METHOD AND DEVICE FOR DETECTING A NEURAL RESPONSE IN A NEURAL MEASUREMENT

Abstract

A method for processing a neural measurement obtained in the presence of artifact, in order to detect whether a neural response is present in the neural measurement. A neural measurement is obtained from one or more sense electrodes. The neural measurement is correlated against a filter template, the filter template comprising at least three half cycles of an alternating waveform, amplitude modulated by a window. From an output of the correlating, it is determined whether a neural response is present in the neural measurement.

Claims

1. A method for processing a neural measurement in order to determine a magnitude of a neural response in the neural measurement, the method comprising: applying a first electrical stimulus to neural tissue of a patient, the first electrical stimulus defined by at least one stimulus parameter; obtaining a neural measurement from one or more sense electrodes subsequent to the first electrical stimulus; determining, based on the neural measurement, a time delay of a window to be applied to a subsequent neural measurement; applying a window at the determined time delay to the subsequent neural measurement to produce a windowed neural measurement; and determining from the windowed neural measurement a magnitude of a neural response evoked by an electrical stimulus in the subsequent neural measurement.

2. The method of claim 1, wherein the determining the magnitude of the neural response comprises correlating the windowed neural measurement against a filter template.

3. The method of claim 2, wherein the filter template comprises at least three half cycles of an alternating waveform, amplitude modulated by a template window.

4. The method of claim 3 wherein the template window comprises a triangular window.

5. The method of claim 4 wherein the triangular window is a standard triangular window of length L comprising coefficients w(n) as follows: $\mathrm{For}L\mathrm{odd}:$ $\begin{array}{c}w\left(n\right)=2n/\left(L+1\right)\mathrm{for}1?n?\left(L+1\right)/2\\ =2-2n\left(L+1\right)\mathrm{for}\left(L+1\right)/2+1?n?L\end{array}$ $\mathrm{For}L\mathrm{even}:$ $\begin{array}{c}w\left(n\right)=\left(2n-1\right)/L\mathrm{for}1?n?L/2\\ =2-\left(2n-1\right)/L\mathrm{for}L/2+1?n?L\end{array}.$

6. The method of claim 4 wherein the triangular window is a Bartlett window of length L in which samples 1 and L are zero.

7. The method of claim 3 wherein the template window comprises one of a Hanning window, a rectangular window, and a Kaiser-Bessel window.

8. The method of claim 3 wherein the window comprises one or more basis functions derived from a sinusoidal binomial transform.

9. The method of claim 3 wherein the filter template comprises four half-cycles of an alternating waveform.

10. The method of claim 3 wherein the filter template comprises half cycles of a sine wave, amplitude modulated by the template window.

11. The method of claim 3 wherein the filter template comprises half cycles of a cosine wave, amplitude modulated by the template window.

12. The method of claim 2 wherein determining the magnitude comprises calculating only a single point of the correlation.

13. The method of claim 2, wherein determining the time delay comprises: applying the window at an approximate time delay to the neural measurement; computing real and imaginary parts of the fundamental frequency of the discrete Fourier Transform (DFT) of the windowed neural measurement; calculating a phase defined by the real and imaginary parts; calculating, based on a fundamental frequency of the filter template, the time adjustment needed to change the calculated phase to ?/2; and determining the time delay as the sum of the approximate time delay and the time adjustment.

14. The method of claim 1, wherein the time delay is re-determined prior to every processing of a neural measurement.

15. The method of claim 1, wherein the time delay is re-determined in response to a detected change in a posture of the patient.

16. The method of claim 1, further comprising using the magnitude of the neural response in a closed loop feedback circuit to determine the at least one stimulus parameter for a subsequent electrical stimulus.

