A First Course in Wavelets with Fourier AnalysisA comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature:
Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level. |
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Contents
Inner Product Spaces | 1 |
Exercises | 34 |
Fourier Series | 38 |
The Fourier Transform | 92 |
Discrete Fourier Analysis | 132 |
Haar Wavelet Analysis | 160 |
Multiresolution Analysis | 190 |
Exercises | 228 |
Other editions - View all
A First Course in Wavelets with Fourier Analysis Albert Boggess,Francis J. Narcowich Limited preview - 2011 |
A First Course in Wavelets with Fourier Analysis Albert Boggess,Francis J. Narcowich Limited preview - 2015 |