An Introduction to Wavelet Analysis

A new text/reference offering a comprehensive and detailed presentation of wavelet theory, principles and methods. It presents basic theory of wavelet bases and transforms without assuming knowledge of advanced mathematics. The material is presented with many examples, exercises and thorough references. An essential text/reference for applied mathematicians, engineers and scientists. The goal of this book is to present the basics of wavelet theory in a complete, rigorous, and cogent fashion, but at a level that is truly appropriate for upper level undergraduates, first year graduate students, or anyone who has had a course in advanced calculus. The book presents the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by doing a detailed exposition of Haar series, and then shows how a more abstract approach allows us to generalize and improve upon Haar series. Once these ideas have been established and explored, variations and extensions of the Haar construction are presented. Applications of the theory are to be stressed throughout the book as a means of motivating the usefulness of the theory, but a more complete treatment of applications will be saved for the last three chapters of the book. The book will also include exercises at the end of each chapter.