Overview
- Includes extensive appendices on Systems and Filters and the Z Transform
- Emphasis is given on ideas and intuition rather than heavy computations
- Provides great detail on different types of wavelets: Orthogonal Wavelets, Biorthogonal Wavelets, Wavelet Design, and Constructing Wavelets
Part of the book series: IMPA Monographs (IMPA, volume 3)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed.
Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable.
This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Reviews
“The authors present a short textbook about the fundamentals of Fourier analysis (such as Fourier series, Fourier transform, and windowed Fourier transform) and wavelet theory (such as continuous/discrete wavelet transforms, multiresolution analysis, decomposition/reconstruction algorithms, and construction of orthogonal/biorthogonal wavelets) with emphasis on the underlying ideas. … This textbook is mainly written for students in computer science, physics, and engineering.” (Manfred Tasche, zbMATH, Vol. 1325.42001, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: From Fourier Analysis to Wavelets
Authors: Jonas Gomes, Luiz Velho
Series Title: IMPA Monographs
DOI: https://doi.org/10.1007/978-3-319-22075-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2015
Hardcover ISBN: 978-3-319-22074-1Published: 25 September 2015
Softcover ISBN: 978-3-319-37022-4Published: 22 October 2016
eBook ISBN: 978-3-319-22075-8Published: 15 September 2015
Edition Number: 1
Number of Pages: XIII, 210
Number of Illustrations: 77 b/w illustrations
Topics: Fourier Analysis, Abstract Harmonic Analysis, Signal, Image and Speech Processing