Randomized time encoding machine for sub-nyquist signal sampling

1. A time encoding machine (TEM) for time encoding an input signal, the time encoding machine comprising:

a hysteresis quantizer having a time encoded sequence output; and

a random sequence generator having a random signal output coupled to the hysteresis quantizer for randomizing switching times of the hysteresis quantizer.

2. The TEM of claim 1 wherein the random sequence generator is clocked by the time encoded sequence output.

3. The TEM of claim 1 wherein the random sequence generator is a pseudorandom sequence generator.

4. The TEM of claim 1 wherein the random sequence generator is a one bit pseudorandom sequence generator.

5. The TEM of claim 1 wherein the hysteresis quantizer comprises a relay or a comparator.

6. The TEM of claim 1 wherein the time encoding machine comprises a second order time encoding machine.

7. The TEM of claim 1 wherein the time encoded sequence output rate is lower than a Nyquist rate for the input signal.

8. The TEM of claim 1 wherein the hysteresis quantizer detects zero crossing time points to form the time encoded sequence output.

9. The TEM of claim 1 wherein the time encoding machine (TEM) comprises time encoded compressive sensing of the input signal.

10. The TEM of claim 1 further comprising:

an integrator having an integrator output, and

a summer coupled to the random signal and the integrator output for summing the random signal and the integrator, the summer having a summer output coupled to the hysteresis quantizer;

wherein switching times of the hysteresis quantizer are randomized.

11. The TEM of claim 10 wherein the summing comprises adding or subtracting the random signal to or from the integrator output, respectively.

12. The TEM of claim 1 further comprising:

an integrator having an integrator output coupled to the hysteresis quantizer; and

a summer coupled to the input signal and to the random signal and having a summer output coupled to the integrator;

wherein switching times of the hysteresis quantizer are randomized.

13. The TEM of claim 12 further comprising:

a mixer coupled to the random signal and the time encoded sequence output, the mixer having a mixer output coupled to the summer.

14. A method for forming a reconstructed signal of an input signal, the method comprising:

forming a diagonal matrix S as an inverse of a column norm of a first measurement matrix AΨ, so that

[ S]= 1/√{square root over ([( A Ψ) T ( A Ψ)] l,l )}{square root over ([( A Ψ) T ( A Ψ)] l,l )};

forming a second measurement matrix AΨS;

using the second measurement matrix to form x 1 =S −1 x; and

forming the reconstructed signal x from x 1 and the diagonal matrix so that x=Sx 1 .

15. A method for time encoded compressive sensing comprising:

randomizing a switching point of a quantizer for time encoding an input signal to form a randomized time encoded sequence output; and

using a two-step process to reconstruct the input signal from the time encoded sequence output.

16. The method of claim 15 wherein using a two-step process to reconstruct the input signal from the time encoded sequence output comprises:

forming a diagonal matrix S as an inverse of a column norm of a first measurement matrix AΨ, so that

[ S]= 1/√{square root over ([( A Ψ) T ( A Ψ)] l,l )}{square root over ([( A Ψ) T ( A Ψ)] l,l )};

forming a second measurement matrix AΨS;

using the second measurement matrix to form x 1 =S −1 x; and

forming the reconstructed signal x from x 1 and the diagonal matrix so that x=Sx 1 .

17. The method of claim 15 wherein the quantizer detects zero crossing time points to form the time encoded sequence output.

18. The method of claim 15 wherein randomizing a switching point of a quantizer for time encoding an input signal to form a randomized time encoded sequence output comprises:

adding a random signal to the input signal.

19. The method of claim 18 wherein the random signal is added to the input signal before integrating the input signal.

20. The method of claim 18 wherein the random signal is added to the input signal after integrating the input signal.

21. The method of claim 15 wherein randomizing a switching point of a quantizer for time encoding an input signal to form a randomized time encoded sequence output comprises:

time encoding an input signal with a hysteresis quantizer; and

providing a random signal input to the hysteresis quantizer for randomizing the switching times of the hysteresis quantizer.

22. The method of claim 21 wherein the random signal input is generated by a random sequence generator.

23. The method of claim 22 wherein the random sequence generator is a pseudorandom sequence generator.

24. The method of claim 22 wherein the random sequence generator is a one-bit pseudorandom sequence generator.