Advertisement

The Wavelet Transform

  • Ram Shankar Pathak
Book

Part of the Atlantis Studies in Mathematics for Engineering and Science book series (ASMES, volume 4)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ram Shankar Pathak
    Pages 1-20
  3. Ram Shankar Pathak
    Pages 21-48
  4. Ram Shankar Pathak
    Pages 49-65
  5. Ram Shankar Pathak
    Pages 67-82
  6. Ram Shankar Pathak
    Pages 83-91
  7. Ram Shankar Pathak
    Pages 129-136
  8. Back Matter
    Pages 171-178

About this book

Introduction

The wavelet transform has emerged as one of the most promising function transforms with great potential in applications during the last four decades. The present monograph is an outcome of the recent researches by the author and his co-workers, most of which are not available in a book form. Nevertheless, it also contains the results of many other celebrated workers of the ?eld. The aim of the book is to enrich the theory of the wavelet transform and to provide new directions for further research in theory and applications of the wavelet transform. The book does not contain any sophisticated Mathematics. It is intended for graduate students of Mathematics, Physics and Engineering sciences, as well as interested researchers from other ?elds. The Fourier transform has wide applications in Pure and Applied Mathematics, Physics and Engineering sciences; but sometimes one has to make compromise with the results obtainedbytheFouriertransformwiththephysicalintuitions. ThereasonisthattheFourier transform does not re?ect the evolution over time of the (physical) spectrum and thus it contains no local information. The continuous wavelet transform (W f)(b,a), involving ? wavelet ?, translation parameterb and dilation parametera, overcomes these drawbacks of the Fourier transform by representing signals (time dependent functions) in the phase space (time/frequency) plane with a local frequency resolution. The Fourier transform is p n restricted to the domain L (R ) with 1 p 2, whereas the wavelet transform can be de?ned for 1 p

Keywords

Hilbert transformation Processing Sobolev space Sobolov space approximation theory convolution differential equation distribution equation form integral partial differential equation signal processing wavelet wavelet transform

Authors and affiliations

  • Ram Shankar Pathak
    • 1
  1. 1.Department of MathematicsBanaras Hindu UniversityVaranasiIndia

Bibliographic information