Birkhauser Transforms and Fast Algorithms for Signal Analysis and Representations (Applied and Numerical Harmonic Analysis)

This book is a comprehensive presentation of recent results and developments on several widely used transforms and their fast algorithms. In many cases, new options are provided for improved or new fast algorithms, some of which are not well known in the digital signal processing community. The book is suitable as a textbook for senior undergraduate and graduate courses in digital signal processing. It may also serve as an excellent self-study reference for electrical engineers and applied mathematicians whose work is related to the fields of electronics, signal processing, image and speech processing, or digital design and communication. Review "This is perhaps the best text on transforms for signal processing since Nussbaumer's Fast Fourier Transform and Convolution Algorithms (Springer, 1982) and Elliott and Rao's, Fast Transforms: Algorithms, Analyses, Applications (Academic Press, 1982). Its nine chapters encompass almost all the knowledge needed to apply signal processing transforms successfully in practice. It is expected that the reader has had some exposure to transforms, so the first introductory chapter is very short; it mainly provides a sort of plan of things to come.... The authors have chosen to provide proofs only to essential theorems, like the Chinese remainder theorem, a good decision for a reference book, but perhaps not so good for a textbook. However, this book does lean more towards serving as a professional reference than does the more academic Nussbaumer text. The lack of proofs felt by some readers is largely offset by an abundance of concrete examples.... Chapter 8 is unique, in the sense that 'to the best of my knowledge' this material has never appeared in a book before. The chapter deals with integer transforms, which might be thought of as derived from the DCT and discrete sine transforms; these are gaining in popularity in various transform coding schemes for both video and audio.... In conclusion, this book is a highly practical and very welcome addition to the collection of texts on signal processing techniques and applications."   ―Analog Dialogue   ―