Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - E-Book

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Caner Ozdemir

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Beschreibung

This book provides a full representation of Inverse Synthetic Aperture Radar (ISAR) imagery, which is a popular and important radar signal processing tool. The book covers all possible aspects of ISAR imaging. The book offers a fair amount of signal processing techniques and radar basics before introducing the inverse problem of ISAR and the forward problem of Synthetic Aperture Radar (SAR). Important concepts of SAR such as resolution, pulse compression and image formation are given together with associated MATLAB codes. After providing the fundamentals for ISAR imaging, the book gives the detailed imaging procedures for ISAR imaging with associated MATLAB functions and codes. To enhance the image quality in ISAR imaging, several imaging tricks and fine-tuning procedures such as zero-padding and windowing are also presented. Finally, various real applications of ISAR imagery, like imaging the antenna-platform scattering, are given in a separate chapter. For all these algorithms, MATLAB codes and figures are included. The final chapter considers advanced concepts and trends in ISAR imaging.

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Veröffentlichungsjahr: 2012

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Table of Contents

Cover

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING

Title page

Copyright page

Dedication

Preface

Acknowledgments

CHAPTER ONE: Basics of Fourier Analysis

1.1 FORWARD AND INVERSE FOURIER TRANSFORM

1.2 FT RULES AND PAIRS

1.3 TIME-FREQUENCY REPRESENTATION OF A SIGNAL

1.4 CONVOLUTION AND MULTIPLICATION USING FT

1.5 FILTERING/WINDOWING

1.6 DATA SAMPLING

1.7 DFT AND FFT

1.8 ALIASING

1.9 IMPORTANCE OF FT IN RADAR IMAGING

1.10 EFFECT OF ALIASING IN RADAR IMAGING

1.11 MATLAB CODES

CHAPTER TWO: Radar Fundamentals

2.1 ELECTROMAGNETIC (EM) SCATTERING

2.2 SCATTERING FROM PECS

2.3 RADAR CROSS SECTION (RCS)

2.4 RADAR RANGE EQUATION

2.5 RANGE OF RADAR DETECTION

2.6 RADAR WAVEFORMS

2.7 PULSED RADAR

2.8 MATLAB CODES

CHAPTER THREE: Synthetic Aperture Radar

3.1 SAR MODES

3.2 SAR SYSTEM DESIGN

3.3 RESOLUTIONS IN SAR

3.4 SAR IMAGE FORMATION: RANGE AND AZIMUTH COMPRESSION

3.5 RANGE COMPRESSION

3.6 PULSE COMPRESSION

3.7 AZIMUTH COMPRESSION

3.8 SAR IMAGING

3.9 EXAMPLE OF SAR IMAGERY

3.10 PROBLEMS IN SAR IMAGING

3.11 ADVANCED TOPICS IN SAR

3.12 MATLAB CODES

CHAPTER FOUR: Inverse Synthetic Aperture Radar Imaging and Its Basic Concepts

4.1 SAR VERSUS ISAR

4.2 THE RELATION OF SCATTERED FIELD TO THE IMAGE FUNCTION IN ISAR

4.3 ONE-DIMENSIONAL (1D) RANGE PROFILE

4.4 1D CROSS-RANGE PROFILE

4.5 2D ISAR IMAGE FORMATION (SMALL BANDWIDTH, SMALL ANGLE)

4.6 2D ISAR IMAGE FORMATION (WIDE BANDWIDTH, LARGE ANGLES)

4.7 3D ISAR IMAGE FORMATION

4.8 MATLAB CODES

CHAPTER FIVE: Imaging Issues in Inverse Synthetic Aperture Radar

5.1 FOURIER-RELATED ISSUES

5.2 IMAGE ALIASING

5.3 POLAR REFORMATTING REVISITED

5.4 ZERO PADDING

5.5 POINT SPREAD FUNCTION (PSF)

5.6 WINDOWING

5.7 MATLAB CODES

CHAPTER SIX: Range-Doppler Inverse Synthetic Aperture Radar Processing

6.1 SCENARIOS FOR ISAR

6.2 ISAR WAVEFORMS FOR RANGE-DOPPLER PROCESSING

6.3 DOPPLER SHIFT’S RELATION TO CROSS RANGE

6.4 FORMING THE RANGE-DOPPLER IMAGE

6.5 ISAR RECEIVER

6.6 QUADRADURE DETECTION

6.7 RANGE ALIGNMENT

6.8 DEFINING THE RANGE-DOPPLER ISAR IMAGING PARAMETERS

6.9 EXAMPLE OF CHIRP PULSE-BASED RANGE-DOPPLER ISAR IMAGING

6.10 EXAMPLE OF SFCW-BASED RANGE-DOPPLER ISAR IMAGING

6.11 MATLAB CODES

CHAPTER SEVEN: Scattering Center Representation of Inverse Synthetic Aperture Radar

7.1 SCATTERING/RADIATION CENTER MODEL

7.2 EXTRACTION OF SCATTERING CENTERS

7.3 MATLAB CODES

CHAPTER EIGHT: Motion Compensation for Inverse Synthetic Aperture Radar

8.1 DOPPLER EFFECT DUE TO TARGET MOTION

8.2 STANDARD MOCOMP PROCEDURES

8.3 POPULAR MOCOMP TECHNIQUES IN ISAR

8.4 MATLAB CODES

CHAPTER NINE: Some Imaging Applications Based on Inverse Synthetic Aperture Radar

9.1 IMAGING ANTENNA-PLATFORM SCATTERING: ASAR

9.2 IMAGING PLATFORM COUPLING BETWEEN ANTENNAS: ACSAR

9.3 IMAGING SCATTERING FROM SUBSURFACE OBJECTS: GPR-SAR

Appendix

Index

WILEY SERIES IN MICROWAVE AND OPTICAL ENGINEERING

KAI CHANG, Editor

Texas A&M University

FIBER-OPTIC COMMUNICATION SYSTEMS, Fourth Edition · Govind P. Agrawal

ASYMMETRIC PASSIVE COMPONENTS IN MICROWAVE INTEGRATED CIRCUITS · Hee-Ran Ahn

COHERENT OPTICAL COMMUNICATIONS SYSTEMS · Silvello Betti, Giancarlo De Marchis, and Eugenio Iannone

PHASED ARRAY ANTENNAS: FLOQUET ANALYSIS, SYNTHESIS, BFNs, AND ACTIVE ARRAY SYSTEMS · Arun K. Bhattacharyya

HIGH-FREQUENCY ELECTROMAGNETIC TECHNIQUES: RECENT ADVANCES AND APPLICATIONS · Asoke K. Bhattacharyya

RADIO PROPAGATION AND ADAPTIVE ANTENNAS FOR WIRELESS COMMUNICATION LINKS: TERRESTRIAL, ATMOSPHERIC, AND IONOSPHERIC · Nathan Blaunstein and Christos G. Christodoulou

COMPUTATIONAL METHODS FOR ELECTROMAGNETICS AND MICROWAVES · Richard C. Booton, Jr.

ELECTROMAGNETIC SHIELDING · Salvatore Celozzi, Rodolfo Araneo, and Giampiero Lovat

MICROWAVE RING CIRCUITS AND ANTENNAS · Kai Chang

MICROWAVE SOLID-STATE CIRCUITS AND APPLICATIONS · Kai Chang

RF AND MICROWAVE WIRELESS SYSTEMS · Kai Chang

RF AND MICROWAVE CIRCUIT AND COMPONENT DESIGN FOR WIRELESS SYSTEMS · Kai Chang, Inder Bahl, and Vijay Nair

MICROWAVE RING CIRCUITS AND RELATED STRUCTURES, Second Edition · Kai Chang and Lung-Hwa Hsieh

MULTIRESOLUTION TIME DOMAIN SCHEME FOR ELECTROMAGNETIC ENGINEERING · Yinchao Chen, Qunsheng Cao, and Raj Mittra

