 with x8, x7 and x6 prepended to the data. y9-yl 1 are not calculated. The calculation of yl to y3 requires values from the end of the sample window. Completion of any of these calculations must wait for the arrival of the associated values x6 to x8.

As the filter progresses, outputs y4 to y8 are completely calculated using xl to x8 inputs as they arrive. Calculation of yl to y3 awaits the arrival of X8. In this case partial results for yl to y3 are saved as each new input value x arrives. The (number of taps - 1) items stored are all partial results, and there is no need to retain x input data that has already contributed to the appropriate partial sums. The final results can be rapidly calculated as soon as x8 is available by adding the additional products to which x8 contributes into the previously calculated partial sums.

Figure 5D shows the calculation of y4 to yl 1 (y9 to yll being used instead of yl to y3) with xl, x2 and x3 appended to the data. Calculation of y9 to yl 1 requires the xl to x3 values from the beginning of the sample window. Retention of xl to x3 until x6 and beyond become available is sufficient for completing the calculations. Here the first (number of taps - 1) data points are saved (repeated) until the end of the data set. The calculations proceed through the data acquisition and the last points calculated (y9 to yell) are placed at the beginning of the output data set. No calculations are done during the time when the first (number of taps - 1) data points are acquired.

All this calculation is put off to the end of the data acquisition. Thus, as the filter progresses, outputs y4 to y8 are completely calculated using xl to x8 inputs as they arrive. Then outputs y9 to yl 1 are calculated using some of the saved xl to x3 values.

The processes described with Figures 5C and 5D are opposite extremes.

The Figure 5C process calculates all possible partial results as the data arrives and stores the partial results (without having to retain any input data) for completion once the last data point arrives. This minimizes the time spent finishing the core convolutions at the end. However, the processing code must know or decide how much additional processing is done to complete each partial result since they need progressively less data. For example, yl requires convolution of X6, X7 and x8 to finish while y3 only needs X8.

The Figure 5D process, on the other hand, just stores the earliest data for use after the final data arrives. y4 to y8 are calculated as data arrives and y9 to yl 1 are done after the last data point arrives. With judicious choices of memory locations for the data xl to x3 and y9 to yl 1, the convolution code can have the same structure for y4 to y8 and y9 to yell. With a simple memory allocation of the data, the core convolution code could be the same but some memory accesses would be different for y9 to yl 1.

The choice between the Figure 5C process and the Figure 5D process may depend on the speed of the convolution calculation versus code or memory mapping overheads needed to do each of the later convolutions differently. Where the convolution calculation takes the most time, the Figure 5C process is probably best, since it does as much of the real work as possible when the data is input. It will be done processing sooner after the last data point than would a Figure 5D process.

It is also possible to select an intermediate option between these two options. For example, prepending x8 to the data set and appending xl and x2 permits calculation of y3-y10. This process requires storing two data points (xl and x2 for the y9 and y10 calculations) and a keeping a partial sum for y3 until x8 arrives and the calculation completed.

IV. Digital Filter Transition Bands In accordance with another technique provided by the present invention, the transition band of the multi-rate FIR low pass filter, especially the second filter stage in the preferred embodiment, is optimized to reduce transients while at the same time providing a very sharp filter roll off so as to allow the maximum usable MR image field of view.

The width of the low pass filter transition zone between fp ("pass frequency") and s ("stop frequency") helps to determine the duration of the transient created by the FIR filter. A wider transition zone yields a faster decaying transient and smaller filter order, which is desirable, but also reduces the "sharpness" of the low pass filter. The reduced sharpness results in a smaller useful image field of view since fp must be lower.

A strategy for achieving shorter transient response with a multi-rate FIR filter and still having a passband (signal > -3db) corner frequency f-3db as large a percentage of F2/4 as possible is to allow the stop frequency to be greater than F1/4 for the second (last) filter stage. Here F1 is the sampling frequency at the output of the first filter/decimator stage and F2 is the sampling frequency at the output of the second stage, where F2 = F1/2.After decimation by second stage factor M2 = 2, the somewhat attenuated noise between F1/4 and fs will be aliased back into the frequencies below F2/2 (F1/4). However, if the -3dB point of the second filter stage is further from F1/4 than is s (i.e., F1/4 f-3db > - F1/4) then the aliased noise will add to the unusable MRI signal which has been attenuated by more than 3dB.In other words, the second filter is made to be less "sharp" or selective in order to reduce its transient response -- but there is no loss of MR image data because the effect of reducing filter sharpness in this case is simply to alias noise into portions of the frequency spectrum that already are significantly attenuated by the overall low pass filter roll-off and therefore are unusable. To do this correctly, the new fs > F1/4 is used to compute the stop frequency of the first filter, which slightly reduces the width of the transition zone in the first filter.

