Sparse sampling of signal innovations

• US 8,326,580 B2
• Filed: 06/13/2008
• Issued: 12/04/2012
• Est. Priority Date: 01/29/2008
• Status: Active Grant

• Current Assignee: Qualcomm, Inc.
• Original Assignee: Qualcomm, Inc.
• Inventors: Blu, Thierry, Vetterli, Martin, Coulot, Lionel
• Primary Examiner(s): Le, John H
• Application Number:
  US12/139,117
• Publication Number:
  US 20090191814A1
• Time in Patent Office: 1,635 Days
• Field of Search: 702/17, 702/69, 702/71, 702/74, 702/111, 702/127, 702/189, 702/191, 327/100, 375/130, 375/260, 375/285, 375/316, 375/322, 375/355, 455/41.3, 455/63.1, 381/74, 381/94.1, 708/814
• US Class Current: 702/189
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: H03M 1/0626 by filtering
• CPC Class Codes: H03M 1/127 at intervals varying with the rate of change of the input signal
• CPC Class Codes: H04B 1/71637 Receiver aspects H04B1/7183 takes precedence
• CPC Class Codes: H04L 25/03006 Arrangements for removing intersymbol interference
• CPC Class Codes: H04L 27/2647 Arrangements specific to the receiver only equalisation H04L27/01

Abstract

The present invention relates to a method of processing a signal which is received by a receiver, comprising, obtaining an analog signal (y_t) based on another signal (x_t) and noise; defining a sampling kernel based on the noise; and using the sampling kernel to obtain at least one sample (y_n) from the analog signal (y_t). The invention also relates to a corresponding apparatus; computer program product; headset; watch, and sensing device.

Claims

1. A method of processing a signal which is received by a receiver, comprising:

obtaining an analog signal (y_t) based on another signal (x_t) and noise;

defining a sampling kernel based on the noise; and

using the sampling kernel to obtain at least one sample (y_n) from the analog signal (y_t).

2. The method of claim 1, wherein a sampling rate for obtaining the at least one sample (y_n) is lower than the minimal sampling rate given by the Shannon theorem applied to the analog signal (y_t).

3. The method of claim 1, wherein bandwidth of the sampling kernel is based on an estimate of the noise.

4. The method of claim 1, further comprising estimating information relating to the another signal (x_t) through the use of an annihilating filter.

5. The method of claim 4, further comprising defining the annihilating filter by performing a singular value decomposition method and minimizing a norm of a matrix associated with the singular value decomposition method.

6. The method of claim 1, further comprising reconstructing the another signal (x_t) through use of an annihilating filter applied to the at least one sample (y_n).

7. The method of claim 1, further comprising retrieving an estimate of shifts (t_k) associated with the another signal (x_t) through use of an annihilating filter.

8. The method of claim 7, further comprising retrieving an estimate of weights (x_k) associated with the another signal (x_t).

9. The method of claim 1, further comprising using a denoising process to provide a denoised signal (y′

_n) based on the at least one sample (y_n).

10. The method of claim 1, further comprising determining a sampling rate for obtaining the at least one sample (y_n) based on an estimate of the noise.

11. The method of claim 10, wherein the estimated noise comprises an estimated signal-to-noise ratio.

12. The method of claim 10, wherein the determination of the sampling rate is further based on a desired level of accuracy for reconstructing the another signal (x_t).

13. The method of claim 10, wherein the determination of the sampling rate is further based on a comparison between an assumption of an expected signal to noise ratio and a signal to noise ratio of a reconstructed signal that is based on the at least one sample (y_n).

14. An apparatus for signal processing, comprising:

a circuit arranged to obtain an analog signal (y_t) based on another signal (x_t) and noise; and

a sampler arranged to use a sampling kernel that is defined based on the noise to obtain at least one sample (y_n) from the analog signal (y_t).

15. The apparatus of claim 14, wherein a sampling rate for obtaining the at least one sample (y_n) is lower than the minimal sampling rate given by the Shannon theorem applied to the analog signal (y_t).

16. The apparatus of claim 14, wherein bandwidth of the sampling kernel is based on an estimate of the noise.

17. The apparatus of claim 14, further comprising an estimator arranged to estimate information relating to the another signal (x_t) through use of an annihilating filter.

18. The apparatus of claim 17, wherein the estimator is further arranged to define the annihilating filter by performing a singular value decomposition method and minimizing a norm of a matrix associated with the singular value decomposition method.