DIODE LASERS AND PHOTONIC INTEGRATED CIRCUITS · Larry Coldren and Scott Corzine

EM DETECTION OF CONCEALED TARGETS · David J. Daniels

RADIO FREQUENCY CIRCUIT DESIGN · W. Alan Davis and Krishna Agarwal

RADIO FREQUENCY CIRCUIT DESIGN, Second Edition · W. Alan Davis

MULTICONDUCTOR TRANSMISSION-LINE STRUCTURES: MODAL ANALYSIS TECHNIQUES · J. A. Brandão Faria

PHASED ARRAY-BASED SYSTEMS AND APPLICATIONS · Nick Fourikis

SOLAR CELLS AND THEIR APPLICATIONS, Second Edition · Lewis M. Fraas and Larry D. Partain

FUNDAMENTALS OF MICROWAVE TRANSMISSION LINES · Jon C. Freeman

OPTICAL SEMICONDUCTOR DEVICES · Mitsuo Fukuda

MICROSTRIP CIRCUITS · Fred Gardiol

HIGH-SPEED VLSI INTERCONNECTIONS, Second Edition · Ashok K. Goel

FUNDAMENTALS OF WAVELETS: THEORY, ALGORITHMS, AND APPLICATIONS, Second Edition · Jaideva C. Goswami and Andrew K. Chan

HIGH-FREQUENCY ANALOG INTEGRATED CIRCUIT DESIGN · Ravender Goyal (ed.)

RF AND MICROWAVE TRANSMITTER DESIGN · Andrei Grebennikov

ANALYSIS AND DESIGN OF INTEGRATED CIRCUIT ANTENNA MODULES · K. C. Gupta and Peter S. Hall

PHASED ARRAY ANTENNAS, Second Edition · R. C. Hansen

STRIPLINE CIRCULATORS · Joseph Helszajn

THE STRIPLINE CIRCULATOR: THEORY AND PRACTICE · Joseph Helszajn

LOCALIZED WAVES · Hugo E. Hernández-Figueroa, Michel Zamboni-Rached, and Erasmo Recami (eds.)

MICROSTRIP FILTERS FOR RF/MICROWAVE APPLICATIONS, Second Edition · Jia-Sheng Hong

MICROWAVE APPROACH TO HIGHLY IRREGULAR FIBER OPTICS · Huang Hung-Chia

NONLINEAR OPTICAL COMMUNICATION NETWORKS · Eugenio Iannone, Francesco Matera, Antonio Mecozzi, and Marina Settembre

FINITE ELEMENT SOFTWARE FOR MICROWAVE ENGINEERING · Tatsuo Itoh, Giuseppe Pelosi, and Peter P. Silvester (eds.)

INFRARED TECHNOLOGY: APPLICATIONS TO ELECTROOPTICS, PHOTONIC DEVICES, AND SENSORS · A. R. Jha

SUPERCONDUCTOR TECHNOLOGY: APPLICATIONS TO MICROWAVE, ELECTRO-OPTICS, ELECTRICAL MACHINES, AND PROPULSION SYSTEMS · A. R. Jha

TIME AND FREQUENCY DOMAIN SOLUTIONS OF EM PROBLEMS USING INTEGTRAL EQUATIONS AND A HYBRID METHODOLOGY · B. H. Jung, T. K. Sarkar, S. W. Ting, Y. Zhang, Z. Mei, Z. Ji, M. Yuan, A. De, M. Salazar-Palma, and S. M. Rao

OPTICAL COMPUTING: AN INTRODUCTION · M. A. Karim and A. S. S. Awwal

INTRODUCTION TO ELECTROMAGNETIC AND MICROWAVE ENGINEERING · Paul R. Karmel, Gabriel D. Colef, and Raymond L. Camisa

MILLIMETER WAVE OPTICAL DIELECTRIC INTEGRATED GUIDES AND CIRCUITS · Shiban K. Koul

ADVANCED INTEGRATED COMMUNICATION MICROSYSTEMS · Joy Laskar, Sudipto Chakraborty, Manos Tentzeris, Franklin Bien, and Anh-Vu Pham

MICROWAVE DEVICES, CIRCUITS AND THEIR INTERACTION · Charles A. Lee and G. Conrad Dalman

ADVANCES IN MICROSTRIP AND PRINTED ANTENNAS · Kai-Fong Lee and Wei Chen (eds.)