In designing the second filter h2, we see that both fp and f-3db are important. We design the second filter so that F1/4 - f-3db > f; -Fl/4. It is possible to experiment with sizes of transition zones and filter length to reduce the transient response duration. This has been done, and the following example design is one possibility that can be arrived at by increasing the transition band s - fp from 0.0025 F1 with s = F1/4 to 0.0250 F1. This filter is at -lOdb at F1/4 = F2/2.The percentage of the band below F2/2 with response below -3.2db is 3.9% (271 Hz if Fr = 1/72psec). The band above F,/2 is fs - F/2 (217 Hz, if F. = 1/7'psec) which is smaller than F1/4 'f-3db and at -50db response just above fs will not allow noise to alias below the -3db point of the filter.

Here is one example of suitable relevant filter parameters: f = 0.2325 F1 = 0.01291667Fo f's = 0.2575 F1 = 0.0143055Fo f-3db = 0.2402 F1 (= 6673 Hz if Fl = 1/36Rsec) f-sodb = 0.2578 F1 (= 7161 Hz if Fl = 1/36psec) Fl = 0.0555556 F0 F1 - f5 = 0.041250 F0 where Fo is the ADC sampling frequency, in this case 1/2zsec F1 is the output frequency of the first filter stage hl and first decimator F2 is the output frequency of the second filter stage h2 and second decimator f is the pass frequency of the FIR multi-rate low pass filter is the stop frequency of the FIR multi-rate low pass filter An exemplary plot of this example filter passband is shown in Figure 8.

V. Digital Filter Order In accordance with another aspect provided by the present invention, the "order" (number of coefficients or length) of the FIR low pass filter stages is made as short as is consistent with reasonable performance, since the duration of the transient due to a digital filter increases with the order of the FIR filter. The transient duration is related to the order of the FIR filter, since large transients are output by the convolution for the first ORDER/2 + b points, b a small positive integer. Minor transients of the signal amplitude continue until the FIR filter stage is full of data.

The Order of the second (last) FIR filter is important to the transient effects the second filter exhibits. For example, if the "syncl" point is located at sample 32, then the following transient condition exists: Outputs FIR Filter Order = 384 Transient from syncl = 32 0-79 half full to full 1 - 2% 80-159 full 0% 160-255 full to half frill 1 - 2% Here there is no significant output transient due to the filling/emptying of the FIR filter.If the value of syncl was only 8, then we have Outputs FIR Filter Order = 384 Transient from syncl = 8 0-91 half full to full I - 2% 92-159 full 0% 160-255 full to half full 1 - 2% If the FIR filter is shorter but otherwise identical in design, then the number of output points affected by the transient due to filling/emptying is less (but the roll off provided by the filter stage will not be as steep): Outputs FIR Filter Order = 120 Transient from synci = 32 0-13 half full to full 1 - 2% 14-225 full 0% 226-255 full to half full 1 - 2% Looking at this another way, with the preferred embodiment two stage filter, the minimum number of input data points sampled is the number of output points times the decimation ratios of each stage. For example, if the decimation factors are 18 and 2, then a 72,usec output period results from a 2 sec input period. For 256 output points the number of input points is 256 * 2 * 18 = 9216 and the sample window is 2 llsec * 9216 = 18.432 msec.

If the number of taps in the first and second stages are 320 and 120 respectively, then the number of taps span the data 9216/320 = 28.8 times for the first stage and (9216/18)/120 = 512/120 = 4.267 times for the second stage.

The response delay is usually about half the number of taps. This means that the response delay of the second stage is 1/(2*4.267) or about one eighth of the data set or 32 points. The transient response lasts beyond this time. In accordance with this approach provided by one aspect of the present invention, the order of the second (last) filter is as small as possible to reduce transient duration.

Digital Filter Performance To understand the capabilities of the digital filters, we describe below the performance of two analog filters used in prior MRI products sold by Toshiba America Medical Imaging (TAMI). We then describe and compare the performance of the preferred embodiment digital filters.

The two analog anti-aliasing filters are an 8 pole Butterworth filter (used in TAMl's MRT-35A and ACCESS products), and a 6 pole 6 zero elliptic filter (used in TAMI's MTS product). Performance characteristics of the Butterworth filter are shown graphically in Figures 9(A)-9(F).

Corresponding performance characteristics of the elliptic filter are shown graphically in Figures 10(A)-10(F). Equations of the filters' frequency responses were used to provide their spectra. An inverse Fourier transform and integration provides their response to a step at time zero. The step response of each filter was also measured by applying a step input to the filter and ADC system. Step response is a standard way of characterizing a system's transient response. Here it is particularly useful in modeling the transient from no-signal to signal when the receiver is turned on by Receiver Gate.

Figures 9(A) & 10(A) show the magnitude of the frequency response of the Butterworth and elliptic filters, respectively, in dB from 0 to -100. Figures 9(B) & 10(B) plot the magnitude of the frequency response of the Butterworth and elliptic filters, respectively, in dB from 0 to -20. Figures 9(C) & 10(C) show the magnitude of the frequency response of the Butterworth and elliptic filters, respectively, on a linear scale from 1 to 0. Figures 9(D) & 10(D) show the phase response of the Butterworth and elliptic filters, respectively, in radians from 0 to -12 (about 4 pi). Figures 9(E) and 10(E) plot calculated step responses of the Butterworth and elliptic filters, respectively. Figures 9(F) and 10(F) graph points measured on the step response of the Butterworth and elliptic filters, respectively.

