Skip to main content
SpringerLink
Log in

Ripples in Mathematics

The Discrete Wavelet Transform

  • Textbook
  • © 2001

Overview

Authors:
  1. Arne Jensen

    1. Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Anders Cour-Harbo

    1. Department of Control Engineering, Aalborg University, Aalborg, Denmark

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Based on a novel approach to discrete wavelets called lifting

  • Elementary introduction

  • Problems with finite length signals are treated in detail

  • MATLAB is used as the computational environment for examples and implementations

  • Includes supplementary material: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 59.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Introduction

    • Arne Jensen, Anders la Cour-Harbo
    Pages 1-5

  3. A First Example

    • Arne Jensen, Anders la Cour-Harbo
    Pages 7-10

  4. The Discrete Wavelet Transform via Lifting

    • Arne Jensen, Anders la Cour-Harbo
    Pages 11-24

  5. Analysis of Synthetic Signals

    • Arne Jensen, Anders la Cour-Harbo
    Pages 25-35

  6. Interpretation

    • Arne Jensen, Anders la Cour-Harbo
    Pages 37-50

  7. Two Dimensional Transforms

    • Arne Jensen, Anders la Cour-Harbo
    Pages 51-60

  8. Lifting and Filters I

    • Arne Jensen, Anders la Cour-Harbo
    Pages 61-86

  9. Wavelet Packets

    • Arne Jensen, Anders la Cour-Harbo
    Pages 87-98

  10. The Time-Frequency Plane

    • Arne Jensen, Anders la Cour-Harbo
    Pages 99-126

  11. Finite Signals

    • Arne Jensen, Anders la Cour-Harbo
    Pages 127-150

  12. Implementation

    • Arne Jensen, Anders la Cour-Harbo
    Pages 151-187

  13. Lifting and Filters II

    • Arne Jensen, Anders la Cour-Harbo
    Pages 189-209

  14. Wavelets in Matlab

    • Arne Jensen, Anders la Cour-Harbo
    Pages 211-232

  15. Applications and Outlook

    • Arne Jensen, Anders la Cour-Harbo
    Pages 233-237

  16. Back Matter

    Pages 239-246
    Download chapter PDF
Back to top

Keywords

About this book

Yet another book on wavelets. There are many books on wavelets available, written for readers with different backgrounds. But the topic is becoming ever more important in mainstream signal processing, since the new JPEG2000 standard is based on wavelet techniques. Wavelet techniques are also impor­ tant in the MPEG-4 standard. So we thought that there might be room for yet another book on wavelets. This one is limited in scope, since it only covers the discrete wavelet trans­ form, which is central in modern digital signal processing. The presentation is based on the lifting technique discovered by W. Sweldens in 1994. Due to a result by I. Daubechies and W. Sweldens from 1996 this approach covers the same class of discrete wavelet transforms as the one based on two channel filter banks with perfect reconstruction. The goal of this book is to enable readers, with modest backgrounds in mathematics, signal analysis, and programming, to understand wavelet based techniques in signal analysis, and perhaps to enable them to apply such methods to real world problems. The book started as a set of lecture notes, written in Danish, for a group of teachers of signal analysis at Danish Engineering Colleges. The material has also been presented to groups of engineers working in industry, and used in mathematics courses at Aalborg University.

Reviews

From the reviews:

"This book is a very well-written introduction to discrete wavelet transforms, very convenient for students in electrical engineering, computer science, and applied mathematics. It is based on the lifting approach to discrete wavelet transforms ... . MATLAB is used as the computational environment for examples and implementations of discrete wavelet transforms." (Manfred Tasche, Zentralblatt MATH, Vol. 989 (14), 2002)

"This is an algorithm based, completely elementary introduction to the discrete wavelet transform (DWT) and wavelet packet transform, easy to read and easy to understand, well suited for an introductory course on wavelets for undergraduate students of applied sciences or mathematics. ... Implementations and examples using basic Matlab (TM) as well as the public domain ubi-wave wavelet toolbox help to further a deeper understanding of the algorithms." (C. Cenker, Internationale Mathematische Nachrichten, Vol. 56 (189), 2002)

"This book gives an introduction to the discrete wavelet transform and some of its applications. It is based on a novel approach to discrete wavelets called lifting. ... MATLAB is used as the computational environment for examples and implementation of transforms. The book is well suited for undergraduate mathematics and electrical engineering students and engineers in industry." (ETDE Energy Database, December, 2001)

Authors and Affiliations

  • Department of Mathematical Sciences, Aalborg University, Aalborg, Denmark

    Arne Jensen

  • Department of Control Engineering, Aalborg University, Aalborg, Denmark

    Anders Cour-Harbo

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation