One and two dimensional discrete wavelet transforms

Abstract

Fourier transform techniques have been the favored methods in the analysis of signals and systems. One major drawback of Fourier methods is the difficulty in analyzing transient and/or non-stationary behavior. Recent advances in the field of wavelet theory show much promise in alleviating these problems. This thesis considers the realizations of the wavelet decomposition and reconstruction algorithms for the discrete case. The major discussion will involve both the one and two dimensional transforms. We also present a multiple-phase development as a second and possibly a preferable method for decomposing signals.