17. An implantable device for processing a neural measurement in order to determine a magnitude of a neural response in the neural measurement, the device comprising: an electrical stimulus source configured to generate a first electrical stimulus to be applied to neural tissue, the first electrical stimulus defined by at least one stimulus parameter; measurement circuitry for obtaining a neural measurement from one or more sense electrodes subsequent to the first electrical stimulus; and a processor configured to: determine, based on the neural measurement, a time delay of a window to be applied to a subsequent neural measurement; apply a window at the determined time delay to the subsequent neural measurement to produce a windowed neural measurement; and determine from the windowed neural measurement a magnitude of a neural response evoked by an electrical stimulus in the subsequent neural measurement.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0060] An example of the invention will now be described with reference to the accompanying drawings, in which:

[0061] FIG. 1 illustrates an implantable device suitable for implementing the present invention;

[0062] FIG. 2 is a schematic of a feedback controller to effect stimulus control in response to recruitment;

[0063] FIG. 3a illustrates a neural response detector in accordance with one embodiment of the invention, and FIG. 3b illustrates a modified version of the embodiment of FIG. 3a;

[0064] FIG. 4 illustrates the amplitude profile of the filter template used in the detector of FIG. 3; and a cosine filter template, and the Bartlett window;

[0065] FIG. 5a illustrates the ability of the filter template to pass an evoked response, and FIG. 5b illustrates the ability of the filter template to block artefact;

[0066] FIG. 6 illustrates hardware to compute a complex term of the windowed DFT;

[0067] FIGS. 7a and 7b illustrate the effect of a clinical fitting procedure of the evoked response detector;

[0068] FIG. 8 illustrates the dependency of the phase of the DFT terms of an exponential on the time constant of the exponential;

[0069] FIGS. 9a and 9b illustrate, at respective times, the detector output vector components arising from artefact only, when modelled as two exponentials;

[0070] FIGS. 10a and 10b illustrate, at respective times, the detector output vector components arising from artefact modelled as two exponentials and from an evoked response;

[0071] FIGS. 11a and 11b illustrate a four point measurement technique for measuring a CAP;

[0072] FIG. 12 illustrates exponential estimation and subtraction;

[0073] FIG. 13 illustrates a system for 6 point detection for when relative phase between evoked response and sampling window is unknown;

[0074] FIG. 14 illustrates an alternative embodiment for 6-point detection;

[0075] FIGS. 15a and 15b illustrates generation of filter templates having three, four and five lobes, respectively; and

[0076] FIGS. 16a and 16b respectively illustrate four and three lobed filter template point values, derived from the approach of FIG. 15.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0077] FIG. 1 illustrates an implantable device 100 suitable for implementing the present invention. Device 100 comprises an implanted control unit 110, which controls application of neural stimuli, and controls a measurement process for obtaining a measurement of a neural response evoked by the stimuli from each of a plurality of electrodes. The control unit 110 includes a storage memory (or other storage device(s), not shown) for storing a lookup table that contains data defining a therapy map, setting out a relationship between applied stimuli regimes and the desired neural response. Device 100 further comprises an electrode array 120 consisting of a three by eight array of electrodes 122, each of which may be selectively used as either the stimulus electrode or sense electrode, or both.

[0078] FIG. 2 is a schematic of a feedback controller implemented by the control unit 110, based on recruitment. An important component of such feedback control is a recruitment estimator 210, which is tasked with the difficult operation of, in a simple form, detecting whether a neural response is present in a neural measurement output by the spinal cord potential (SCP) amplifier, or in a more complex form determining an amplitude of any such neural response.

[0079] The evoked CAP measurements in this embodiment are made by use of the neural response measurement techniques set out in International Patent Publication No. WO2012/155183.

[0080] FIG. 3a illustrates a neural response detector 300 in accordance with one embodiment of the invention. A digitised sampled form of the neural measurement obtained by the SCP amplifier is taken as the input 302. A filter template 304 is created at 306 by modulating a sine wave 308 with a Bartlett window 310. In alternative embodiments the template is likely to be predefined in this manner and simply retrieved from a memory or the like within control unit 110. A dot product of a suitable window of the neural measurement 302 and the filter template 304 is calculated at 312, 314, to produce the detector output 316, which is a single value scalar. The detector 300 may be modified as shown in FIG. 3b by the addition of a gain term a for example to allow the correlator to produce approximately the same result as a peak-to-peak ECAP detector for comparison.

