METHOD AND APPARATUS FOR RECONSTRUCTING DIGITIZED DISTORTED SIGNALS

• US 20100259428A1
• Filed: 10/29/2008
• Published: 10/14/2010
• Est. Priority Date: 10/30/2007
• Status: Active Grant

• Current Assignee: TECHNION RESEARCH AND DEVELOPMENT FOUNDATION, LTD. (Technion-Israel Institute Of Technology)
• Original Assignee: Technion City
• Inventors: Dvorkind, Tsvi Gregory, Eldar, Yonina
• Granted Patent: US 8,228,218 B2
• Time in Patent Office: Days
• US Class Current: 341/110
• CPC Class Codes: H03M 1/0614 of harmonic distortion H03M1/0617 takes precedence
• CPC Class Codes: H03M 1/12 Analogue/digital converters H03M1/001 – H03M1/10 take precedence

Abstract

A method of reproducing an original analog signal modified by a distortion and sampled. The distortion may be linear or nonlinear, and the samples may be either ideal or non-ideal. The method determines a stationary point of a cost function based on an error vector. The method iteratively computes approximated analog signals until the approximated analog signals converge to the original analog signal. The method may utilize Fr?chet derivatives and Moore-Penrose pseudo inverse transformations in order to iteratively compute the original analog signal. An apparatus performing said method is also disclosed.

Claims

1. A method for recovering an original analog signal from a sampling of the original analog signal, the original analog signal is modified by a first distortion and sampled by a first digitizing process, the method comprising:

obtaining a first signal representing an initial analog signal;

reconstructing the original analog signal by;

applying a second distortion on the first signal as a function of the first distortion thus obtaining a second signal representing a distorted version of the initial analog signal;

sampling the second signal by a second digitizing process substantially equivalent to the first digitizing process thus obtaining a sampling of the second signal;

providing a reconstructed analog signal based on the sampling of the original analog signal and the sampling of the second signal; and

outputting a signal based on the reconstructed analog signal.

2. The method of claim 1, wherein reconstructing the original analog signal is performed in a digital domain.

3. The method of claim 1, wherein reconstructing the original analog signal is performed in an analog domain.

4. The method of claim 1, wherein said step of obtaining the initial analog signal comprises generating the initial analog signal as a function of known characteristics of the original analog signal.

5. The method of claim 1, wherein the distortion is a nonlinear distortion.

6. The method of claim 5, wherein the first digitizing process is a non-ideal sampling process.

7. The method of claim 6, wherein the original analog signal represents audio data.

8. The method of claim 6, wherein the original analog signal represents visual or image data.

9. The method of claim 6, wherein the original analog signal represents temperature, air pressure or chemical process.

10. The method of claim 4, wherein the original analog signal is an electrical or electromagnetic signal.

11. The method of claim 5, wherein said step of reconstructing the original analog signal further comprises a step of computing an additional analog signal using an error vector based on the sampling of the second signal and samples of the original analog signal, wherein the additional analog signal is based on the initial analog signal;

and said step of providing the reconstructed analog signal is based on the additional analog signal.

12. The method of claim 11, wherein said step of reconstructing the original analog signal is performed in order to determine a stationary point in an error function based on the error vector.

13. The method of claim 11, wherein said step of reconstructing the original analog signal is performed iteratively.

14. The method of claim 13, wherein said step of iteratively reconstructing the original analog signal is completed upon a sufficient convergence of the additional analog signal or upon determination that the additional analog signal is substantially equivalent to the original analog signal.

15. The method of claim 14, wherein the first digitizing process is a non-ideal sampling process.

16. The method of claim 15, wherein said determination of the stationary point utilizes an inductive equation;

the inductive equation is a_n+1=a_n−

α

_ne(a_n).

17. The method of claim 16, wherein said determination of the stationary point utilizes a derivative.

18. The method of claim 17, wherein said determination of the stationary point utilizes an inductive equation;

the inductive equation is a_n+1=a_n−

α

_n(S*M′

_nA)^\e(a_n).

19. An apparatus for reconstructing an original analog signal;

said apparatus receiving samples of a distorted version of the original analog signal;

the apparatus comprises;

a distorting module for applying a first distortion on a signal representing an analog signal;

the first distortion is substantially equivalent to a second distortion affected the original analog signal;

a sampler for sampling a signal representing an analog signal;

said sampler for performing sampling substantially equivalent to a sampling process that obtained the samples of the distorted version of the original analog signal; and

a processing module for computing a first approximated analog signal.

20. The apparatus of claim 19, wherein said processing module computes the first approximated analog signal based on an initial analog signal or a second approximated analog signal;

the first approximated analog signal computed based on a second approximated analog signal is a changed approximation.

21. The apparatus of claim 20, wherein the changed approximation is a refined approximation.

22. The apparatus of claim 20 further comprising an error estimation module.

23. The apparatus of claim 21, wherein the first distortion is a nonlinear distortion.

24. The apparatus of claim 22, wherein the sampler is a non-ideal sampler.

25. The apparatus of claim 23 further comprising a digital-to-analog converter.

26. The apparatus of claim 19, wherein at least one of said distorting module, said sampler and said processing module operate in a digital domain.

27. The apparatus of claim 19, wherein said distorting module utilizes a module that caused the first distortion.

28. The apparatus of claim 19 wherein said sampler utilizes sampler module that performed the sampling process that obtained the samples of the distorted version of the original analog signal.