"This book is suitable as a textbook for an introductory undergraduate
mathematics course on discrete Fourier and wavelet transforms for
students with background in calculus and linear algebra. The particular
strength of this book is its accessibility to students with no
background in analysis. The exercises and computer explorations provide
the reader with many opportunities for active learning. Studying from
this text will also help students strengthen their background in linear
algebra."
Mathematical Association of America
This textbook for undergraduate mathematics, science, and engineering
students introduces the theory and applications of discrete Fourier and
wavelet transforms using elementary linear algebra, without assuming
prior knowledge of signal processing or advanced analysis.
It explains how to use the Fourier matrix to extract frequency
information from a digital signal and how to use circulant matrices to
emphasize selected frequency ranges. It introduces discrete wavelet
transforms for digital signals through the lifting method and
illustrates through examples and computer explorations how these
transforms are used in signal and image processing. Then the general
theory of discrete wavelet transforms is developed via the matrix
algebra of two-channel filter banks. Finally, wavelet transforms for
analog signals are constructed based on filter bank results already
presented, and the mathematical framework of multiresolution analysis is
examined.
