Open AccessAsymptotic Expansions of the Wavelet Transform for Large and Small Values of b
Author(s) -
R. S. Pathak,
Ashish Pathak
Publication year - 2009
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/2009/270492
Subject(s) - mathematics , morlet wavelet , wavelet transform , wavelet , discrete wavelet transform , fourier transform , harmonic wavelet transform , mathematical analysis , function (biology) , asymptotic expansion , stationary wavelet transform , artificial intelligence , computer science , biology , evolutionary biology
Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values of b when asymptotic expansions of the function and the wavelet near origin are given
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