Fourier And Wavelet Signal Processing

The aim of this book is to provide a set of tools for users of state-of-the-art signal processing technology and a solid foundation for those hoping to advance the theory and practice of signal processing. Many of the results and techniques presented here, while rooted in classic Fourier techniques for signal representation, first appeared during a flurry of activity in the 1980s and 1990s. New constructions for local Fourier transforms and orthonormal wavelet bases during that period were motivated both by theoretical interest and by applications, in particular in multimedia communications. New bases with specified time–frequency behavior were found, with impact well beyond the original fields of application. Areas as diverse as computer graphics and numerical analysis embraced some of the new constructions—no surprise given the pervasive role of Fourier analysis in science and engineering.

Now that the dust has settled, some of what was new and esoteric is now fundamental. Our motivation is to bring these new fundamentals to a broader audience to further expand their impact. We thus provide an integrated view of classical Fourier analysis of signals and systems alongside structured representations with time–frequency locality and their myriad of applications.