The calculated analog filters' responses are normalized in frequency and time.

All filters have scale factors that match the performance to a 7 kHz filter corner frequency.

As can be seen from Figures 9(A)-9(C), the 8 pole Butterworth filter has a slow frequency roll off. Figure 9(D) shows that the phase response of the Butterworth filter is fairly linear. It starts deviating near the corner frequency (noted as "1" on the x axis of Figure 9(D)). Since the Butterworth filter has such a slow roll off, one would expect its step response to be quite fast. As Figures 9(E) and 9(F) show, the filter rings only a few times before settling.

Note that the measured step response illustrated in Figure 9(F) is a little smoother than the calculated response shown in Figure 9(E). This is because the calculated waveform is more finely sampled. This is true for all the filters.

Figures 10(A)-10(C) show that the 6 pole 6 zero elliptic filter has a much faster frequency roll off and also has the expected ripples in the pass and stop bands. As can be seen from Figure 10(D), the elliptic filter's phase response is linear only to a moderate frequency, is quite deviated near the corner frequency, and has jumps at the frequencies of the zeros. Since the elliptic filter has a faster roll off, its step response rings more times before settling (as can be seen in Figures 10(E) and 10(F)).

The digital system has several expected advantages over the analog system: it eliminates DC offset and drift, the I and Q channels have perfect gain and phase matching, ADC noise is spread over a wide bandwidth compared to the signal bandwidth, and oversampling improves the ADC's quantization. As improved analog-to-digital converters become available, it will also be possible to increase the dynamic range of the data beyond 16 bits.

The spectra shown in Figures 11(A)-I 1(C), 12(A)-12(C) also demonstrate an additional advantage: very little passband ripple coupled with a sharp roll off.

Figures 1 1(A)-l 1(D) show performance characteristics for an example first stage preferred digital filter acting as a 14 kHz lowpass filter that eliminates frequencies between 14 kHz and 250 kHz. This preferred first-stage filter has 320 taps in the preferred implementation. Figures 12(A)-12(D) show performance characteristics for an example second stage preferred digital filter acting as a 7 kHz lowpass filter that eliminates frequencies between 7 kHz and 14 kHz. This second stage filter has 124 taps in the preferred embodiment.

Figures 13(A) & 13(B) show the measured time zero step response for the cascaded first and second filter stages at the beginning and end of the step, respectively, and Figure 13(C) shows measured response for the cascaded first and second filter stages to a step at the center of an MRI "Sample Gate" window. Comparing the step at the middle (Figure 13C) with the one at the beginning (Figure 13A) shows the transient reduction achieved by starting data output from the center of the last filter. Part of this reduction increases the transient at the end of the sample window (Figure 13B).

Figures 11(A)-lI (C) show the moderate frequency roll off of the first digital filter (it passes only a small part of its wide bandwidth). It has ripples in the stop band but always stays below the design attenuation. Since the phase response of the first digital filter is linear over the full range, it is not shown. Since it has a moderate roll off its step response is quick and it has little ringing. See Figure 11(D), which shows both normal and expanded step response graphs. Since the first filter is essentially a convolution with an impulse response, there is a delay of the step. During this delay there is ringing before the step occurs. Depending on how we prime the convolution with points before the "Sample Gate" or wrap around points from the end of the sample window, we can make this ringing occur at either the beginning or the end of the window.

The step response of the first filter has far less effect on the digital receivers overall performance than the second stage filter's step response. To achieve the narrow bandwidth of the first filter, relative to the Nyquist frequency, it has a large number of taps (e.g., 320). As shown in Figures 12(A)-12(C), the second digital filter passes only half its 14kHz input range.

Figure 12(A)-12(C) compress this range onto the left half of the figures to be comparable with the Figures showing the first digital filters performance.

Figures 12(A)-12(C) show that the second filter has a steep frequency roll off, along with passing half of its bandwidth. Achieving the steep roll off of this filter requires a moderate number of taps (e.g., 124), since the filter passes a large fraction of its Nyquist frequency. Ripples in the stop band can be seen in Figure 12(A). Since the second digital filter's phase response is linear over the full range, it is not shown. Since the second filter has a steep roll off, its step response rings for a time comparable to the elliptic filter (see Figure 12(D)). The step up portion of the transition and the ringing are fast since the passband is a large portion of the total bandwidth. Like the first stage filter, there is a delay of the step.During this delay there is ringing before the step occurs (prefilling the convolution with points before the sample gate modifies this ringing at the beginning of the window). This second stage step response dominates the response for the two stages.

Figures 13(A)-13(B) plot measured step responses of the cascaded digital filters at the beginning and end of the sample window. This response is different than the analog filters' response or the calculated response of the digital filters because of the way we prefill the filters. Our filter prefilling uses 860 points (1.72 msec duration) acquired after "Receiver Gate" and before the sample window begins to fill the first filter. They are filtered and decimated to 47 points. These and an effective 15 points containing zero are aligned with the second 62 taps of the second digital filter. The second filter begins processing with these and all subsequent decimated points. The result is that the response to a step at the beginning of the sample window is: ringing, a step up, and very slight ringing (see Figure 13(A)).This prefilling makes the ringing after the transition smaller than any of the analog filters (compare with Figures 9(F) and 10(F)).

The behavior at the end of the sample window is also different. Since we don't know what the data is after the sample window, the convolution anticipates that the data is zero. An analog filter basically treats the data as if it stays constant at the value of the last sample. The digital filter thus begins ringing before the end of the sample window in anticipation of a transition to zero (see Figure 13(B)). This behavior can be changed to be like that of the analog filter.

Figure 13(C) shows the digital filters' response to a step that occurs in the middle of the sample window. The step is applied at 9.2 msec into the 18.432 msec sample window. Figure 13(C) shows a transient response like that calculated for the digital filter because the prefilling at the beginning of the sample window is long forgotten. The ringing at the end of the sample window is the same as in the previous measurement, and is therefore not shown. The step up portion of the transition of the digital filter is similar to the elliptical filter and the ringing after the transition is smaller. This is impressive considering the sharp roll off of the digital filter.

A number of step response parameters were derived from the calculated step responses of the various filters. These are: the time to rise from zero to the first crossing of the final step value (in all cases this is 1), the time of the first peak, the value of the peak, the time of the second crossing of 1, the time to settle within 10% of 1, the time to settle within 1% of 1 and the time to settle within 0.1% of 1. These are tabulated below for the Butterworth, elliptic and second stage digital filters. The zero time of the digital filter is somewhat arbitrary since it rings before the step.

Butterworth Filter

Time from Value Time t first unity crossing First unity crossing 690 psec O Rsec Peak Peak 792 102 1.163 Second Second unity crossing 992 302 Settles within 10% 936 246 Settles within 1% 2016 1326 Settles within .1% 3024 2334 Elliptic Filter

Time Time from Value first unity crossing First unity crossing 634 ,usec O Rsec Peak 792 158 1.193 Second unity crossing 962 328 Settles within 10% 936 302 Settles within 1% 3240 2606 Settles within 1% 5616 4982 Digital Filter

Time Time from Value first unity crossing First unity crossing 962 ,usec O Rsec Peak 1008 46 1.100 Second unity crossing 1098 136 Settles within 10% 1008 46 Settles within 1% 2016 1054 Settles within 1% 5112 4150 Comparing the times from the first unity crossing takes out the uncertainty in the zero time of the digital filter. On this basis the settling times of the digital filter are better than the elliptic filter. Surprisingly the 10% and 1% settling times of the digital filter are faster than the Butterworth. This is partly due to its smaller peak overshoot.

Effect on Imagine The imaging implications of the digital filter's frequency performance are firstly an improved field of view (FOV). The edge of the FOV is usually at or slightly above the corner frequency of the filter. For the analog filters, preventing aliasing requires placing the corner frequency inside the FOV. The edges of the FOV thus fade with the frequency response. The much steeper edge of the digital filter allows its corner frequency to be higher with the same elimination of aliasing. Analog filters also allow some aliasing of noise into the edge of the image.

The present filter produces images on the MRT-35A reflecting the sharper roll off with no noticeable effect from the phase or transient responses.

The imaging implications of the analog filters' frequency performance also relate to the field of view. The sharper roll off of the 6 pole 6 zero elliptic filter near the corner frequency was quite effective in eliminating aliasing. It thus has less wrap around and slower step response. If the system samples a large field of view and discards half of it after reconstruction, aliasing is eliminated and the filter response is not very important. Since the filter is set at twice the images' FOV its step response is twice as fast. This operating mode acquires and processes twice the data actually needed for the final image. An 8 pole Butterworth can be substituted since one would expect that the two extra poles would provide enough sharpness and that the improved transient response would be a help. The filter is not as effective in eliminating aliasing.

Experimental Results A 3DFT head image produced using a digital receiver provided by the preferred embodiment is shown in Figure 14(A) and a similar head image produced using a prior art analog receiver is shown in Figure 14(B). Figures 15(A) and 15(B) show body images, with Figure 15(A) being produced based upon the output of the preferred embodiment digital receiver and Figure 15(B) being produced by a prior art analog receiver. Comparing Figures 14(A) and 14(B), and comparing Figures 15(A) and 15(B), shows that the digital receiver provides noticeable increase in field of view and noticeable decrease in noise due to aliasing.

The digital receiver's low pass filter cutoff (-3 dB) frequency is 6673 Hz and the response drops to -50 dB above 7300 Hz. Inband ripple is less than 0.4 dB. The response ripples in the stop band, but never rises above -50 dB.

The analog Butterworth low pass filter had a cutoff (-3 dB) frequency of 7000 Hz and the response drops to -48dB above 14000 Hz.

