Method and apparatus for reconstructing digitized distorted signals
First Claim
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1. A method for recovering an original analog signal from a sampling of the original analog signal, the method comprising:
- obtaining the samples by applying a first distortion to the original analog signal forming a distorted original analog signal and then sampling the distorted original signal by a first digitizing process forming a representation of digitized samples of the original signal;
calculating a signal representing an initial approximation of the original analog signal;
reconstructing the original analog signal by;
(a) applying a second distortion on the calculated signal forming a distorted calculated signal;
wherein said second distortion is substantially equivalent to the first distortion;
(b) sampling the distorted calculated signal by a second digitizing process;
wherein said second digitizing process is substantially equivalent to the first digitizing process forming a representation of digitized samples of the distorted calculated signal;
(c) comparing the representations by forming an error representation of the difference between the representations of the digitized samples of the original signal and the digitized samples of the calculated signal;
if the representations are substantially equivalent then the calculated signal is considered to be substantially equivalent to the original signal and the calculated signal is output;
otherwise the error representation is used to calculate a refined approximation of the original signal and the reconstructing of the original signal is performed iteratively using the refined calculated signal.
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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.
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Citations
24 Claims
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1. A method for recovering an original analog signal from a sampling of the original analog signal, the method comprising:
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obtaining the samples by applying a first distortion to the original analog signal forming a distorted original analog signal and then sampling the distorted original signal by a first digitizing process forming a representation of digitized samples of the original signal; calculating a signal representing an initial approximation of the original analog signal; reconstructing the original analog signal by; (a) applying a second distortion on the calculated signal forming a distorted calculated signal;
wherein said second distortion is substantially equivalent to the first distortion;(b) sampling the distorted calculated signal by a second digitizing process;
wherein said second digitizing process is substantially equivalent to the first digitizing process forming a representation of digitized samples of the distorted calculated signal;(c) comparing the representations by forming an error representation of the difference between the representations of the digitized samples of the original signal and the digitized samples of the calculated signal; if the representations are substantially equivalent then the calculated signal is considered to be substantially equivalent to the original signal and the calculated signal is output;
otherwise the error representation is used to calculate a refined approximation of the original signal and the reconstructing of the original signal is performed iteratively using the refined calculated signal. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
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17. An apparatus for reconstructing an original analog signal, comprising:
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an input/output (I/O) module for receiving a representation of digitized samples of a distorted version of the original analog signal distorted by a first distortion; an initial signal generator for generating an initial calculated signal of an approximation of the original analog signal; a distorting module for applying a second distortion on the calculated signal forming a distorted calculated signal;
wherein said second distortion is substantially equivalent to the first distortion;a sampler for sampling the distorted calculated signal forming a representation of digitized samples of the calculated signal;
wherein said sampler performs a sampling process that is substantially equivalent to a sampling process that obtained the digitized samples of the distorted version of the original analog signal; anda processing module for comparing the representations by forming an error representation of the difference between the representation of the digitized samples of the original signal and the digitized samples of the calculated signal; if the representations are substantially equivalent then the calculated signal is considered to be substantially equivalent to the original signal and the calculated signal is output from the I/O module by the processing module; otherwise the error representation is used to calculate a refined approximation of the original signal and the reconstructing of the original signal is performed iteratively using the refined calculated signal. - View Dependent Claims (18, 19, 20, 21, 22, 23, 24)
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Specification