Lecture Notes on Wavelet Transforms

Lokenath Debnath, Firdous A. Shah (Autoren)

Buch | Softcover

XII, 220 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-59432-3 (ISBN)

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This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor.

These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets.

The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors' teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.

Lokenath Debnath is a Professor of Mathematics at the University of Texas-Pan American. Firdous A. Shah is a Professor of Mathematics at the University of Kashmir in India.

The Fourier Transform.- The Time-Frequency Analysis.- The Wavelet Transforms.- Construction of Wavelets via MRA.- Elongations of MRA Based Wavelets.

"This textbook is mainly written for advanced undergraduates and master students in mathematics, physics, computer sciences, and electrical engineering. It presents a short, well-written introduction to wavelet transforms and the underlying Fourier theory. ... This textbook is very convenient for all students interested in an introduction to wavelet transforms." (Manfred Tasche, zbMATH 1379.42001, 2018)

“This textbook is mainly written for advanced undergraduates and master students in mathematics, physics, computer sciences, and electrical engineering. It presents a short, well-written introduction to wavelet transforms and the underlying Fourier theory. … This textbook is very convenient for all students interested in an introduction to wavelet transforms.” (Manfred Tasche, zbMATH 1379.42001, 2018)

Erscheinungsdatum	29.09.2017
Reihe/Serie	Compact Textbooks in Mathematics
Zusatzinfo	XII, 220 p. 32 illus., 3 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	426 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Abstract harmonic analysis • Complex analysis, complex variables • fast wavelet transform • fourier analysis • Functional Analysis • Functional analysis & transforms • Functional analysis & transforms • Imaging Systems & Technology • Imaging Systems & Technology • Mathematics • mathematics and statistics • multiresolution analysis • Signal, Image and Speech Processing • Signal Processing • time-frequency analysis • Wavelets • wavelet transforms
ISBN-10	3-319-59432-X / 331959432X
ISBN-13	978-3-319-59432-3 / 9783319594323
Zustand	Neuware