Wavelets: A Mathematical Tool for Signal Analysis

Wavelets continue to be powerful mathematical tools for solving problems where the Fourier (spectral) method does not perform well or cannot be used. This text is for engineers, applied mathematicians and other scientists who want to learn about using wavelets to analyze, process and synthesize images and signals. Applications are described in detail and there are step-by-step instructions about how to construct and apply wavelets. A mathematically rigorous monograph, the book was written specifically by a mathematician for non-specialists. It describes the basic concepts of these mathematical techniques, outlines the procedures for using them, compares the performance of various approaches and provides information for problem solving. Methods and topics include: multidimensional and multifrequency wavelet transforms; spline wavelets with uniform or arbitrary knots on a bounded interval; procedures to construct all the well-known wavelets and to find their corresponding filter sequences; and detailed comparisons of the most popular wavelets with tables of values for evaluating their filtering performance.