Wavelet Basics

Since the study of wavelets is a relatively new area, much of the research coming from mathematicians uses terminology, concepts and proofs that may, at times, be difficult and intimidating for the engineer. This text has therefore been written as an introductory book for scientists and engineers. The mathematical presentation has been kept simple, the concepts being presented in detail and in a terminology that engineers will find familiar. Difficult ideas are illustrated with examples which will also aid in the development of an intuitive insight. Chapter 1 reviews the basics of signal transformation and discusses the concepts of duals and frames. Chapter 2 introduces the wavelet transform, contrasts it with the short-time Fourier transform and clarifies the names of the different types of wavelet transforms. Chapter 3 links multi-resolution analysis, orthonormal wavelets and the design of digital filters. Chapter 4 gives a tour d'horizon of topics of current interest such as wavelet packets and discrete time wavelet transforms and concludes with applications in signal processing.