Wavelets and filter banks. A signal processing perspective

Abstract

Wavelets are a relative newcomer to signal decomposition, and offer a flexible analog transform to provide multiresolution signal decomposition. Their advantages over Fourier and short-time Fourier transforms (STFTs) are significant, and the linkages and practical commonalities of these two transform techniques have generated interdisciplinary research activities among mathematicians, physicists and electrical engineers. This article presents the fundamentals of wavelet transform theory. In this context, the subject's mathematical rigor is avoided. We discuss the differences between the conventional STFT and wavelet transforms from a time-frequency "tiling" point of view. Then, we highlight the significant role of discrete-time filter banks in wavelet theory, and assess the practicality of wavelets in signal processing applications.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>