A First Course in Wavelets with Fourier Analysis (PDF)

A 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:

* The development of a Fourier series, Fourier transform, and
discrete Fourier analysis

* Improved sections devoted to continuous wavelets and
two-dimensional wavelets

* The analysis of Haar, Shannon, and linear spline wavelets

* The general theory of multi-resolution analysis

* Updated MATLAB code and expanded applications to signal
processing

* The construction, smoothness, and computation of Daubechies'
wavelets

* Advanced topics such as wavelets in higher dimensions,
decomposition and reconstruction, and wavelet transform

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.