[0081] FIG. 4 illustrates the amplitude profile of the filter template 304 used in the detector 300 of FIG. 3. FIG. 4 further illustrates the Bartlett window 310 used to amplitude modulate the sine wave 308. To assist in the following discussion, FIG. 4 also shows an additional filter template 402, comprising a cosine wave amplitude modulated by the Bartlett window 310. It is noted on the x-axis of FIG. 4 that the filter templates 304 and 402 cach comprise a sufficient number of points such that at the sampling rate used the filter templates each cover a time period of almost 2 ms, which is four-thirds of the duration of an expected neural response in this embodiment.

[0082] FIG. 5a illustrates an evoked response 502 in the absence of artefact, the four-lobe filter template 304, and the sliding dot product or cross correlation thereof, 504. Again, it is noted that the response 502 comprises three lobes, whereas the filter template 304 comprises four lobes and is four-thirds the expected length of the response 502. As can be seen in the sliding dot product 504, the evoked response 502 is substantially passed to the output of the detector 300 by the filter template 304. In contrast FIG. 5b illustrates the correlation 508 of the four lobe filter template 304 with pure artefact 506, illustrating that artefact is substantially blocked or heavily attenuated by the filter template 304 and thus not passed to the output of the detector 300. In this embodiment, the performance of the four-lobe filter template 304 at passing an expected neural response is within 2 dB of that of a matched filter, but with significantly improved artifact rejection.

[0083] It is noted that when sampling at 10 kHz, for example, 20 samples will be obtained in a 2 ms window, so that to determine the entire cross correlation will require 400 multiply/add operations. Accordingly, rather than calculating the entire cross-correlation between a measured neural response and the filter template, the present embodiment further provides for calculation of only a single point of the correlation as the output 316 of detector 300, as a single point requires only 20 samples when sampling a 2 ms window at 10 kHz. Noting that the arrival time of the neural response, or its position within the neural measurement 302, is not known a priori, it is necessary to determine an optimal time delay or offset between the neural measurement and the template filter, at which the single point of the correlation should then be calculated. The aim is to calculate the single point at the peak of the curve 504, and no other. To this end, the present embodiment efficiently determines the optimal time delay, by noting the following.

[0084] The DFT is defined by:

[00002]$\begin{array}{cc}{X}_k=\underset{n=0}{\overset{N-1}{.Math.}}{x}_n.Math.e^{i2?\mathrm{kn}/N}& \left(1\right)\end{array}$

[0085] In equation (1), and in the rest of this document, frequency-domain signals are represented by capital letters, and time-domain signals using lower-case. When using the DFT for spectral analysis, it is usual to multiply the data by a window W(n) so this becomes:

[00003]$\begin{array}{cc}{X}_k^{}=\underset{n=0}{\overset{N-1}{.Math.}}{x}_n.Math.W\left(n\right).Math.e^{i2?\mathrm{kn}/N}& \left(2\right)\end{array}$

[0086] This can be expressed in traditional magnitude and phase terms where the magnitude of the windowed DFT term is

=?{square root over (Re().sup.2+Im().sup.2)}(3)

and the phase of the windowed DFT term is

[00004]$\begin{array}{cc}{?}_k^{}={\tan }^{-1}\left(\frac{\mathrm{Re}\left(V_k^{}\right)}{\mathrm{Im}\left(V_k^{}\right)}\right)& \left(4\right)\end{array}$

[0087] The hardware 600 used to compute one term of is illustrated in FIG. 6. Notably, the sine template 304 and cosine template 402 shown in FIG. 4 are used in the circuit 600. Comparing this arrangement to the previous equation, for which the third term is:

[00005]$\begin{array}{cc}{X}_2^{}=\underset{n=0}{\overset{N-1}{.Math.}}{x}_n.Math.W\left(n\right).Math.e^{-i4?n/N},& \left(5\right)\end{array}$

it is noted that detector 300 using the filter template 304 (FIG. 3) computes the imaginary part of the third term of the windowed DFT. Thus, references to the output of the detector 300 are to be understood as being the imaginary part of the third term of the windowed DFT, and this is important to an understanding of the following further refinements of the invention.

