From Fourier Analysis to Wavelets by Jonas Gomes, et al.
From Fourier Analysis to Wavelets - Table of Contents
1. Preamble
2. Introduction by Alain Fournier
3. Multiresolution and Wavelets by Leena-Maija Reissell
4. Building Your Own Wavelets at Home by Wim Sweldens, Peter Schröder
5. Wavelets, Signal Compression and Image Processing by Wim Sweldens
6. Curves and Surfaces by Leena-Maija Reissell, Tony D. DeRose, Michael Lounsbery
7. Wavelet Radiosity by Peter Schröder
8. More Applications by Michael F. Cohen, Wim Sweldens, Alain Fournier
9. Pointers and Conclusions
What You Will Learn in From Fourier Analysis to Wavelets
"From Fourier Analysis to Wavelets" by Jonas Gomes and Luiz Velho is a clear introduction to modern "signal processing" techniques, connecting classical "Fourier analysis" with "wavelet transforms". The book starts with the fundamentals of the "Fourier transform" and windowed Fourier transform, building a foundation for understanding multiresolution representations of signals and functions. It emphasizes conceptual understanding while gradually introducing practical tools for function decomposition and reconstruction in both continuous and discrete domains.
The text covers essential topics such as "filter banks", orthogonal and biorthogonal wavelets, and the Fast Wavelet Transform, illustrating how these methods extend Fourier techniques to capture local signal features efficiently. It also includes appendices on linear systems, filtering, and the Z transform, providing context and mathematical tools that support the transition from classical to modern analysis frameworks.
Designed for students and practitioners with a background in linear algebra and calculus, "From Fourier Analysis to Wavelets" bridges theory and application. By combining "Fourier analysis", "wavelet transforms", and multiresolution ideas, it equips readers to analyze and process signals effectively in applications ranging from image and audio processing to applied mathematics and engineering. The book balances rigor with clarity, making complex concepts accessible without sacrificing depth.
Book Details & Specifications
Title:
From Fourier Analysis to Wavelets by Jonas Gomes, et al.
Publisher:
California Institute of Technology
Year:
1994
Pages:
239
Type:
PDF
Language:
English
ISBN-10 #:
1558603751
ISBN-13 #:
978-1558603752
License:
External Educational Resource
Amazon:
Amazon
About the Author: Jonas Gomes and Luiz Velho
The author
Jonas Gomes and Luiz Velho
are leading mathematicians in "computational mathematics" and "signal processing". Gomes is a professor at IMPA, Brazil, specializing in computer graphics, modeling, and visualization, while Velho focuses on applied mathematics and digital imaging. Their work provides a clear introduction to "Fourier transforms", "wavelets", and multiresolution methods. It blends rigorous "mathematical analysis" with practical applications, making complex concepts accessible for students, engineers, and researchers.
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