SPHEROIDAL WAVE FUNCTIONS IN ELECTROMAGNETIC THEORY · Le-Wei Li, Xiao-Kang Kang, and Mook-Seng Leong

ARITHMETIC AND LOGIC IN COMPUTER SYSTEMS · Mi Lu

OPTICAL FILTER DESIGN AND ANALYSIS: A SIGNAL PROCESSING APPROACH · Christi K. Madsen and Jian H. Zhao

THEORY AND PRACTICE OF INFRARED TECHNOLOGY FOR NONDESTRUCTIVE TESTING · Xavier P. V. Maldague

METAMATERIALS WITH NEGATIVE PARAMETERS: THEORY, DESIGN, AND MICROWAVE APPLICATIONS · Ricardo Marqués, Ferran Martín, and Mario Sorolla

OPTOELECTRONIC PACKAGING · A. R. Mickelson, N. R. Basavanhally, and Y. C. Lee (eds.)

OPTICAL CHARACTER RECOGNITION · Shunji Mori, Hirobumi Nishida, and Hiromitsu Yamada

ANTENNAS FOR RADAR AND COMMUNICATIONS: A POLARIMETRIC APPROACH · Harold Mott

INTEGRATED ACTIVE ANTENNAS AND SPATIAL POWER COMBINING · Julio A. Navarro and Kai Chang

ANALYSIS METHODS FOR RF, MICROWAVE, AND MILLIMETER-WAVE PLANAR TRANSMISSION LINE STRUCTURES · Cam Nguyen

LASER DIODES AND THEIR APPLICATIONS TO COMMUNICATIONS AND INFORMATION PROCESSING · Takahiro Numai

FREQUENCY CONTROL OF SEMICONDUCTOR LASERS · Motoichi Ohtsu (ed.)

INVERSE SYNTHETIC APERTURE RADAR IMAGING WITH MATLAB ALGORITHMS · Caner Özdemir

SILICA OPTICAL FIBER TECHNOLOGY FOR DEVICE AND COMPONENTS: DESIGN, FABRICATION, AND INTERNATIONAL STANDARDS · Un-Chul Paek and Kyunghwan Oh

WAVELETS IN ELECTROMAGNETICS AND DEVICE MODELING · George W. Pan

OPTICAL SWITCHING · Georgios Papadimitriou, Chrisoula Papazoglou, and Andreas S. Pomportsis

MICROWAVE IMAGING · Matteo Pastorino

ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES · Clayton R. Paul

INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY, Second Edition · Clayton R. Paul

ADAPTIVE OPTICS FOR VISION SCIENCE: PRINCIPLES, PRACTICES, DESIGN AND APPLICATIONS · Jason Porter, Hope Queener, Julianna Lin, Karen Thorn, and Abdul Awwal (eds.)

ELECTROMAGNETIC OPTIMIZATION BY GENETIC ALGORITHMS · Yahya Rahmat-Samii and Eric Michielssen (eds.)

INTRODUCTION TO HIGH-SPEED ELECTRONICS AND OPTOELECTRONICS · Leonard M. Riaziat

NEW FRONTIERS IN MEDICAL DEVICE TECHNOLOGY · Arye Rosen and Harel Rosen (eds.)

