A First Course in Wavelets with Fourier Analysis by Albert Boggess, Francis J.Narcowich

A First Course in Wavelets with Fourier Analysis by Albert Boggess, Francis J.Narcowich

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A comprehensive and autonomous treatment of Fourier analysis and wavelets, now in a new edition

Through extensive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition offers a self-contained mathematical treatment of Fourier and wavelet analysis, while presenting unique signal analysis problems and applications. The essential and foundational ideas are presented in an effort to make the book accessible to a wide audience, and its applications for signal processing remain at an elementary level.

The book begins with an introduction to vector spaces, interior product spaces, and other preliminary topics under discussion. Characteristic of later chapters:

The development of a Fourier series, Fourier transform and discrete Fourier analysis
Enhanced sections dedicated to continuous wavelets and two-dimensional wavelets
Analysis of Haar, Shannon and linear spline wavelets
The general theory of multiple resolution analysis.
Updated MATLAB code and extended applications for signal processing
The construction, smoothness and calculation of the Daubechies wavelets.
Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transformation

Applications for signal processing are provided throughout the book, most involving filtering and compression of audio or video signals. Some of these applications are first presented in the context of Fourier analysis and then explored in the wavelet chapters. New exercises present additional applications, and complete tests accompany the discussion of each theory presented. Extensive appendices describe more advanced tests and partial solutions for exercises, as well as updated MATLAB routines that complement the examples presented.

A First Course in Wavelets with Fourier Analysis, Second Edition, is an excellent book for math and engineering courses at the undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who want to learn about wavelet theory and Fourier analysis at the elementary level.

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