International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 270492, 13 pages
doi:10.1155/2009/270492

Asymptotic expansions of the wavelet transform for large and small values of $b$

Abstract

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.