Spectral averaging

1. A method for recovering a periodic signal from a random signal, comprising:

for each of multiple acquisitions:

receiving a plurality of time-domain samples of a single-channel signal;

cross-power spectrum analyzing first and second portions of the plurality of samples to obtain a cross-power spectrum between the first and second portions; and

accumulating the cross-power spectrum into a cumulative cross-power spectrum using a vector sum of the cross-power spectrum and the cumulative cross-power spectrum;

calculating a vector average cross-power spectrum based on the cumulative cross-power spectrum and the quantity of acquisitions; and

displaying a magnitude function corresponding to the vector average cross-power spectrum.

2. The method of claim 1 , wherein a beginning time of the first portion of the plurality of samples is separated from a beginning time of the second portion of the plurality of samples by a predetermined, consistent time difference.

3. The method of claim 2 , wherein the predetermined, consistent time difference is equal to a time length of the first portion, wherein the time length of the first portion is equal to a time length of the second portion.

4. The method of claim 1 , wherein the first and second portions of the plurality of samples overlap by at least one sample that is common to both the first and second portions.

5. The method of claim 1 , wherein the plurality of samples used in said cross-power spectrum analyzing includes at least twice a number of samples than used in a scalar spectral analysis.

6. The method of claim 1 , wherein the plurality of samples includes at least an integer multiple of the periodic signal's period worth of samples greater than a number of samples used in a scalar spectral analysis, and wherein the plurality of samples is also at least twice a number of samples used in a scalar spectral analysis.

7. The method of claim 6 , wherein a beginning of the first portion is separated from a beginning of the second portion by an integer multiple of the periodic signal's period.

8. The method of claim 6 , wherein the periodic signal to be recovered from the random signal is a repeated pseudo-random sequence with a known period.

9. The method of claim 1 , further comprising:

for each of the multiple acquisitions, calculating an intermediate vector average based on the cumulative cross-power spectrum, and displaying the magnitude of the intermediate vector average.

10. A non-transitory computer-readable storage medium storing program instructions, wherein the program instructions are computer-executable to implement:

for each of multiple acquisitions:

receiving a plurality of time-domain samples of a single-channel signal;

cross-power spectrum analyzing first and second portions of the plurality of samples to obtain a cross-power spectrum between the first and second portions; and

accumulating the cross-power spectrum into a cumulative cross-power spectrum using a vector sum of the cross-power spectrum and the cumulative cross-power spectrum;

calculating a vector average cross-power spectrum based on the cumulative cross-power spectrum and the quantity of acquisitions; and

displaying a magnitude function corresponding to the vector average cross-power spectrum.

11. The non-transitory computer-readable storage medium of claim 10 , wherein a beginning of the first portion is separated from a beginning of the second portion by a predetermined time difference.

12. The non-transitory computer-readable storage medium of claim 11 , wherein the predetermined time difference is equal to a length of the first portion, wherein the length of the first portion is equal to a length of the second portion.

13. The non-transitory computer-readable storage medium of claim 10 , wherein the first and second portions of the plurality of samples overlap by at least one sample that is common to both the first and second portions.

14. The non-transitory computer-readable storage medium of claim 10 , wherein a beginning of the first portion is separated from a beginning of the second portion by an integer multiple of a periodic signal's period.

15. The non-transitory computer-readable storage medium of claim 10 , wherein the plurality of samples used in said cross-power spectrum analyzing includes at least twice a number of samples than used in a scalar spectral analysis.

16. A system, comprising:

at least one processor; and

a memory storing program instructions, wherein the program instructions are executable by the at least one processor to:

for each of multiple acquisitions:

receive a plurality of time-domain samples of a single-channel signal;

cross-power spectrum analyze first and second portions of the plurality of samples to obtain a cross-power spectrum between the first and second portions; and

accumulate the cross-power spectrum into a cumulative cross-power spectrum using a vector sum of the cross-power spectrum and the cumulative cross-power spectrum;

calculate a vector average cross-power spectrum based on the cumulative crosspower spectrum and the quantity of acquisitions; and

display a magnitude function corresponding to the vector average cross-power spectrum.

17. The system of claim 16 , wherein a start of the first portion is separated from a start of the second portion by a predetermined time difference.

18. The system of claim 17 , wherein the predetermined time difference is equal to a length of the first portion, wherein the length of the first portion is equal to a length of the second portion.

19. The system of claim 16 , wherein the first and second portions of the plurality of samples overlap by at least one sample that is common to both the first and second portions.

20. The system of claim 16 , wherein a beginning of the first portion is separated from a beginning of the second portion by an integer multiple of a periodic signal's period.