FOURIER ANALYSIS TO WAVELET ANALYSIS

Print ISSN: 2319-1023

Abstract

From a very modest presentation as an introductory composition of wavelets by Chui in 1992 to a very specialist and advanced monographs by Meyer in 1990, and by Daubechies in 1992, one will certainly experience the beauty of this subject, which in the recent time has attracted both the pure and applied mathematicians. Wavelet transform, more correctly called the integral wavelet transform, is one of the two entities of the wavelet analysis. Possibly the window Fourier transform, also called the Gabor transform ( rst introduced by Gabor in 1946), is the initiation for wavelet transform. In this brief note we attempt to discuss some of its aspects.

Keywords and Phrases

Wavelet transform, Fourier transform, Gabor transform, Multiresolution analysis, Wavelet series, Fourier series, General distributions, Tempered distributions.

A.M.S. subject classification

42A38, 42B05, 42C40, 65T50, 65T60, 65T99.

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