The 3D head imaging shown in Figure 14A with 16-bit data is not quantization noise limited so we do not see a S/N improvement. The S/N for the analog receiver is 54.0 and for the digital receiver is 52.2. See Figures 14(A) and 14(B). A 3D image of an oil filled phantom has a S/N of 130 for the analog receiver and 145 for the digital receiver. Verification of this quantization advantage will require a wider data path to the host computer.

The DC level for the analog receiver is 3.8 bits (580 ,uv). The apparent DC (due to any 125 kHz carrier leakage to the input of the ADC) for the DR is only 0.055 bits (8.4 lav).

With body imaging we have a noticeable improvement in alias rejection along the read out direction (Figures 15(A) and 15(B)). This verifies the superior performance of the digital filter. We have not identified any change due to the linear phase response.

While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (101)

WHAT IS CLAIMED IS:

1. A method for reducing effects of NMR signal transients on the output of a magnetic resonance imaging digital receiver including a digital filter, said method comprising: (a) sampling a signal envelope including an NMR signal of interest and other, non-zero signals occurring before said NMR signal of interest occurs; (b) prefilling said digital filter with samples produced by said sampling step (a) representing said other signals occurring before said NMR signal of interest occurs; and (c) digitally filtering, with said prefilled digital filter, samples produced by said sampling step (a) representing said NMR signal of interest.

2. A method as in claim 1 wherein said digital filter comprises a FIR lowpass filter that performs a sum of products calculation.

3. A method as in claim 1 wherein said digital filter comprises a multi-rate digital filter arrangement having plural digital filter stages.

4. A method as in claim 1 wherein said digital filter comprises a multi-rate digital filter arrangement having more than two digital filter stages.

5. A method as in claim 1 wherein: said method includes (i) turning on said digital receiver, and (ii) subsequently activating an output of said digital receiver; said sampling step (a) is performed beginning when said digital receiver is turned on and includes acquiring plural samples between the time said digital receiver is turned on and the time said digital receiver is activated; and said prefilling step comprises prefilling said digital filter with said plural samples.

6. A method as in claim 1 further including increasing image field of view by: optimizing the passband of at least one stage of said digital filter to reduce transients, and providing sharp roll-off of said digital filter.

7. A method as in claim 1 further including minimizing the length of at least one stage of said digital filter.

8. A method as in claim 1 further including: producing, with said digital filter, more outputs than required for MR imaging; and discarding ones of said digital filter outputs representing major transients.

9. A method as in claim 8 wherein said discarding step includes discarding filter outputs generated in response to an initial set of said samples entering said digital filter.

10. A method as in claim 8 wherein said discarding step includes discarding digital filter outputs generated in response to a last set of said samples entering said digital filter.

11. A method as in claim 1 wherein said method further includes: turning off said digital receiver after said digital filter filters said NMR signal of interest, and defining the characteristics of said digital filter so as to position unavoidable transients near a portion of said digital receiver output associated with when said digital receiver is turned off.

12. A method as in claim 1 wherein said prefilling step (b) comprises prefilling said digital filter with a number of samples.

13. A method as in claim 1 wherein said prefilling step (b) ensures that the magnitude of a transient caused by initially applying samples to said digital filter has fallen to a low level by the time said step (c) is performed.

14. A method as in claim 1 further including selectively enabling said digital receiver output, and performing said sampling step (a) continually at times other than when said digital receiver output is enabled.

15. A method as in claim 1 wherein said digital filter comprises at least first and last cascaded digital filter stages, and said prefilling step (b) comprises prefilling at least about half of said first digital filter stage.

16. A method as in claim 1 wherein: said digital filter comprises at least first and second cascaded digital filter stages, said prefilling step (b) includes prefilling both said first and second digital filter stages; and said method further includes discarding at least some outputs from said second digital filter stage resulting from said prefilling.

17. A method as in claim 1 wherein: said digital filter comprises at least first and last cascaded digital filter stages, and said prefilling step (b) includes prefilling said first digital filter stage.

18. A method as in claim 1 wherein said discarding step comprises not calculating said at least some digital filter outputs.

19. A method as in claim 1 wherein: said digital filter comprises at least first and last cascaded digital filter stages; and said method further includes setting the length of said last digital filter stage to cause noise components to be aliased into portions of the digital filter frequency spectrum output that already are significantly attenuated by low pass filter rolloff characteristics of said digital filter.

20. A method for reducing effects of NMR signal transients on the output of a magnetic resonance imaging digital receiver including a digital filter, said method comprising: (a) sampling a signal envelope including an NMR signal of interest and other, non-zero signals occurring while NMR signal of interest is growing; (b) prefilling said digital filter with samples produced by said sampling step (a) representing said other signals occurring while said NMR signal of interest is growing; and (c) digitally filtering, with said prefilled digital filter, samples produced by said sampling step (a) representing said NMR signal of interest.

