Computational Signal Processing with Wavelets (Applied and Numerical Harmonic Analysis)

Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is due to many factors, not the least of which is that they offer an intuitively satisfying view of signals as being composed of little pieces of wa'ues. Making this concept mathematically precise has resulted in a deep and sophisticated wavelet theory that has seemingly limitless applications. This book and its supplementary hands-on electronic: component are meant to appeal to both students and professionals. Mathematics and en­ gineering students at the undergraduate and graduate levels will benefit greatly from the introductory treatment of the subject. Professionals and advanced students will find the overcomplete approach to signal represen­ tation and processing of great value. In all cases the electronic component of the proposed work greatly enhances its appeal by providing interactive numerical illustrations. A main goal is to provide a bridge between the theory and practice of wavelet-based signal processing. Intended to give the reader a balanced look at the subject, this book emphasizes both theoretical and practical issues of wavelet processing. A great deal of exposition is given in the beginning chapters and is meant to give the reader a firm understanding of the basics of the discrete and continuous wavelet transforms and their relationship. Later chapters promote the idea that overcomplete systems of wavelets are a rich and largely unexplored area that have demonstrable benefits to offer in many applications.

This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets.  With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. 

The text is written in a clear, accessible style avoiding unnecessary abstractions and details.  From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification.  Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the world wide web. 

Topics and Features:

* Continuous wavelet and Gabor transforms
* Frame-based theory of discretization and reconstruction of analog signals is developed
* New and efficient "overcomplete" wavelet transform is introduced and applied
* Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available

This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems.  Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools.