Methods and apparatus for neuromodulation
A neuromodulator accurately measures—in real time and over a range of frequencies—the instantaneous phase and amplitude of a natural signal. For example, the natural signal may be an electrical signal produced by neural tissue, or a motion such as a muscle tremor. The neuromodulator generates signals that are precisely timed relative to the phase of the natural signal. For example, the neuromodulator may generate an exogenous signal that is phase-locked with the natural signal. Or, for example, the neuromodulator may generate an exogenous signal that comprises short bursts which occur only during a narrow phase range of each period of an oscillating natural signal. The neuromodulator corrects distortions due to Gibbs phenomenon. In some cases, the neuromodulator does so by applying a causal filter to a discrete Fourier transform in the frequency domain, prior to taking an inverse discrete Fourier transform.
1. A method comprising:
(a) measuring, via a sensor of an apparatus, a physiological signal;
(b) calculating, via one or more processors of the apparatus, a discrete signal that comprises samples of the physiological signal;
(c) calculating a second signal, which second signal is a discrete Fourier transform of the discrete signal;
(d) calculating a smoothed signal, by performing calculations that include (i) applying a causal filter to the second signal, which causal filter deforms a front-segment but not an end-segment of the second signal in such a way that the start point of the smoothed signal is equal in value to the endpoint of the smoothed signal, and (ii) removing negative frequency components;
(e) calculating a portion of an analytic signal, which analytic signal is equal to an inverse discrete Fourier transform of the smoothed signal;
(f) calculating, based on said portion of the analytic signal, instantaneous phase of the physiological signal;
(g) outputting instructions, based on the instantaneous phase; and
(h) outputting a neuromodulation signal, based on the instructions.
2. The method of claim 1 , wherein the physiological signal is an electrical signal produced by neural tissue.
3. The method of claim 1 , wherein the physiological signal is motion caused by a muscular tremor.
4. The method of claim 1 , wherein phase of the neuromodulation signal is a function of phase of the physiological signal.
5. The method of claim 1 , wherein the neuromodulation signal comprises light, sound, or haptic or electrical stimulation.
6. The method of claim 1 , further comprising repeating steps (d)-(f) with a different causal filter.
7. The method of claim 1 , wherein step (f) further comprises calculating instantaneous amplitude of the physiological signal.
8. The method of claim 1 , wherein the calculating a smoothed signal comprises computing a product of:
(a) a discrete Fourier transform of an impulse response of the causal filter;
(b) a scrubber signal; and
(c) the second signal.
9. The method of claim 1 , wherein:
(a) the analytic signal has an imaginary component, which imaginary component is a Hilbert transform signal; and
(b) the start point of the Hilbert transform signal is equal in value to the endpoint of the Hilbert transform signal.
10. A method comprising:
(a) measuring, via a sensor of an apparatus, a physiological signal;
(b) calculating, via one or more processors of the apparatus, a discrete signal that comprises samples of the physiological signal;
(c) calculating a padded signal by front-padding, which front-padding adds a segment at the beginning of the discrete signal, which segment is a replica of an end-segment of the discrete signal;
(d) calculating a modified signal, by performing calculations that comprise applying a causal filter to the padded signal and then removing data values that correspond in time to the segment added by the front-padding, which calculations cause the start point of the modified signal to have a value that is equal to the value of the endpoint of the modified signal;
(e) calculating a fourth signal, which fourth signal is a discrete Fourier transform of the modified signal;
(f) calculating a fifth signal by removing negative frequency components from the fourth signal;
(g) calculating a portion of an analytic signal, which analytic signal is equal to an inverse discrete Fourier transform of the fifth signal;
(h) calculating, based on said portion of the analytic signal, instantaneous phase of the physiological signal;
(i) outputting instructions, based on the instantaneous phase; and
(j) outputting a neuromodulation signal, based on the instructions.
11. The method of claim 10 , further comprising repeating steps (d)-(h) with a different causal filter.
12. The method of claim 10 , wherein phase of the neuromodulation signal is a function of phase of the physiological signal.
13. The method of claim 10 , wherein the applying a causal filter comprises convolving (a) an impulse response of the causal filter and (b) the padded signal.
14. The method of claim 10 , wherein the neuromodulation signal comprises light, sound, haptic or electrical stimulation.
15. The method of claim 10 , wherein:
(a) the analytic signal has an imaginary component, which imaginary component is a Hilbert transform signal; and
(b) the start point of the Hilbert transform signal is equal in value to the endpoint of the Hilbert transform signal.
16. A method comprising:
(a) measuring, via a sensor of an apparatus, a physiological signal;
(b) calculating, via one or more processors of the apparatus, a discrete signal that comprises samples of the physiological signal;
(c) creating a padded signal by end-padding;
(d) calculating a filtered signal, by applying a causal filter to the padded signal in such a way that the causal filter produces ringing artifacts which modify data values added by the end-padding;
(e) calculating a fourth signal, which fourth signal is a discrete Fourier transform of the filtered signal;
(f) calculating a fifth signal by removing negative frequency components from the fourth signal;
(g) calculating a portion of an analytic signal, which analytic signal is equal to an inverse discrete Fourier transform of the fifth signal;
(h) calculating, based on said portion of the analytic signal, instantaneous phase of the physiological signal;
(i) outputting instructions, based on the instantaneous phase; and
(j) outputting a neuromodulation signal, based on the instructions.
17. The method of claim 16 , wherein the neuromodulation signal comprises light, sound, haptic or electrical stimulation.
18. The method of claim 16 , wherein phase of the neuromodulation signal is a function of phase of the physiological signal.
19. The method of claim 16 , wherein the applying a causal filter comprises convolving (a) an impulse response of the causal filter and (b) the padded signal.
20. The method of claim 16 , wherein the method further comprises truncating the padded signal by removing a front-segment of the padded signal, before applying the causal filter.
21. The method of claim 16 , wherein:
(a) the physiological signal is a periodic signal; and
(b) the end-padding comprises adding a segment that consists of data values that correspond an interval of time that is at least as long as three quarters of a period of the discrete signal.
22. The method of claim 16 , further comprising repeating steps (d)-(h) with a different causal filter.
23. The method of claim 16 , wherein step (h) further comprises calculating instantaneous amplitude of the physiological signal.