This resource examines both theoretical and practical aspects of computational signal processing using wavelets. Computationally, wavelet signal processing algorithms are presented and applied to signal compression, noise supression, and signal identification. Numerical illustrations of these computational techniques are further discussed in the text (using MATLAB) and the software M-Files are available via the World Wide Web site for the book. Starting from basic principles of signal representation with atomic functions, a mathematically well-founded theory of the discretization of analogue signals is developed. General families are specialized to wavelet families, with discrete representation specialized to generally non-orthogonal wavelet transforms. The theory leads naturally to the computer implementation of the non-orthagonal wavelet transform. Specific topics covered include general signal representation, continuous wavelet transform, multi-resolution analysis, continuous wavelet transform, non-orthagonal wavelet transform, and wavelet based signal processing algorithms for compression, noise supression, and identification.
The technical discussion is at the begninning graduate level and is accessible to all signal processing professionals and practitioners.