Math 472/572 - Fourier analysis and wavelets
FOURIER ANALYSIS AND WAVELETS
The literature for Fourier Analysis and Wavelets is large. Here is a commented
list of texts appropriate for different audiences.
- Good for undergraduates with strong linear algebra background:
An Introduction to Wavelets Through Linear Algebra
Michael Frazier Springer Verlag, Feb 1999; ISBN: 0387986391.
- More appropriate for graduate students:
Introduction to Fourier Analysis and Wavelets
by Mark A. Pinsky.
The Brooks/Cole Series in Advanced Mathematics, 2002;
- This book is of encyclopedic nature, excellent for graduate students
in engineering and also in statistics/math:
A Wavelet Tour of Signal Processing. The sparse way
Third Edition, Academic Press, 2008; ISBN 978-0123743701
There are many excellent books devoted to the classical theory of
Fourier analysis (starting with Trigonometric Series by A. Zygmund
2nd edition, Cambridge University Press, Cambridge 1959,
and following with a long list).
- Appropriate for advanced undergraduate students:
Fourier Analysis: An Introduction
by E. M. Stein and R. Shakarchi,
Princeton lectures in Analysis I, Princeton University Press, 2003;
- Appropriate for advanced undergraduate students, full of historical
notes and anecdotes: Fourier Analysis
by T. Korner. Cambridge University Press, 1989;
- A bit more advanced: Fourier series and integrals
by H. Dym and H.P. McKean.
Academic Press, 1986; ISBN: 0122264517
- A bit more advanced: An Introduction to Harmonic Analysis
by Y. Katznelson.
Dover Publications Inc. New York, NY 1976;
In the last 15-20 years there have been
published a number of books on wavelets,
as well as countless articles. Here is a limited guide:
- A classic, for graduate students: Ten lectures on wavelets, by Ingrid Daubechies, 1992.
- For graduate students: A mathematical introduction to wavelets, by P. Wojtaszczyk, 1997.
- For advanced graduate students: A first course on wavelets, by E. Hernandez and G.
- For advanced graduate students: Wavelets and operators, by Yves Meyer, 1992.
For a wider audience or emphasis on applications
- Wavelets and Filter Banks, by G. Strang and
T. Nguyen, 1996.
- An introduction to wavelets, by C. K. Chui, 1992.
- A friendly guide to wavelets, by G. Keiser, 1994.
There is a wealth of information available at
- The world according to wavelets, by B. Burke Hubbard,
2nd edition, 1998.
- Wavelets: Tools for science and technology, by
S. Jaffard, Y. Meyer, R. D. Ryan, 2001.
Department of Mathematics and Statistics,
University of New Mexico
Last updated: August 6, 2019