21. A method for reducing NMR signal transients in a magnetic resonance imaging digital receiver output, said digital receiver having at least one digital filter, said method comprising: (a) turning on said digital receiver without yet enabling a digital receiver output; (b) acquiring, with said turned-on digital receiver, plural samples of an input signal; (c) prefilling said digital filter with said plural samples; (d) subsequent to said step (c), enabling said digital receiver output; and (d) sampling and digitally filtering said input signal with said prefilled digital filter, wherein said plural samples used to prefill said digital filter reduce NMR signal transients in said enabled digital receiver output.

22. A magnetic resonance imaging digital receiver system including: means for sampling a signal envelope including an NMR signal and non-zero noise signals occurring before said NMR signal occurs; a digital filter including means for digitally filtering samples produced by said sampling means; and means for prefilling said digital filter with samples produced by said sampling means representing said noise signals occurring before said NMR signal occurs.

23. A system as in claim 22 wherein said digital filter comprises a FIR lowpass filter that performs a sum of products calculation.

24. A system as in claim 22 wherein said digital filter comprises a multi-rate digital filter arrangement having plural digital filter stages.

25. A system as in claim 22 wherein: said system includes means turning on said digital receiver system, and means for subsequently activating an output of said digital receiver system; said sampling means samples beginning when said digital receiver system is turned on and includes means for producing plural samples "p" between the time said digital receiver system is turned on and the time said digital receiver filter is activated; and said prefilling means comprises means for prefilling said digital filter with said plural samples "p."

26. A system as in claim 22 further including means for increasing magnetic resonance image field of view by: optimizing the passband of said digital filter to reduce transients, and providing sharp filter roll-off.

27. A system as in claim 22 further including means for minimizing the length of said digital filter.

28. A system as in claim 22 further including: means for producing, with said digital filter, more outputs than required for MR imaging; and means for discarding digital filter outputs representing major transients.

29. A system as in claim 28 wherein said discarding means includes means for discarding filter outputs generated in response to an initial set of said samples entering said filter.

30. A system as in claim 28 wherein said discarding means includes means for discarding filter outputs generated in response to a last set of said samples entering said filter.

31. A system as in claim 22 wherein said system further includes: means for turning off said digital receiver after said digital filter filters said NMR signal, and means defining the characteristics of said digital filter so as to place unavoidable transients near the time said digital receiver is turned off.

32. A system as in claim 22 wherein said prefilling means comprises prefilling said digital filter with a number of samples within the range of 20 to 50.

33. A system as in claim 22 wherein said prefilling means comprises means for enabling said digital receiver system output only after the magnitude of a transient caused by said samples prefilled by said prefilling means has fallen to a low level.

34. A system as in claim 22 wherein said sampling means continually samples an input signal applied thereto.

35. A system as in claim 22 wherein said digital filter comprises first and last cascaded digital filter stages, and said prefilling means comprises means for prefilling at least about half of said first digital filter stage.

36. A system as in claim 22 wherein: said digital filter comprises first and second cascaded digital filter stages, said prefilling means includes means for prefilling both said first and second digital filter stages; and said system further includes means for discarding at least some outputs from said second digital filter stage resulting from said prefilling.

37. A system as in claim 22 wherein: said digital filter comprises first and last cascaded digital filter stages, said prefilling means includes means for prefilling one of said first and last digital filter stages; and said system further includes means for discarding at least some filter outputs resulting from said prefilling.

38. A system as in claim 37 wherein said prefilling means comprises means for prefilling only said first digital filter stage.

39. A system as in claim 37 wherein said discarding means comprises means for not calculating said at least some filter outputs.

40. A system as in claim 22 wherein: said digital filter comprises first and last cascaded digital filter stages; and said system further includes means for setting the length of said second digital filter stage to cause noise components to be aliased into portions of the digital filter frequency spectrum output that already are significantly attenuated by low pass filter rolloff characteristics of said digital filter.

41. A magnetic resonance imaging digital receiver system including: means for sampling a signal envelope including an NMR signal component and non-zero noise signals occurring while said NMR signal grows; a digital filter including means for digitally filtering samples produced by said sampling means; and means for prefilling said digital filter with samples produced by said sampling means representing said noise signals occurring while said NMR signal grows.

42. A system for reducing NMR signal transients in a magnetic resonance imaging digital receiver output, said system comprising: receiver gate means for turning on said digital receiver; sample gate means for subsequently activating a digital receiver output; sampling means, coupled to said receiver gate means and to said sample gate means, for sampling an input signal beginning when said digital receiver is turned on, including means for producing plural samples between the time said digital receiver is turned on and the time said digital receiver output is activated; and means, coupled to said sampling means, for minimizing transients in said digital receiver output by prefilling a digital filter means with said plural samples, said digital filter means for digitally filtering input signal samples produced by said sampling means subsequent to when said digital receiver output is activated.

43. A method for reducing NMR signal transients in a magnetic resonance imaging digital receiver output, said method comprising: (a) defining a limited-time digital receiver output window; (b) providing at least one digital filter having a delay time that is a significant fraction of the limited-time digital receiver output window; (c) sampling an input signal for a time period somewhat less than said digital filter delay time; (d) filtering said sampled input signal with said digital filter to produce a digital filter output; and (e) discarding at least a portion of said digital filter output occurring outside of said limited-time digital receiver output window.

