The Wavelet Transforms and Their Basic Properties

Abstract

Morlet et al. (1982a,b) modified the Gabor wavelets to study the layering of sediments in a geophysical problem of oil exploration. He recognized certain difficulties of the Gabor wavelets in the sense that the Gabor analyzing function g t, ω(τ) = g(τ − t) e iωτ oscillates more rapidly as the frequency ω tends to infinity. This leads to significant numerical instability in the computation of the coefficients 〈f, g ω, t 〉.