DocumentCode :
1099553
Title :
Minimax Approximation of Representation Coefficients From Generalized Samples
Author :
Dvorkind, Tsvi G. ; Kirshner, Hagai ; Eldar, Yonina C. ; Porat, Moshe
Author_Institution :
Israel Inst. of Technol., Haifa
Volume :
55
Issue :
9
fYear :
2007
Firstpage :
4430
Lastpage :
4443
Abstract :
Many sources of information are of analog or continuous-time nature. However, digital signal processing applications rely on discrete data. We consider the problem of approximating L2 inner products, i.e., representation coefficients of a continuous-time signal, from its generalized samples. Adopting a robust approach, we process these generalized samples in a minimax optimal sense. Specifically, we minimize the worst approximation error of the desired representation coefficients by proper processing of the given sample sequence. We then extend our results to criteria which incorporate smoothness constraints on the unknown function. Finally, we compare our methods with the piecewise-constant approximation technique, commonly used for this problem, and discuss the possible improvements by the suggested schemes.
Keywords :
approximation theory; signal representation; signal sampling; continuous-time signal; digital signal processing; discrete data; generalized samples; minimax approximation; representation coefficients; robust approach; smoothness constraints; worst approximation error; Approximation error; Digital signal processing; Information resources; Interpolation; Minimax techniques; Robustness; Signal analysis; Signal sampling; Speech; Wavelet analysis; Generalized sampling; interpolation; robust approximation; smoothness;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2007.896284
Filename :
4291852
Link To Document :
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