Wavelet Packets and Their Statistical Applications

Khalil Ahmad, Abdullah (Autoren)

Buch | Softcover

238 Seiten

2019 | Softcover reprint of the original 1st ed. 2018
Springer Verlag, Singapore
978-981-13-4375-9 (ISBN)

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This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.

Khalil Ahmad has been a Professor at the Department of Mathematics, Al-Falah University, India, since 2015. He previously served as a Professor at the Department of Mathematics, Jamia Millia Islamia, New Delhi, from 1975 to 2014, and worked at Aligarh Muslim University and DAV College, Kanpur. He received his PhD in Mathematics from the University of Delhi in 1982. His major fields of research are functional analysis and applicable mathematics. A life member of several academic societies such as the Indian Mathematical Society, Indian Society of Industrial and Applied Mathematics, Jammu Mathematical Society and Gwalior Academy of Mathematical Sciences, Professor Ahmad has over 50 research papers to his credit, published in national and international journals of repute. The author of 12 books, Professor Ahmad has delivered lectures at over 60 mathematical conferences. Abdullah is an Assistant Professor at the Department of Mathematics, Zakir Husain Delhi College, University of Delhi, New Delhi, India. His main fields of research are wavelet analysis and frame theory. He received his PhD in Mathematics from Jamia Millia Islamia, New Delhi, in 2007. Dr Abdullah has over 25 research papers to his credit and has attended more than 20 mathematical conferences.

Chapter 1. Preliminaries.- Chapter 2. Wavelet Packets.- Chapter 3. Convergence of Wavelet Packet Series.- Chapter 4. Function Spaces and Wavelet Packets.- Chapter 5. Applications in Signal Processing.- Chapter 6. Applications in Image Processing.

Erscheinungsdatum	20.06.2019
Reihe/Serie	Forum for Interdisciplinary Mathematics
Zusatzinfo	36 Illustrations, color; 34 Illustrations, black and white; XVII, 238 p. 70 illus., 36 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	denoising • function spaces • Image Processing • Signal Processing • Wavelet Packets • Wavelets
ISBN-10	981-13-4375-6 / 9811343756
ISBN-13	978-981-13-4375-9 / 9789811343759
Zustand	Neuware