ELECTROMAGNETIC PROPAGATION IN MULTI-MODE RANDOM MEDIA · Harrison E. Rowe

ELECTROMAGNETIC PROPAGATION IN ONE-DIMENSIONAL RANDOM MEDIA · Harrison E. Rowe

HISTORY OF WIRELESS · Tapan K. Sarkar, Robert J. Mailloux, Arthur A. Oliner, Magdalena Salazar-Palma, and Dipak L. Sengupta

PHYSICS OF MULTIANTENNA SYSTEMS AND BROADBAND PROCESSING · Tapan K. Sarkar, Magdalena Salazar-Palma, and Eric L. Mokole

SMART ANTENNAS · Tapan K. Sarkar, Michael C. Wicks, Magdalena Salazar-Palma, and Robert J. Bonneau

NONLINEAR OPTICS · E. G. Sauter

APPLIED ELECTROMAGNETICS AND ELECTROMAGNETIC COMPATIBILITY · Dipak L. Sengupta and Valdis V. Liepa

COPLANAR WAVEGUIDE CIRCUITS, COMPONENTS, AND SYSTEMS · Rainee N. Simons

ELECTROMAGNETIC FIELDS IN UNCONVENTIONAL MATERIALS AND STRUCTURES · Onkar N. Singh and Akhlesh Lakhtakia (eds.)

ANALYSIS AND DESIGN OF AUTONOMOUS MICROWAVE CIRCUITS · Almudena Suárez

ELECTRON BEAMS AND MICROWAVE VACUUM ELECTRONICS · Shulim E. Tsimring

FUNDAMENTALS OF GLOBAL POSITIONING SYSTEM RECEIVERS: A SOFTWARE APPROACH, Second Edition · James Bao-yen Tsui

SUBSURFACE SENSING · Ahmet S. Turk, A. Koksal Hocaoglu, and Alexey A. Vertiy (eds.)

RF/MICROWAVE INTERACTION WITH BIOLOGICAL TISSUES · André Vander Vorst, Arye Rosen, and Youji Kotsuka

InP-BASED MATERIALS AND DEVICES: PHYSICS AND TECHNOLOGY · Osamu Wada and Hideki Hasegawa (eds.)

COMPACT AND BROADBAND MICROSTRIP ANTENNAS · Kin-Lu Wong

DESIGN OF NONPLANAR MICROSTRIP ANTENNAS AND TRANSMISSION LINES · Kin-Lu Wong

PLANAR ANTENNAS FOR WIRELESS COMMUNICATIONS · Kin-Lu Wong

FREQUENCY SELECTIVE SURFACE AND GRID ARRAY · T. K. Wu (ed.)

ACTIVE AND QUASI-OPTICAL ARRAYS FOR SOLID-STATE POWER COMBINING · Robert A. York and Zoya B. Popovic (eds.)

OPTICAL SIGNAL PROCESSING, COMPUTING AND NEURAL NETWORKS · Francis T. S. Yu and Suganda Jutamulia

ELECTROMAGNETIC SIMULATION TECHNIQUES BASED ON THE FDTD METHOD · Wenhua Yu, Xiaoling Yang, Yongjun Liu, and Raj Mittra

SiGe, GaAs, AND InP HETEROJUNCTION BIPOLAR TRANSISTORS · Jiann Yuan

PARALLEL SOLUTION OF INTEGRAL EQUATION-BASED EM PROBLEMS · Yu Zhang and Tapan K. Sarkar

ELECTRODYNAMICS OF SOLIDS AND MICROWAVE SUPERCONDUCTIVITY · Shu-Ang Zhou

MICROWAVE BANDPASS FILTERS FOR WIDEBAND COMMUNICATIONS · Lei Zhu, Sheng Sun, and Rui Li

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Özdemir, Caner.

 Inverse synthetic aperture radar imaging with MATLAB / Caner Özdemir.

p. cm. – (Wiley series in microwave and optical engineering ; 210)

 Includes bibliographical references.

