**Meet the editor**

Dr Salih Mohammed Salih (Member IEEE) was born in Babylon-1970. He received the B.Sc. degree from the Electrical Department, University of Baghdad (1999- Iraq), M.Sc. and Ph.D. degrees in Communication Engineering from the University of Technology-Iraq in 2003 and 2008 respectively. Part of his Ph.D. was completed at the National Technical University of Athens (Scholar-

ship: 2006-2007). Since 2005, he has been working at the University of Anbar-Iraq, where he is a lecturer in Electrical Engineering Department. His research interests include MC-CDMA, OFDM, Wireless Communication, Signal Processing, Optical Communication, Radar, Computer Networks, Security, and Renewable Energy Resources. He published more than 30 papers in different international Journals and Conferences.

Contents

**Preface IX** 

Krzysztof Duda

Omar Mustaf

Lianming Sun

Chapter 3 **FFT-Based Efficient Algorithms** 

Chapter 4 **Channel Identification for OFDM** 

**Part 1 DFT and FFT Applications 1** 

Chapter 1 **Interpolation Algorithms of DFT for Parameters** 

Chapter 2 **A Proposed Model-Based Adaptive System** 

**for Time Delay Estimation 55** 

Renbiao Wu, Wenyi Wang and Qiongqiong Jia

Chapter 5 **Fast Fourier Transform Processors: Implementing** 

Somayeh Mohammady, Nasri Sulaiman,

A. Cortés, I. Vélez, M. Turrillas and J. F. Sevillano

Chapter 6 **FPGA Implementation of Inverse Fast Fourier Transform** 

Chapter 7 **Fault Diagnosis of Induction Motors Based on FFT 157** 

**Communication System in Frequency Domain 81** 

**FFT and IFFT Cores for OFDM Communication Systems 111** 

**in Orthogonal Frequency Division Multiplexing Systems 135** 

Roslina M. Sidek, Pooria Varahram, and M. Nizar Hamidon

Castelli Marcelo, Juan Pablo Fossatti and José Ignacio Terra

**Estimation of Sinusoidal and Damped Sinusoidal Signals 3** 

**for DFT Coefficients Estimation Using SIMULINK 33** 

## Contents

### **Preface XI**


#### X Contents

### **Part 2 Time, Frequency and Phase Estimation 183**


#### **Part 3 Image Processing 277**


## Preface

This book focuses on the Fourier transform applications in signal processing techniques. The field of signal processing has seen explosive growth during the past decades, as phenomenal advances both in research and application have been made. During the preparation of this book, we found that almost all the textbooks on signal processing have a section devoted to the Fourier transform theory. Most of those describe some formulas and algorithms, but one can easily be lost in seemingly incomprehensible mathematics. The basic idea behind all those horrible looking formulas is rather simple, even fascinating: *it is possible to form any function as a summation of a series of sine and cosine terms of increasing frequency*. In other words, any space or time varying data can be transformed into a different domain called the *frequency space*. A fellow called *Joseph Fourier* first came up with the idea in the 19th century, and it was proven to be useful in various applications, mainly in signal processing. As far as we can tell, Gauss was the first to propose the techniques that we now call the Fast Fourier Transform (FFT) for calculating the coefficients in a trigonometric expansion of an asteroid's orbit in 1805. However, it was the seminal paper by Cooley and Tukey in 1965 that caught the attention of the science and engineering community and, in a way, founded the discipline of Digital Signal Processing (DSP). While the Discrete Fourier Transform (DFT) transform can be applied to any complex valued series, in practice for large series it can take considerable time to compute, the time taken being proportional to the square of the number on points in the series. It is hard to overemphasis the importance of the DFT, convolution, and fast algorithms. The FFT may be the most important numerical algorithm in science, engineering, and applied mathematics. New theoretical results still are appearing, advances in computers and hardware continually restate the basic questions, and new applications open new areas for research. It is hoped that this book will provide the background, references and incentive to encourage further research and results in this area as well as provide tools for practical applications. One of the attractive features of this book is the inclusion of extensive simple, but practical, examples that expose the reader to real-life signal processing problems, which has been made possible by the use of computers in solving practical design problems. The aim of this book is to expand the analysis of many topics related to Fourier transform. It includes three sections:

#### X Preface

The first section deals with *DFT and FFT algorithms and their applications*. It consists of seven chapters. The first two chapters are related to the DFT: Interpolation of DFT, and DFT coefficients estimation, while the last five chapters are related to the FFT applications: FFT-based efficient algorithms for time delay estimation, channel identification for OFDM communication system, implementing FFT and IFFT cores for OFDM communication systems, FPGA implementation of IFFT in OFDM systems, fault diagnosis of induction motors based on FFT.

The chapters of the second section discuss some advanced methods used in Fourier transform analysis which are related to the *time, frequency, and phase estimation.*

This section consists of four chapters, the chapters are related to: estimation of the periodic signal parameters in the frequency domain, the uncertainty principles in the Fourier transform, the chirp excitation for estimation of bioimpedance spectrum, and the identification of systems via simple signals.

The third section includes the Fourier transform applications in *image processing techniques*. This section consists of four chapters, the chapters are concerns to: the invariant correlation using a nonlinear filter, the pattern recognition of digital images by one-dimensional signatures, the vectorial signatures for pattern recognition, and the multidimensional features extraction methods in frequency domain.

Finally, we would like to thank all the authors who have participated in this book for their valuable contribution. Also we would like to thank all the reviewers for their valuable notes. While there is no doubt that this book may have omitted some significant findings in the Fourier transform field, we hope the information included will be useful for Electrical Engineers, Communication Engineers, Signal Processing Engineers and the Mathematicians, in addition to the academic researchers working in this field.

> **Salih Mohammed Salih** College of Engineering University of Anbar Iraq

X Preface

this field.

The first section deals with *DFT and FFT algorithms and their applications*. It consists of seven chapters. The first two chapters are related to the DFT: Interpolation of DFT, and DFT coefficients estimation, while the last five chapters are related to the FFT applications: FFT-based efficient algorithms for time delay estimation, channel identification for OFDM communication system, implementing FFT and IFFT cores for OFDM communication systems, FPGA implementation of IFFT in OFDM systems,

The chapters of the second section discuss some advanced methods used in Fourier

This section consists of four chapters, the chapters are related to: estimation of the periodic signal parameters in the frequency domain, the uncertainty principles in the Fourier transform, the chirp excitation for estimation of bioimpedance spectrum, and

The third section includes the Fourier transform applications in *image processing techniques*. This section consists of four chapters, the chapters are concerns to: the invariant correlation using a nonlinear filter, the pattern recognition of digital images by one-dimensional signatures, the vectorial signatures for pattern recognition, and

Finally, we would like to thank all the authors who have participated in this book for their valuable contribution. Also we would like to thank all the reviewers for their valuable notes. While there is no doubt that this book may have omitted some significant findings in the Fourier transform field, we hope the information included will be useful for Electrical Engineers, Communication Engineers, Signal Processing Engineers and the Mathematicians, in addition to the academic researchers working in

> **Salih Mohammed Salih** College of Engineering University of Anbar

> > Iraq

transform analysis which are related to the *time, frequency, and phase estimation.*

the multidimensional features extraction methods in frequency domain.

fault diagnosis of induction motors based on FFT.

the identification of systems via simple signals.

**Part 1** 

**DFT and FFT Applications** 
