1. Introduction; 2. Normed vector spaces; 3. Analytic tools; 4. Fourier series; 5. Fourier transforms; 6. Compressive sensing; 7. Discrete transforms; 8. Linear filters; 9. Windowed Fourier transforms, continuous wavelets, frames; 10. Multiresolution analysis; 11. Discrete wavelet theory; 12. Biorthogonal filters and wavelets; 13. Parsimonious representation of data; Bibliography; Index.
Develops mathematical and probabilistic tools needed to give rigorous derivations and applications of fundamental results in signal processing theory.
Steven B. Damelin is currently Full Professor at Georgia Southern University and Visiting Full Professor at the University of the Witwatersrand in Johannesburg. Willard Miller, Jr is Professor Emeritus in the School of Mathematics at the University of Minnesota.
'Damelin and Miller provide a very detailed and thorough treatment
of all the important mathematics related to signal processing. This
includes the required background information found in elementary
mathematics courses, so their book is really self-contained. The
style of writing is suitable not only for mathematicians, but also
for practitioners from other areas. Indeed, Damelin and Miller
managed to write their text in a form that is accessible to
nonspecialists, without giving up mathematical rigor.' Kai
Diethelm, Computing Reviews
'In the last 20 years or so, many books on wavelets have been
published; most of them deal with wavelets from either the
engineering or the mathematics perspective, but few try to connect
the two viewpoints. The book under review falls under the last
category … Overall, the book is a good addition to the literature
on engineering mathematics.' Ahmed I. Zayed, Mathematical Reviews
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