[0088] This also provides insight into what happens as the time delay is adjusted during a clinical fitting procedure, as shown in FIGS. 7a and 7b. While FIG. 7b shows a triangular window and a single lobed response, this is for simplicity of representation and is intended to represent the four lobed filter template 304 and the three lobed response 502, respectively. Exploring different time delay adjustments by sliding the offset or delay in the time domain (FIG. 7b), rotates the coordinate system of the measurement (FIG. 7a). When the evoked response phase aligns with the imaginary axis of FIG. 7a, the output of the detector 300 is at its maximum. This also presents a computationally efficient solution to the problem when at this phase; when the correlator output is maximum, the real part of the spectral component is zero, so its calculation can be avoided as depicted in FIG. 3, saving processor cycles. The output of the detector 300 is the projection of the (complex) evoked response onto the imaginary axis.

[0089] When considering the entire cross correlation as the evoked response slides across the window (FIG. 7b), the evoked response vector in FIG. 7a rotates a full 360 degrees around the origin at least twice, and thus changes relatively quickly. However as shown at the bottom of FIG. 7b, the amplitude of the convolution of the evoked response and the window changes relatively slowly. Accordingly, the present embodiment recognises that a swift technique to align the evoked response with the imaginary axis and thus find the peak in the correlator output is to: [0090] 1. Roughly align the window and the signal S(t); [0091] 2. Calculate the imaginary (sin) and real (cosine) terms: [0092] a. I=S(t).W(t).sin( 1 KHz.2?.t), and [0093] b. Q=S(t).W(t).cos(1 KHz.2?.t); [0094] 3. Find the angle to the y-axis using atan(Q/I); [0095] 4. As the template has fixed known frequency, calculate the time shift needed to set the sin term to its maximum; [0096] 5. Calculate the imaginary (sin) and real (cosine) terms for the new delay. The cosine term should be much smaller than the sin term confirming that the method worked.

[0097] Such embodiments may be particularly advantageous as compared to a clinical process requiring exploration of the varying delays in order to find a peak

[0098] The present embodiment further incorporates the third and fourth aspects of the invention, and recognises that the artifact 506 can be well modelled as being a sum of two exponentials, of differing time constant. Each exponential component has a voltage and a time value, leading to

[00006]$\begin{array}{cc}a\left(t\right)=v_1\exp \left(\frac{-t}{{?}_1}\right)+v_2\exp \left(\frac{-t}{{?}_2}\right)& \left(6\right)\end{array}$

where ?.sub.i and ?.sub.i are constants for each component.

If

e(t)=vexp(?t/?)(7)

then we can consider its windowed DFT E.sub.k, for which each term will have a magnitude and phase, and the term E.sub.2 can be calculated with the complex correlator 600 of FIG. 6.

[0099] If we take some signal e.sup.?t/? and shift the point in the signal at which the correlation is performed by some arbitrary time T, since

e.sup.?(t+T)/?=e.sup.?t/?e.sup.?T/?

e.sup.?(t+T)/?=c.Math.e.sup.?t/?(8)

where c is some constant.

[0100] Thus, the phase of the DFT terms of a single exponential depend on the time constant of the exponential, as shown in FIG. 8 for the filter template 304. However, the present embodiment recognises that the phase of each DFT term is unchanged by time delay.