19. The apparatus of claim 14, further comprising an estimator arranged to reconstruct the another signal (x_t) through use of an annihilating filter applied to the at least one sample (y_n).

20. The apparatus of claim 14, further comprising an estimator arranged to retrieve an estimate of shifts (t_k) associated with the another signal (x_t) through use of an annihilating filter.

21. The apparatus of claim 20, wherein the estimator is further arranged to retrieve an estimate of weights (x_k) associated with the another signal (x_t).

22. The apparatus of claim 14, further comprising a denoiser arranged to provide a denoised signal (y′

_n) based on the at least one sample (y_n).

23. The apparatus of claim 14, arranged to determine a sampling rate for obtaining the at least one sample (y_n) based on an estimate of the noise.

24. The apparatus of claim 23, wherein the estimated noise comprises an estimated signal-to-noise ratio.

25. The apparatus of claim 23, wherein the determination of the sampling rate is further based on a desired level of accuracy for reconstructing the another signal (x_t).

26. The apparatus of claim 23, wherein the determination of the sampling rate is further based on a comparison between an assumption of an expected signal to noise ratio and a signal to noise ratio of a reconstructed signal that is based on the at least one sample (y_n).

27. An apparatus for signal processing, comprising:

means for obtaining an analog signal (y_t) based on another signal (x_t) and noise;

means for defining a sampling kernel based on the noise; and

means for using the sampling kernel to obtain at least one sample (y_n) from the analog signal (y_t).

28. The apparatus of claim 27, wherein a sampling rate for obtaining the at least one sample (y_n) is lower than the minimal sampling rate given by the Shannon theorem applied to the analog signal (y_t).

29. The apparatus of claim 27, wherein bandwidth of the sampling kernel is based on an estimate of the noise.

30. The apparatus of claim 27, further comprising means for estimating information relating to the another signal (x_t) through the use of an annihilating filter.

31. The apparatus of claim 30, further comprising means for defining the annihilating filter by performing a singular value decomposition method and minimizing a norm of a matrix associated with the singular value decomposition method.

32. The apparatus of claim 27, further comprising means for reconstructing the another signal (x_t) through use of an annihilating filter applied to the at least one sample (y_n).

33. The apparatus of claim 27, further comprising means for retrieving an estimate of shifts (t_k) associated with the another signal (x_t) through use of an annihilating filter.

34. The apparatus of claim 33, further comprising means for retrieving an estimate of weights (x_k) associated with the another signal (x_t).

35. The apparatus of claim 27, further comprising means for using a denoising process to provide a denoised signal (y′

_n) based on the at least one sample (y_n).

36. The apparatus of claim 27, further comprising means for determining a sampling rate for obtaining the at least one sample (y_n) based on an estimate of the noise.

37. The apparatus of claim 36, wherein the estimated noise comprises an estimated signal-to-noise ratio.

38. The apparatus of claim 36, wherein the determination of the sampling rate is further based on a desired level of accuracy for reconstructing the another signal (x_t).

39. The apparatus of claim 36, wherein the determination of the sampling rate is further based on a comparison between an assumption of an expected signal to noise ratio and a signal to noise ratio of a reconstructed signal that is based on the at least one sample (y_n).

40. A computer readable medium embodying a computer program product for signal processing, said computer program product comprising codes executable to:

obtain an analog signal (y_t) based on another signal (x_t) and noise;

define a sampling kernel based on the noise; and

use the sampling kernel to obtain at least one sample (y_n) from the analog signal (y_t).

41. A headset, comprising:

a circuit arranged to obtain an analog signal (y_t) based on another signal (x_t) and noise;

a sampler arranged to use a sampling kernel that is defined based on the noise to obtain at least one sample (y_n) from the analog signal (y_t); and

a transducer arranged to provide an audio output based on the at least one sample (y_n).

42. A watch, comprising:

a circuit arranged to obtain an analog signal (y_t) based on another signal (x_t) and noise;

a sampler arranged to use a sampling kernel that is defined based on the noise to obtain at least one sample (y_n) from the analog signal (y_t); and

a user interface arranged to provide an indication based on the at least one sample (y_n).

43. A sensing device, comprising:

a circuit arranged to obtain an analog signal (y_t) based on another signal (x_t) and noise;

a sampler arranged to use a sampling kernel that is defined based on the noise to obtain at least one sample (y_n) from the analog signal (y_t); and

a sensor arranged to sense based on the at least one sample (y_n).