Hardware-efficient reconstruction for periodic non-uniformly sampled signals

1. A method for signal reconstruction, the method comprising:

receiving a periodically non-uniformly sampled signal, wherein the sampled signal is considered in the time-domain signal and in the frequency-domain, and for each sampling period, one or more samples is missing;

dividing the signal in the time-domain in M periods of K length;

dividing the signal in the frequency-domain in K groups of length M;

applying assumptions to the received signal, the assumptions comprising:

for the signal in the time-domain, for each sampling period, the same samples are missing;

for the signal in the frequency-domain, at least one of the groups is zero; and

the number of number of zero groups is larger than the number of missing time-domain samples per period; and

reconstructing the signal using a known formula for a non-uniformly sampled signal while applying the assumptions.

2. The method of claim 1 , further comprising skipping a first sample in each period of K samples.

3. The method of claim 1 , further comprising skipping a first sample and a K/2′th sample of K samples.

4. The method of claim 1 , wherein the signal is centered around DC, the method further comprising skipping a first sample in four samples of a period.

5. The method of claim 1 , wherein the signal is centered around f s /4, the method further comprising skipping a first sample and a K/2′th sample of K samples.

6. The method of claim 1 , further comprising:

applying a radix K FFT; and

applying a radix K IFFT.

7. An apparatus for reconstructing a signal, the apparatus comprising:

FFT element coupled to receive the signal;

a permutation element (indicated by X 0 -X N−1 ) coupled to receive an output of the FFT element;

a reconstruction kernel coupled to receive an output of the permutation element;

a reverse permutation element coupled to receive an output of the reconstruction kernel; and

an inverse FFT element coupled to receive an output of the inverse permutation element and to output a reconstructed signal to an analog-to-digital converter, wherein the analog-to-digital converter is shared among a plurality of signals.

8. The apparatus of claim 7 , wherein the reconstruction kernel is configured to:

receive a periodically non-uniformly sampled signal, wherein the sampled signal is considered in the time-domain signal and in the frequency-domain, and for each sampling period, one or more samples is missing;

divide the signal in the time-domain in M periods of K length;

divide the signal in the frequency-domain in K groups of length M;

apply assumptions to the received signal, the assumptions comprising:

for the signal in the time-domain, for each sampling period, the same samples are missing;

for the signal in the frequency-domain, at least one of the groups is zero; and

the number of number of zero groups is larger than the number of missing time-domain samples per period; and

reconstruct the signal using a known formula for a non-uniformly sampled signal while applying the assumptions.

9. The apparatus of claim 8 , wherein the reconstruction kernel is further configured to skip a first sample in each period of K samples.

10. The apparatus of claim 8 , wherein the reconstruction kernel is further configured to skip a first sample and a K/2′th sample of K samples.

11. The apparatus of claim 8 , wherein the signal is centered around DC, and wherein the reconstruction kernel is further configured to skip a first sample in four samples of a period.

12. The apparatus of claim 8 , wherein the signal is centered around f s /4, and wherein the reconstruction kernel is further configured to skip a K/2′th sample of K samples.

13. A signal reconstructing system, comprising:

a reconstruction kernel configured to,

receive a periodically non-uniformly sampled signal, wherein the sampled signal is considered in the time-domain and in the frequency-domain, and for each sampling period, one or more samples is missing;

divide the signal in the time-domain in M periods of K length;

divide the signal in the frequency-domain in K groups of length M;

apply assumptions to the received signal, the assumptions comprising:

for the signal in the time-domain, for each sampling period, the same samples are missing;

for the signal in the frequency-domain, at least one of the groups is zero; and

the number of number of zero groups is larger than the number of missing time-domain samples per period; and

reconstruct the signal using a known formula for a non-uniformly sampled signal while applying the assumptions.

14. The system of claim 13 , further comprising a radix K FFT coupled to receive the signal and to output a result to the reconstruction kernel.

15. The system of claim 14 , further comprising a radix K IFFT coupled to receive an output of the reconstruction kernel and to output a result to an analog-to-digital converter, wherein the analog-to-digital converter is shared among a plurality of signals.

16. The system of claim 13 , wherein the reconstruction kernel is further configured to skip a first sample in each period of K samples.

17. The system of claim 13 , wherein the reconstruction kernel is further configured to skip a first sample and a K/2′th sample of K samples.

18. The system of claim 13 , wherein the signal is centered around DC, and wherein the reconstruction kernel is further configured to skip a first sample in four samples of a period.

19. The system of claim 13 , wherein the signal is centered around f s /4, and wherein the reconstruction kernel is further configured to skip a K/2′th sample of K samples.

20. The system of claim 13 , comprising a wireless receiver that comprises the reconstruction kernel.

21. The system of claim 13 , comprising a plurality of sensors, wherein at least one of the sensors comprises the reconstruction kernel.