[0101] FIG. 9 illustrates the filter output vector components arising from artefact only, when modelled as two exponentials. At a first time, shown in FIG. 9a, A.sub.2 and B.sub.2 are the two artifact phase vectors. These can be added using vector addition to produce the total artefact 902. The detector 300 will thus produce an output 904 which is the imaginary part of this vector; the projection of 902 onto the y-axis. As time passes, the lengths of the two vectors reduce exponentially, but at different rates as the time constants are different, B2 decaying rapidly and A2 decaying slowly. However, the phases remain unchanged as per equation (8), resulting in the situation shown in FIG. 9b. The total artefact vector is now 912, which due to the different relative contributions from each exponential component is of slightly changed phase to 902. The detector 300 will thus produce an output 914.

[0102] FIGS. 10a and 10b illustrate, at respective times, the detector output vector components arising from artefact modelled as two exponentials and from an evoked response. At a first time t, shown in FIG. 10a, V.sub.1 and V.sub.2 are the two artifact phase vectors, and CAP is the evoked response vector. These can be added using vector addition to produce the total artefact 1002. The detector 300 will thus produce an output 1004 which is the imaginary part of this vector; the projection of 1002 onto the y-axis. At a later time t+dt, the lengths of the two artefact vectors have reduced exponentially, at different rates as the time constants are different, with V.sub.2 decaying rapidly and V.sub.1 decaying slowly. However, the phases remain unchanged as per equation (8), as shown in FIG. 10b. In contrast, the amplitude of the evoked response vector CAP changes relatively slowly as discussed in relation to FIG. 7b, but undergoes a change in phase as discussed in relation to FIG. 7a. Thus, as shown in FIG. 10b, the CAP vector rotates without undergoing a significant amplitude change. Thus, at one moment (FIG. 10a) the CAP vector can be orthogonal to V.sub.2, and at a later time (FIG. 10b) can be aligned with V.sub.2.

[0103] When modelling the artefact as a sum of two exponential terms, it has been determined from measurements of actual artefact that the time constant ?.sub.1 of the first (slow) exponential term is typically in the range 300 ?s to 30 ms, more typically 500 ?s to 3 ms and most commonly about 1 ms, and that the time constant ?.sub.2 of the second (fast) exponential term is typically in the range 60-500 ?s, more typically 100-300 ?s, and most commonly about 150 ?s.

[0104] The method of this embodiment, utilising the third and fourth aspects of the invention, relies on making two complex measurements of the evoked response, at points in time separated by one quarter of a cycle, as shown in FIG. 11a. The timing of the measurements is optimised in the manner described above in relation to FIGS. 7a and 7b, so that the first measurement (m1 and m2) has a purely imaginary evoked response contribution (i.e. the evoked response aligns with the sin correlator 304), and the second measurement (m3 and m4) is purely real (i.e. aligns with the cosine 402). This leads to four measurements, m1 to m4. There are four unknownsthe magnitude of the artifact, the magnitude of the evoked response, the phase of the artifact and the time constant of the fast exponential. The slow exponential component of the artifact is well rejected by the filter template 304 and thus can be omitted. It is known that the artifact contribution to the sin and cos correlators has a fixed ratio. Using simple algebra the unknowns can be eliminated. Therefore any CAP present in the neural measurement can be calculated as being:

[00007]$\begin{array}{cc}\mathrm{CAP}=m_4-k.m_2& \left(9\right)\end{array}$$\begin{array}{cc}\mathrm{Where}k=\frac{m4-m1?\sqrt{{\left(m4-m1\right)}^2+4.Math.m2.Math.m3}}{2.Math.m2}& \left(10\right)\end{array}$

[0105] FIG. 11b illustrates the locations of these four measurements m1 to m4 on the real and imaginary detector outputs.