44. A method as in claim 43 wherein said discarding step (e) comprises discarding a portion of said digital filter output occurring before said output window.

45. A method as in claim 44 wherein said discarding step (e) further comprises discarding a portion of said digital filter output occurring after said output window.

46. A method as in claim 43 wherein said discarding step (e) comprises discarding a portion of said digital filter output occurring after said output window.

47. A method as in claim 43 further including designing said digital filter to position unavoidable transients at the end of said output window.

48. A method as in claim 43 wherein said filtering step (d) comprises filtering said samples with a multirate FIR lowpass filter having at least first and last stages, and said method further includes increasing image field of view by designing said last filter stage to reduce transients while at the same time providing a very sharp filter roll off.

49. A method as in claim 43 wherein said filtering step (d) comprises filtering said samples with a multirate FIR lowpass filter having plural stages, and said method further includes minimizing transient duration by providing at least one of said plural stages with a length as short as is consistent with reasonable performance.

50. A method for reducing NMR signal transients in a magnetic resonance imaging digital receiver output, said method comprising: (a) defining a limited-time digital receiver output window; (b) sampling an input signal; (c) filtering said sampled input signal with a digital filter having digital filtering characteristics that position unavoidable transients due to input signal response at or near the end of said limited-time digital receiver output window; and (d) producing a digital receiver output corresponding to said limitedtime digital receiver output window and based on said filtered sampled input signal.

51. A method as in claim 50 wherein said digital filter has a delay time, and said sampling step comprises sampling said input signal for a time period a little less than said digital filter delay time.

52. A method of increasing field of view of a magnetic resonance image based on a digital receiver output, said method comprising: (a) providing a multirate FIR lowpass digital filter having at least first and last stages; (b) widening the transition band of said last filter stage to reduce its transient response while causing noise due to said widening to be aliased into portions of the digital filter frequency spectrum output that already are significantly attenuated by low pass filter rolloff characteristics of said digital filter; (c) filtering a sampled input signal with said digital filter; and (d) generating an image based on said filtered sampled input signal.

53. A method as in claim 52 wherein a frequency F1 corresponds to the sampling frequency at the output of said first filter stage, and said step (b) comprises allowing the stop frequency of said last frequency stage to be greater than Fl/4.

54. A method of increasing field of view of a magnetic resonance image based on a digital receiver output, said method comprising: (a) providing a multirate FIR lowpass digital filter having at least first and last stages; (b) optimizing the passband of said last filter stage to reduce its transient response; (c) filtering a sampled input signal with said digital filter; and (d) generating an image based on said filtered sampled input signal.

55. A method as in claim 54 wherein said optimizing step comprises widening said last filter stage passband to cause noise due to said widening to be aliased into portions of the digital filter frequency spectrum output that already are significantly attenuated by low pass filter rolloff characteristics of said digital filter.

56. A method of reducing transients in the output of a magnetic resonance imaging digital filter, comprising: (a) providing a multistage digital filter having at least first and last stages; (b) minimizing the order of at least one of said first and last stages; (c) filtering a sampled input signal with said digital filter; and (d) producing an image based on said sampled input signal.

57. In a MRI system, a method of digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples of said NMR signal; (b) forming an input data set including said series of digital samples and at least one at least partial repeat of said series of digital samples; (c) convolving said input data set with a set of filter coefficients; and (d) generating a filtered digital output responsive to said convolved input data set, said generated filtered digital output exhibiting a Fourier Transform like response.

58. A method as in claim 57 wherein said forming step (b) comprises forming said input data set consisting of said series of digital samples and a partial repeat of said series.

59. A method as in claim 57 wherein said forming step comprises repeating a number k of said digital samples, where k is one less than the number of filter coefficients in said filter coefficient set.

60. A method as in claim 57 wherein said generating step (d) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

61. A method as in claim 57 wherein said generating step (d) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

62. A method as in claim 57 wherein said forming step comprises prepending said partial repeat onto said series.

63. A method as in claim 57 wherein said forming step comprises appending said partial repeat onto said series.

64. A method as in claim 57 wherein said forming step comprises appending part of said partial repeat onto said series and prepending the rest of said partial repeat onto said series.

65. In a MRI system, a method of digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples of said NMR signal; (b) providing a input data set comprising said series repeated so that said input data set is structured like a Fourier series; and (c) generating a digital filter output based at least in part on said input data set.

66. A method as in claim 65 wherein said providing step (b) comprises providing an input data set comprising said series and less than one repetition of said series so that said input data set is structured like part of a Fourier series.

67. A method as in claim 65 wherein said providing step comprises repeating a number k of said digital samples, where k is one less than the number of filter coefficients in said filter coefficient set.

68. A method as in claim 65 wherein said generating step (d) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

69. A method as in claim 65 wherein said generating step (d) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

70. In an MRI system, a method of digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples of said NMR signal; (b) calculating a sum-of-products based on said sequence and at least one repeat thereof and a set of filter coefficients; and (c) generating a digital filter output based at least in part on said calculated sum-of-products.

