Book description
A thorough guide to the classical and contemporary mathematical
methods of modern signal and image processing
Discrete Fourier Analysis and Wavelets presents a
thorough introduction to the mathematical foundations of signal and
image processing. Key concepts and applications are addressed in a
thought-provoking manner and are implemented using vector, matrix, and
linear algebra methods. With a balanced focus on mathematical theory
and computational techniques, this self-contained book equips readers
with the essential knowledge needed to transition smoothly from
mathematical models to practical digital data applications.
The book first establishes a complete vector space and matrix
framework for analyzing signals and images. Classical methods such as
the discrete Fourier transform, the discrete cosine transform, and
their application to JPEG compression are outlined followed by
coverage of the Fourier series and the general theory of inner product
spaces and orthogonal bases. The book then addresses convolution,
filtering, and windowing techniques for signals and images. Finally,
modern approaches are introduced, including wavelets and the theory of
filter banks as a means of understanding the multiscale localized
analysis underlying the JPEG 2000 compression standard.
Throughout the book, examples using image compression demonstrate how
mathematical theory translates into application. Additional
applications such as progressive transmission of images, image
denoising, spectrographic analysis, and edge detection are discussed.
Each chapter provides a series of exercises as well as a MATLAB
project that allows readers to apply mathematical concepts to solving
real problems. Additional MATLAB routines are available via the book's
related Web site.
With its insightful treatment of the underlying mathematics in image
compression and signal processing,
Discrete Fourier Analysis and Wavelets is an ideal
book for mathematics, engineering, and computer science courses at the
upper-undergraduate and beginning graduate levels. It is also a
valuable resource for mathematicians, engineers, and other
practitioners who would like to learn more about the relevance of
mathematics in digital data processing.
S. Allen Broughton, PhD, is Professor and Head of
Mathematics at the Rose-Hulman Institute of Technology. The author or
coauthor of over twenty published articles, Dr. Broughton's research
interests include finite group theory, Riemann surfaces, the
mathematics of image and signal processing, and wavelets.
Kurt Bryan, PhD, is Professor of Mathematics at the Rose-Hulman
Institute of Technology. Dr. Bryan has published more than twenty
journal articles, and he currently focuses his research on partial
differential equations related to electrical and thermal imaging.
