Sampling approximation of smooth functions via generalized coiflets

Author

Wei, Dong ; Bovik, Alan C.

Author_Institution

Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA

Volume

46

Issue

4

fYear

1998

fDate

4/1/1998 12:00:00 AM

Firstpage

1133

Lastpage

1138

Abstract

We present the sampling approximation power of a newly constructed class of compactly supported orthonormal wavelets called generalized coiflets. We study the accuracy of generalized coiflets-based sampling approximation of smooth functions by developing convergence rates for the pointwise approximation error as well as its L^P-norm. We show: (i) that the L²-error due to the approximation of expansion coefficients by function samples is asymptotically negligible compared with that due to projection and (ii) that generalized coiflets can achieve asymptotically better approximation than the original coiflets

Keywords

approximation theory; convergence of numerical methods; error analysis; signal resolution; signal sampling; smoothing methods; wavelet transforms; L²-error; L^P-norm; asymptotic approximation; compactly supported orthonormal wavelets; convergence rates; expansion coefficients; generalized coiflets; multiresolution analysis; pointwise approximation error; projection; sampling approximation; signal processing; smooth functions; Algorithm design and analysis; Autocorrelation; Equations; Fourier transforms; Sampling methods; Signal design; Signal processing; Signal processing algorithms; Signal resolution; Wavelet analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.668564

Filename

668564