Wavelets and Other Orthogonal Systems

A bestselling text and reference in its first edition, Wavelets and Other Orthogonal Systems, Second Edition was fully updated and expanded to reflect the phenomenal growth and development of this field, especially in the area of multiwavelets. The authors incorporated more examples and numerous illustrations to help clarify concepts. They also added a considerable amount of new material, including sections addressing impulse trains, an alternate approach to periodic wavelets, and positive wavelets. Other discussions new to this edition address irregular sampling in wavelet subspaces, hybrid wavelet sampling, interpolating multiwavelets, and several additional statistics topics.

Walter, Gilbert G.; Shen, Xiaoping

Orthogonal Series. A Primer on Tempered Distributions. An Introduction to Orthogonal Wavelet Theory. Convergence and Summability of Fourier Series. Wavelets and Tempered Distributions. Orthogonal Polynomials. Other Orthogonal Systems. Pointwise Convergence of Wavelet Expansions. A Shannon Sampling Theorem in Wavelet subspaces. Extensions of Wavelet Sampling Theorems. Translation and Dilation Invariance in Orthogonal Systems. Analytic Representations via Orthogonal Series. Orthogonal Series in Statistics. Orthogonal Systems and Stochastic Processes.