DISCRETE WAVELET TRANSFORMS ͳ THEORY AND APPLICATIONS Edited by Juuso Olkkonen Discrete Wavelet Transforms - Theory and Applications Edited by Juuso Olkkonen Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Ivana Lorkovic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright Arvind Balaraman, 2010. Used under license from Shutterstock.com First published March, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Discrete Wavelet Transforms - Theory and Applications, Edited by Juuso Olkkonen p. cm. ISBN 978-953-307-185-5 free online editions of InTech Books and Journals can be found at www.intechopen.com Part 1 Chapter 1 Chapter 2 Chapter 3 Part 2 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Preface IX Non-stationary Signals 1 Discrete Wavelet Analyses for Time Series 3 José S. Murguía and Haret C. Rosu Discrete Wavelet Transfom for Nonstationary Signal Processing 21 Yansong Wang, Weiwei Wu, Qiang Zhu and Gongqi Shen Transient Analysis and Motor Fault Detection using the Wavelet Transform 43 Jordi Cusidó i Roura and Jose Luis Romeral Martínez Image Processing and Analysis 61 A MAP-MRF Approach for Wavelet-Based Image Denoising 63 Alexandre L. M. Levada, Nelson D. A. Mascarenhas and Alberto Tannús Image Equalization Using Singular Value Decomposition and Discrete Wavelet Transform 87 Cagri Ozcinar, Hasan Demirel and Gholamreza Anbarjafari Probability Distribution Functions Based Face Recognition System Using Discrete Wavelet Subbands 95 Hasan Demirel and Gholamreza Anbarjafari An Improved Low Complexity Algorithm for 2-D Integer Lifting-Based Discrete Wavelet Transform Using Symmetric Mask-Based Scheme 113 Chih-Hsien Hsia, Jing-Ming Guo and Jen-Shiun Chiang Contents Contents VI Biomedical Applications 141 ECG Signal Compression Using Discrete Wavelet Transform 143 Mohammed Abo-Zahhad Shift Invariant Biorthogonal Discrete Wavelet Transform for EEG Signal Analysis 169 Juuso T. Olkkonen and Hannu Olkkonen Shift-Invariant DWT for Medical Image Classification 179 April Khademi, Sridhar Krishnan and Anastasios Venetsanopoulos Industrial Applications 213 Discrete Wavelet Transforms for Synchronization of Power Converters Connected to Electrical Grids 215 Alberto Pigazo and Víctor M. Moreno Discrete Wavelet Transform Based Wireless Digital Communication Systems 231 Ali A. A. Part 3 Chapter 8 Chapter 9 Chapter 10 Part 4 Chapter 11 Chapter 12 Pref ac e Discrete wavelet transform (DWT) algorithms have become standards tools for pro- cessing of signals and images in several areas in research and industry. The fi rst DWT structures were based on the compactly supported conjugate quadrature fi lters (CQFs). However, a drawback in CQFs is related to the nonlinear phase eff ects such as image blurring and spatial dislocations in multi-scale analyses. On the contrary, in biorthogo- nal discrete wavelet transform (BDWT) the scaling and wavelet fi lters are symmetric and linear phase. The BDWT algorithms are commonly constructed by a ladder-type network called li ing scheme. The procedure consists of sequential down and upli - ing steps and the reconstruction of the signal is made by running the li ing network in reverse order. Effi cient li ing BDWT structures have been developed for VLSI and microprocessor applications. The analysis and synthesis fi lters can be implemented by integer arithmetics using only register shi s and summations. Many BDWT-based data and image processing tools have outperformed the conventional discrete cosine transform (DCT) -based approaches. For example, in JPEG2000 Standard the DCT has been replaced by the li ing BDWT. As DWT provides both octave-scale frequency and spatial timing of the analyzed sig- nal, it is constantly used to solve and treat more and more advanced problems. One of the main diffi culties in multi-scale analysis is the dependency of the total energy of the wavelet coeffi cients in diff erent scales on the fractional shi s of the analysed signal. If we have a discrete signal x[n] and the corresponding time shi ed signal x[n-τ], where τ ∈ [0,1], there may exist a signifi cant diff erence in the energy of the wavelet coeffi cients as a function of the time shi . In shi invariant methods the real and imaginary parts of the complex wavelet coeffi cients are approximately a Hilbert transform pair. The energy of the wavelet coeffi cients equals the envelope, which provides smoothness and approximate shi -invariance. Using two parallel DWT banks, which are constructed so that the impulse responses of the scaling fi lters have half-sample delayed versions of each other, the corresponding wavelets are a Hilbert transform pair. The dual-tree CQF wavelet fi lters do not have coeffi cient symmetry and the nonlinearity interferes with the spatial timing in diff erent scales and prevents accurate statistical correlations. Therefore the current developments in theory and applications of wavelets are concen- trated on the dual-tree BDWT structures. This book reviews the recent progress in theory and applications of wavelet transform algorithms. The book is intended to cover a wide range of methods (e.g. li ing DWT, shi invariance, 2D image enhancement) for constructing DWTs and to illustrate the utilization of DWTs in several non-stationary problems and in biomedical as well as industrial applications. It is organized into four major parts. Part I focuses on non- X Preface stationary signals. Application examples include non-stationary fractal and chaotic time series, non-stationary vibration and sound signals in the vehicle engineering and motor fault detection. Part II addresses image processing and analysis applications such as image denoising and contrast enhancement, and face recognition. Part III is devoted to biomedical applications, including ECG signal compression, multi-scale analysis of EEG signals and classifi cation of medical images in computer aided diagnosis. Finally, Part IV describes how DWT can be utilized in wireless digital communication systems and synchronization of power converters. It should be pointed that the book comprises of both tutorial and advanced material. Therefore, it is intended to be a reference text for graduate students and researchers to obtain in-depth knowledge on specifi c applications. The editor is indebted to all co-authors for giving their valuable time and expertise in constructing this book. The technical editors are also acknowledged for their tedious support and help. Juuso T. Olkkonen, Ph.D. VTT Technical Research Centre of Finland Espoo, Finland . DISCRETE WAVELET TRANSFORMS ͳ THEORY AND APPLICATIONS Edited by Juuso Olkkonen Discrete Wavelet Transforms - Theory and Applications Edited by Juuso Olkkonen Published. current developments in theory and applications of wavelets are concen- trated on the dual-tree BDWT structures. This book reviews the recent progress in theory and applications of wavelet transform. vanishing moments if and only if it satisfies  ∞ −∞ t k ψ(t)dt = 0 for k = 0,1,. ,n −1 and  ∞ −∞ t k ψ(t)dt �= 0 for k = n. This means that 6 Discrete Wavelet Transforms - Theory and Applications fact,