[0106] Knowing k also allows the evaluation of ?, and of the fast artifact exponential:

[00008]$\begin{array}{cc}?=\frac{-T}{\ln \left(k\right)}& \left(11\right)\end{array}$

[0107] To find the voltage of the fast exponential term for the artifact, one can further calculate the DFT of the exponential which is what would be expected from the detectors for an exponential input of that time constant, normalized to 1.0:

[00009]$\begin{array}{cc}{X}_2^{}=\underset{n=0}{\overset{N-1}{.Math.}}{e}^{\frac{-t}{?}}.Math.W\left(n\right).Math.e^{-i4?n/N}& \left(12\right)\end{array}$

[0108] Then, an estimation of the fast artifact term is:

[00010]$\begin{array}{cc}A\left(t\right)=\frac{e^{-t/?}}{X_2^{}}& \left(13\right)\end{array}$

[0109] Having calculated the above, it is possible to improve the SAR of the signal by subtracting the estimated exponential, as shown in FIG. 12.

[0110] A difficulty in implementing this algorithm with measured data is that it measures two signals at once, namely the evoked response and the fast exponential, and each forms a noise source for the other. Usually, the phase of the evoked response is not known exactly, and this introduces errors into FIG. 11b. When the evoked response is larger than the exponential, and the phase of the evoked response is not known, the exponential estimation algorithm does not always find a solution, so the present embodiment further provides a second estimation method for these circumstances. This further estimation method recognises that the above algorithms can be extended by adding an additional correlation, to allow the phase of the evoked response to be calculated instead of being used as an input.

[0111] When the relative phase (?) of the evoked response to the sampling window is unknown, the proposal of FIG. 11 has 5 unknowns and 4 measurements, so the unknowns cannot be found. By adding two more DFT points this can be overcome, as shown in FIG. 13. These additional points (m5 and m6) are evaluated at a frequency equal to half the fundamental of the evoked responseto which the evoked response is orthogonal. Therefore these two additional points allow k to be evaluated:

[00011]$\begin{array}{cc}k=\frac{m6}{m5}& \left(14\right)\end{array}$

[0112] In turn, the five terms a,b,k,? and c can be found. For some phase ? between the measurement window and the evoked response:

[00012]$\begin{array}{cc}m1=a+c\sin ?& \left(15\right)\end{array}$$m2=b+c\cos ?$$m3=\mathrm{ak}+c\cos ?$$m4=\mathrm{bk}+c\sin ?$$\mathrm{so}:$$\begin{array}{cc}a=\frac{\left(m1-m4\right)+k\left(m2-m3\right)}{1-k^2}& \left(16\right)\end{array}$$\begin{array}{cc}b=m2-m3+\mathrm{ak}& \left(17\right)\end{array}$$\begin{array}{cc}c=\sqrt{{\left(m1-a\right)}^2+{\left(m2-b\right)}^2}& \left(18\right)\end{array}$$\begin{array}{cc}?={\sin }^{-1}\left(\frac{m1-a}{c}\right)& \left(19\right)\end{array}$

[0113] The phase will change slowly, so once ? is known, it is possible to adjust the delay of the sampling window, and then revert to the four point algorithm of FIG. 11.

[0114] When considering implementation of the six point technique of FIG. 13, it is noted that in some embodiments an FFT will compute this faster than a DFT, especially if the FFT is factored to use the smallest number of multiply operations. A good choice of DFT length might be 16, factored as (F.sub.2?F.sub.2)?(F.sub.2?F.sub.2). For this factorization the twiddle factors between the F.sub.2 operations are trivial, and so the only complex multiply required is in the middle.

[0115] FIG. 14 illustrates an alternative embodiment utilising six measurement points.

[0116] It is further noted that running the calculation after the evoked response is finished allows the slow exponential to be measured.

[0117] The evoked response in the spine (having three phases) takes approximately 1 ms. In embodiments employing a sample rate of 30 KHz or a simple interval of 33 us, the evoked response will take around 30 samples. Consequently in such embodiments the filter template having four phases will comprise approximately 40 tap values, or data points. In alternative embodiments, using an alternative sampling rate or measuring a faster or slower CAP, the length of the filter may comprise correspondingly greater or fewer filter taps.

