Lecture Notes on Wavelet Transforms

1. Front Matter

   Pages i-xii

   PDF

2. The Fourier Transforms

   • Lokenath Debnath, Firdous A. Shah

   Pages 1-54

3. The Time-Frequency Analysis

   • Lokenath Debnath, Firdous A. Shah

   Pages 55-91

4. The Wavelet Transforms

   • Lokenath Debnath, Firdous A. Shah

   Pages 93-122

5. Construction of Wavelets via MRA

   • Lokenath Debnath, Firdous A. Shah

   Pages 123-153

6. Elongations of MRA-Based Wavelets

   • Lokenath Debnath, Firdous A. Shah

   Pages 155-209

7. Back Matter

   Pages 211-219

   PDF

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, ar

rangement, 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. 

• wavelet transforms
• time-frequency analysis
• multiresolution analysis
• fourier analysis
• wavelets
• Fast wavelet transform

“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)

• School of Mathematical and Statistical Sciences, University of Texas – Rio Grande Valley, Edinburg, USA

  Lokenath Debnath

• Department of Mathematics, University of Kashmir, Anantnag, India

  Firdous A. Shah

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. 

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