Ripples in Mathematics: The Discrete Wavelet Transform

✍ Scribed by Arne Jensen, Anders la Cour-Harbo (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 249
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-IX
Introduction....Pages 1-5
A First Example....Pages 7-10
The Discrete Wavelet Transform via Lifting....Pages 11-24
Analysis of Synthetic Signals....Pages 25-35
Interpretation....Pages 37-50
Two Dimensional Transforms....Pages 51-60
Lifting and Filters I....Pages 61-86
Wavelet Packets....Pages 87-98
The Time-Frequency Plane....Pages 99-126
Finite Signals....Pages 127-150
Implementation....Pages 151-187
Lifting and Filters II....Pages 189-209
Wavelets in Matlab....Pages 211-232
Applications and Outlook....Pages 233-237
Back Matter....Pages 239-246

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering;Analysis;Linear and Multilinear Algebras, Matrix Theory;Computational Intelligence;Image Processing and Computer Vision;Mathematical Methods in Physics