[0118] While the preceding embodiments have been described in relation to a filter template which comprises four half cycles, alternative embodiments of the present invention may nevertheless usefully employ a filter template comprising greater or fewer lobes. The present invention thus recognises that the ideal number if lobes is four. This is in contrast to a two lobe filter, which will have equal first and second lobes and will thus put more emphasis on the carly parts of the signal where the signal-to-artifact is worse. Further, a filter with an odd number of lobes does not tend to have good artifact rejection properties. Moreover, if one were to use a six-lobe filter, or higher even-number lobed filter, the window becomes too wide relative to the 3-lobed neural response, and at least half the correlation time would just be looking at noise. Since most of the problematic artifact is in the first two lobes, a 6 lobe filter will tend not to provide better artifact rejection than the four-lobe filter. Four lobes thus provides the optimal trade-off between rejection of artifact and noise gain.

[0119] Nevertheless, alternative embodiments of the present invention may usefully employ a filter template comprising greater or fewer lobes. We now describe the mathematical properties of templates of other embodiments of the invention. The term template is used to refer to a filter used via correlation to detect an ECAP. A template may be comprised of one or more wavelets or basis functions, or may be derived by some other method, and is configured to preferentially pass an ECAP but preferentially block or be orthogonal to artifact. FIG. 15a illustrates sinusoidal binomial vectors in accordance with further embodiments of the invention. FIG. 15b shows the generation of three-lobe, four-lobe and five-lobe templates. A notable property of the SBT is that its basis functions of the same length are orthogonal. It is to be appreciated that the method used to generate the templates of FIG. 15 up to five-lobes can be extended to a greater number of lobes. It is further noted that the window is not triangular for three or five lobed filter templates, but has a flat central portion in both cases, and in the case of five lobes the window having a piecewise linear rise and fall. Thus, the three lobed filter template window proposed by the present embodiments is not triangular but is a flat topped window, which has been found to significantly improve artefact rejection as compared to a triangular window of a three lobed filter template.

[0120] That is, an important property of the sinusoidal binomial transform (SBT) is its ability to reject polynomial signals. If an SBT template of order n is used, it will reject all the terms of the Taylor series up to order n.

[0121] FIG. 16a illustrates the point values of a four lobed, 32 point filter template generated in accordance with the teachings of FIG. 15. FIG. 16b illustrates the point values of a three lobed, 33 point filter template generated in accordance with the teachings of FIG. 15 and in particular having a flat topped window.

[0122] It is further to be appreciated that cosine templates of 3, 5 or more lobes can be similarly generated, noting the FIG. 4 example for a four half cycles cosine template 402.

[0123] The preceding embodiments further describe a filter template built using a triangular window. The triangular window is superior to the Bartlett, Hanning, rectangular and the Kaiser-Bessel for a variety of beta values. The performance of the four-lobe triangular template can be within 2 dB of a matched filter for optimised offset. Nevertheless, alternative embodiments may utilise windows other than the triangular window to useful effect, and such embodiments are thus within the scope of the present invention.

[0124] Moreover, while the described embodiments use a single term of the SBT for response detection, the present invention further recognises that there are possible extensions to this method. Therefore, some embodiments of the invention may use multiple identical templates, but shifted in time. Even though these are not orthogonal, a successive approximation method creating a compound template may provide better approximation. Additionally or alternatively, some embodiments may use templates that are a sum of templates of different frequencies, templates of different offset and/or templates of different numbers of lobes.

[0125] A benefit of some embodiments of the present invention is that in some embodiments the detector produces an output based on a single neural measurement, without requiring multiple neural measurements to produce a detector output. Such embodiments may thus provide a swift response time of a feedback control loop utilising the detector output.

[0126] It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.