 ISBN 978-0-470-28484-1 (hardback)

 ISBN 978-1-118-17805-8 (epub)

 ISBN 978-1-118-17808-9 (epdf)

 ISBN 978-1-118-17809-6 (mobi)

 1. Synthetic aperture radar. 2. MATLAB. I. Title.

 TK6592.S95O93 2011

 621.3848'5–dc23

2011031430

To:

My wife,

My three daughters,

My brother,

My father,

and the memory of my beloved mother

Preface

Inverse synthetic aperture radar (ISAR) has been proven to be a powerful signal processing tool for imaging moving targets usually on the two-dimensional (2D) down-range cross-range plane. ISAR imagery plays an important role especially in military applications such as target identification, recognition, and classification. In these applications, a critical requirement of the ISAR image is to achieve sharp resolution in both down-range and cross-range domains. The usual way of obtaining the 2D ISAR image is by collecting the frequency and aspect diverse backscattered field data from the target. For synthetic aperture radar (SAR) and ISAR scenarios, there is always a trade-off between the down-range resolution and the frequency bandwidth. In contrast to SAR, the radar is usually fixed in the ISAR geometry and the cross-range resolution is attained by target’s rotational motion, which is generally unknown to the radar engineer.

In order to successfully form an ISAR image, the target’s motion should contain some degree of rotational component with respect to radar line of sight (RLOS) direction during the coherent integration time (or dwell time) of the radar system. But in some instances, especially when the target is moving along the RLOS direction, the target’s viewing angle width is insufficient to be able to form an ISAR image. This restriction can be eliminated by utilizing bistatic or multistatic configurations that provide adequate look-angle diversity of the target. Another challenging problem occurs when the target’s rotational velocity is sufficiently high such that the target’s viewing angle width is not small during the dwell time of the radar. The target’s translational movement is another issue that has to be addressed before displaying the final motion-free ISAR image. Therefore, motion effects have to be removed or mitigated with the help of motion compensation algorithms.

This book is devoted to the conceptual description of ISAR imagery and the explanation of basic ISAR research. Although the primary audience will be graduate students and other interested researchers in the fields of electrical engineering and physics, I hope that colleagues working in radar research and development or in a related industry may also benefit from the book. Numerical or experimental examples in Matlab technical language are provided for the presented algorithms with the aim of improving the understanding of the algorithms by the reader.

The organization of the book is as follows. In the first chapter, an overview of Fourier theory, which plays an important and crucial role in radar imaging, is presented to provide a fair knowledge of Fourier-based signal processing basics. Noting that the ISAR imaging can also be treated as a signal processing tool, an understanding of signal processing and Fourier theory will be required to get the full benefit from the chapters within the book. The next chapter is devoted to radar fundamentals. Since ISAR itself is a radar, the key parameters of the radar concept that is related to ISAR research are revisited. These include electromagnetic scattering, radar cross section, the radar equation, and the radar waveforms. Then, before stepping into inverse problem of ISAR, the forward problem of SAR is reviewed in Chapter 3. SAR and ISAR provide dual problems and share dual algorithms with similar difficulties. Therefore, understanding the ISAR imagery could not be complete without understanding the SAR concepts. In the SAR chapter, therefore, important concepts of SAR such as resolution, pulse compression, and image formation are given together with associated Matlab codes. Furthermore, some advanced concepts and trends in SAR imaging are also presented.

After providing the fundamentals for SAR imaging, we provide the detailed imaging procedure for conventional ISAR imaging and the basic ISAR concepts with associated Matlab codes in Chapter 4. The topics include range profile concept, range/cross-range resolutions, small-angle small-bandwidth ISAR imaging, large-angle wide-bandwidth ISAR imaging, polar reformatting, and three-dimensional ISAR imaging. In Chapter 5, we provide some design aspects that are used to improve the quality of the ISAR image. Down sampling/up sampling, image aliasing, point spread function and smoothing are covered in this chapter. Several imaging tricks and fine-tuning procedures such as zero-padding and windowing that are used for enhancing the image quality are also presented.

