Wavelet Transforms: Kith and Kin (Textbooks in Mathematics)

Wavelet Transforms: Kith and Kin serves as an introduction to contemporary aspects of time-frequency analysis encompassing the theories of Fourier transforms, wavelet transforms and their respective offshoots.

This book is the first of its kind totally devoted to the treatment of continuous signals and it systematically encompasses the theory of Fourier transforms, wavelet transforms, geometrical wavelet transforms and their ramifications. The authors intend to motivate and stimulate interest among mathematicians, computer scientists, engineers and physical, chemical and biological scientists.

The text is written from the ground up with target readers being senior undergraduate and first-year graduate students and it can serve as a reference for professionals in mathematics, engineering and applied sciences.

Features

• Flexibility in the book’s organization enables instructors to select chapters appropriate to courses of different lengths, emphasis and levels of difficulty

• Self-contained, the text provides an impetus to the contemporary developments in the signal processing aspects of wavelet theory at the forefront of research

• A large number of worked-out examples are included

• Every major concept is presented with explanations, limitations and subsequent developments, with emphasis on applications in science and engineering

• A wide range of exercises are incoporated in varying levels from elementary to challenging so readers may develop both manipulative skills in theory wavelets and deeper insight

• Answers and hints for selected exercises appear at the end

The origin of the theory of wavelet transforms dates back to the 1980s as an outcome of the intriguing efforts of mathematicians, physicists and engineers. Owing to the lucid mathematical framework and versatile applicability, the theory of wavelet transforms is now a nucleus of shared aspirations and ideas.

Firdous A. Shah earned his post-graduate degree in pure mathematics from the University of Kashmir and a PhD in applied mathematics from the Central University, Jamia Millia Islamia, New Delhi, India. He is an associate professor of mathematics at the University of Kashmir, South Campus, India. His research interests include the theory of wavelets, time-frequency analysis, abstract harmonic analysis, sampling theory and applications of wavelets to signal processing and mathematical biology. He is the author/co-author of over 150 journal articles and has co-authored two books with Prof. Lokenath Debnath (University of Texas) on wavelet transforms and their applications, published by Birkhauser, Springer. He has received numerous research grants from NBHM and SERB-DST, Govt. of India. He serves as an editorial board member of several reputed journals and is a lifetime member of several academic societies.

Azhar Y. Tantary is a native of Jammu and Kashmir, India. He completed his BSc and MSc degrees in mathematics from the University of Kashmir during the academic sessions 2010-2012 and 2013-2014, respectively. Presently, he is a researcher in the Department of Mathematics, South Campus, University of Kashmir. His broad field of research is wavelet theory and his research interests include integral transforms, sampling theory and mathematical signal processing. He has authored/co-authored more than 15 research articles in different journals of international repute. He has also presented his research at various national and international forums and has received several awards for excellence in research.