Wavelets: An Analysis Tool (Oxford Mathematical Monographs)

Wavelets analysis—a new and rapidly growing field of research—has been applied to a wide range of endeavors, from signal data analysis (geoprospection, speech recognition, and singularity detection) to data compression (image and voice-signals) to pure mathematics. Written in an accessible, user-friendly style, Wavelets: An Analysis Tool offers a self-contained, example-packed introduction to the subject. Taking into account the continuous transform as well as its discretized version (the ortho-normal basis) the book begins by introducing the continuous wavelets transform in one dimension. It goes on to provide detailed discussions of wavelet analysis of regular functions, tempered distributions, square integrable functions, and the continuous wavelet transform. Throughout, the language of group theory is used to unify various approaches. Profusely illustrated and containing information not available elsewhere, this book is ideal for advanced students and researchers in mathematics, physics, and signal processing engineering.