In Chapter 6, range-Doppler ISAR image processing is given in detail. ISAR waveforms, ISAR receiver for these waveforms, quadrature detection, Doppler shift phenomena, and range-Doppler ISAR imaging algorithms are presented. The design examples with Matlab codes are also provided. In Chapter 7, scattering center representation, which has proven to be a sparse but an effective model of ISAR imaging, is presented. We provide algorithms to reconstruct both the image and the field data from the scattering centers with good fidelity. In Chapter 8, motion compensation (MOCOMP), one of the most important and challenging problems of ISAR imagery, is taken up in detail. The concepts include Doppler effect due to target motion, translational and motion compensation routines, range tracking, and Doppler tracking subjects. Algorithms and numerical examples with Matlab codes are provided for the most popular MOCOMP techniques, namely, cross-correlation method, minimum entropy method, and joint-time frequency (JTF)-based motion compensation. In the final chapter, applications of the ISAR imaging concept to different but related engineering problems are presented. The employment of ISAR imagery to the antenna scattering problem (i.e., antenna SAR) and also to the antenna coupling problem (i.e., antenna coupling SAR) are explained. The imaging algorithms together with numerical examples are given. In addition, the application of the SAR/ISAR concept to the ground penetrating radar application is presented.

All MATLAB files may be accessed on the following ftp site: ftp://ftp.wiley.com/public/sci_tech_med/inverse_synthetic.

CANER ÖZDEMR

Acknowledgments

I would like to address special thanks to the people below for their help and support during the preparation of this book. First, I am thankful to my wife and three children for their patience and continuous support while writing this book. I am very thankful to Dr. Hao Ling of the University of Texas at Austin for being a valuable source of knowledge, ideas, and also inspiration. He has been a great advisor since I met him.

I would like to express my sincere thanks to my former graduate students Betl Yılmaz, Deniz Üstn, Enes Yiit, evket Demirci, and Özkan Kırık, who carried out some of the research detailed in this book.

Last but not least, I would like to show my special thanks to Dr. Kai Chang for inviting me to write this book. Without his kind offer, this study would not have been possible.

C.Ö.

CHAPTER ONE

Basics of Fourier Analysis

1.1 FORWARD AND INVERSE FOURIER TRANSFORM

Fourier transform (FT) is a common and useful mathematical tool that is utilized in numerous applications in science and technology. FT is quite practical, especially for characterizing nonlinear functions in nonlinear systems, analyzing random signals, and solving linear problems. FT is also a very important tool in radar imaging applications as we shall investigate in the forthcoming chapters of this book. Before starting to deal with the FT and inverse Fourier transform (IFT), a brief history of this useful linear operator and its founders is presented.

1.1.1 Brief History of FT

Jean Baptiste Joseph Fourier, a great mathematician, was born in 1768 in Auxerre, France. His special interest in heat conduction led him to describe a mathematical series of sine and cosine terms that can be used to analyze propagation and diffusion of heat in solid bodies. In 1807, he tried to share his innovative ideas with researchers by preparing an essay entitled “On the Propagation of Heat in Solid Bodies.” The work was examined by Lagrange, Laplace, Monge, and Lacroix. Lagrange’s oppositions caused the rejection of Fourier’s paper. This unfortunate decision caused colleagues to wait for 15 more years to read his remarkable contributions on mathematics, physics, and, especially, signal analysis. Finally, his ideas were published in the book The Analytic Theory of Heat in 1822 [1].

Discrete Fourier transform (DFT) was developed as an effective tool in calculating this transformation. However, computing FT with this tool in the 19th century was taking a long time. In 1903, Carl Runge studied the minimization of the computational time of the transformation operation [2]. In 1942, Danielson and Lanczos utilized the symmetry properties of FT to reduce the number of operations in DFT [3]. Before the advent of digital computing technologies, James W. Cooley and John W. Tukey developed a fast method to reduce the computation time in DFT. In 1965, they published their technique that later on became famous as the fast Fourier transform (FFT) [4].

1.1.2 Forward FT Operation

The FT can be simply defined as a certain linear operator that maps functions or signals defined in one domain to other functions or signals in another domain. The common use of FT in electrical engineering is to transform signals from time domain to frequency domain or vice versa. More precisely, forward FT decomposes a signal into a continuous spectrum of its frequency components such that the time signal is transformed to a frequency-domain signal. In radar applications, these two opposing domains are usually represented as “spatial frequency” (or wave number) and “range” (distance). Such use of FT will be examined and applied throughout this book.

The forward FT of a continuous signal () where −∞ < < ∞ is described as

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