71. A method as in claim 70 wherein said providing step comprises repeating a number k of said digital samples, where k is one less than the number of filter coefficients in said filter coefficient set.

72. A method as in claim 70 wherein said generating step (d) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

73. A method as in claim 70 wherein said generating step (d) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

74. In an MRI system, a method of digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples of said NMR signal; (b) calculating a sum-of-products based on said series and less than one repeat thereof and a set of filter coefficients; (c) generating a digital filter output based at least in part on said calculated sum-of-products.

75. A method as in claim 74 wherein said calculating step comprises performing sum-of-products calculations based on repeating a number k of said digital samples, where k is one less than the number of filter coefficients in said filter coefficient set.

76. A method as in claim 74 wherein said calculating step (b) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

77. A method as in claim 74 wherein said calculating step (b) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

78. In an MRI system, a method of non-causally digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples xl-xk; (b) forming an input data set comprising the series xl-xk concatenated with at least one repeat of said series xl-xk; (c) convolving said input data set with a set of filter coefficients; and (d) generating a filtered digital output based at least in part on said convolving step.

79. A method as in claim 78 wherein said forming step (b) concatenates said series with at most one repeat of said series.

80. A method as in claim 78 wherein said forming step comprises repeating a number of said digital samples, where the repeated number of samples is one less than the number of filter coefficients in said filter coefficient set.

81. A method as in claim 78 wherein said generating step (d) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

82. A method as in claim 78 wherein said generating step (d) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

83. In an MRI system, a method of non-causally digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples xl - xk; (b) fonning an input data set comprising the series xl - xk concatenated with a subset of said series xl - xk, xl - xm where 1 < m < (c) convolving said input data set with a set of filter coefficients; and (d) generating a filtered digital output based at least in part on said convolution step.

84. A method as in claim 83 wherein said convolving step (c) comprises convolving said input data set with a set of filter coefficients where the number of said filter coefficients is greater than k but less than k + m.

85. A method as in claim 83 wherein said forming step comprises repeating a number of said digital samples, where the repeated number of samples is one less than the number of filter coefficients in said filter coefficient set.

86. A method as in claim 83 wherein said generating step (d) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

87. A method as in claim 83 wherein said generating step (d) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

88. A method of non-causal digital filtering comprising: (a) acquiring a finite series comprising plural input samples; (b) storing said finite series in a memory; (c) repetitively accessing said stored finite series in such a way as to provide at least a part of a Fourier series comprising at least one at least partial repeat of said finite series; and (d) performing at least one digital filtering operation based on said repetitive accessing.

89. A method as in claim 88 wherein said performing step (d) comprises convolving said at least part of said Fourier series with filter coefficients.

90. A method as in claim 88 wherein said repetitively accessing step (c) comprises repetitively accessing said stored finite series in such a way as to provide part of a Fourier series comprising less than one repetition of said finite series.

91. A method as in claim 88 wherein said repetitively accessing step comprises accessing less than all of said digital samples more than once, where the number of samples k accessed more than once is one less than the number of filter coefficients in said filter coefficient set.

92. A method as in claim 88 wherein said performing step (d) comprises calculating all possible partial results as each new digital sample in said series arrives, and storing said partial results for completion once the last digital sample in said series is available.

93. A method as in claim 88 wherein said performing step (d) comprises retaining partial sum-of-product calculations based on each received digital sample without requiring retention of said digital sample.

94. In a MRI system, a method of digitally filtering an NMR signal comprising: (a) acquiring a series of digital samples of said NMR signal; (b) forming an input data set consisting of: said series of digital samples, a repeat of said series of digital samples, and a partial repeat of said series of digital samples; (c) convolving said input data set with a set of filter coefficients; and (d) generating a filtered digital output responsive to said convolved input data set, said generated filtered digital output exhibiting a Fourier Transform like response.

95. In a MRI system, a method of generating an MRI image of a body comprising: (a) applying a field to said body to generate spin-echo NMR phenomena within said body; (b) receiving NMR signals produced by said spin-echo NMR phenomena; (c) acquiring a series of digital samples of said NMR signals; (d) forming an input data set including said series of digital samples and at least one at least partial repeat of said series of digital samples; (e) convolving said input data set with a set of filter coefficients; (f) generating a filtered digital output responsive to said convolved input data set, said generated filtered digital output exhibiting a Fourier Transform like response; and (g) producing an image in response to said generated filtered digital output.

96. A method for reducing effects of NMR signal transients substantially as hereinbefore described.

97. A agnetic resonance imaging digital re receiver system substantially as hereinbefore described with reference to and as shown in the accampanying dravings.

98. A system for reducing NMR signal transients substantially as hereinbefore described with reference to and as shown in the acoompanying drawings.

99. A method of increasing field of view of a magnetic resonance image based on a digital receiver output substantially as hereinbefore described.

100. A method of digitally filtering NMR signal substantially as hereinbefore described.

101. A method of generating an MRI image of a body substantially as hereinbefore described.