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Wavelet Packets and Their Statistical Applications

  • Khalil Ahmad
  • Abdullah

Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Khalil Ahmad, Abdullah
    Pages 1-36
  3. Khalil Ahmad, Abdullah
    Pages 37-77
  4. Khalil Ahmad, Abdullah
    Pages 79-91
  5. Khalil Ahmad, Abdullah
    Pages 93-129
  6. Khalil Ahmad, Abdullah
    Pages 131-201
  7. Khalil Ahmad, Abdullah
    Pages 203-224
  8. Back Matter
    Pages 225-238

About this book

Introduction

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.

Keywords

Wavelets Wavelet packets Signal Processing Image Processing Denoising Function Spaces

Authors and affiliations

  • Khalil Ahmad
    • 1
  • Abdullah
    • 2
  1. 1.Department of MathematicsAl-Falah UniversityFaridabadIndia
  2. 2.Department of MathematicsZakir Husain Delhi CollegeNew DelhiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-13-0268-8
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-13-0267-1
  • Online ISBN 978-981-13-0268-8
  • Series Print ISSN 2364-6748
  • Series Online ISSN 2364-6756
  • Buy this book on publisher's site