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Fast Fourier Transform and Its Applications by E. Brigham (Auth....pdf

发布时间：2022-06-09 发布人：admin 分类：说明书 资料大小：15.30M 资料格式：pdf 举报 版权申诉
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    CONTENTS
    CHAPTER 1 INTRODUCTION
    1.1 The Ubiquitous FFT
    1.2 Iuterpreting the Fourier Transfonn
    1.3 Digital Fourier Analysis
    CHAPTER 2 THE FOURIER TRANSFORM
    2.1 The Fourier Integral
    2.2 The Inverse Fourier Transform
    2.3 Existence of the Fourier Integral
    2.4 A1ternate Fourier Transform Definitions
    2.5 Fourier Transform Pairs
    CHAPTER 3 FOUFlIER TRANSFORM PROPERTIES
    3.1 Linearity
    3.2 Symmetry
    3.3 Time and Frequency Sca1ing
    3.4 Time and Frequency Shifting
    3.5 Alternate lnversion Formula
    3.6 Even and Odd Functions
    3.7 Waveform Decomposition
    3.8 Complex Time Functions
    3.9 Summary Table of Fourier Transform Properties
    CHAPTER 4 CONVOLUTION AND CORRELATION
    4.1 Convolution lntegral
    4.2 Graphical Evaluation of the Convolution lntegral
    4.3 Alternat巳Form of the Convolution lntegral
    4.4 Convolution lnvolving lmpulse Functions
    4.5 Time-Convolution Theorem
    4.6 Frequency-Convolution Theorem
    4.7 Correlation Theorem
    CHAPTER 5 FOURIER SERIES AND SAMPLED WAVEFORMS
    5.1 Fourier Series
    5.2 Fourier Series as a Special Case of the Fourier lntegral
    5.3 Waveform Sampling
    5.4 Sampling Theorems
    CHAPTER 6 THE DISCRETE FOURIER TRANSFORM
    6.1 A Graphical Development
    6.2 Theoretical Development
    6.3 Discrete lnv巳rse Fourier Transform
    6.4 Relationship Between the Discrete and Continuous Fourier Transform
    6.5 Discrete Fourier Transform Properties
    CHAPTER 7 DISCRETE CONVOlUTION AND CORRElATION
    7.1 Discrete Convolution
    7.2 Graphical Interpretation of Discrete Convolution
    7.3 Relationship Between Discrete and Continuous Convolution
    7.4 Graphical Interpretation of Discrete Correlation
    CHAPTER 8 THE FAST FOURIER TRANSFORM (FFT)
    8.1 Matrix Formulation
    8.2 Intuitive Development
    8.3 Signal Flow Graph
    8.4 Dual Nodes
    8.5 WP Determination
    8.6 Unscrambling the FFT
    8.7 FFT Computation FlowChart
    8.8 FFT BASIC and PASCAL Computer Programs
    8.9 Theoretical Development of the Base-2FFT Algorithm
    8.10 FFT Algorithms for Arbitrary Factors
    CHAPTER 9 FFT TRANSFORM APPlICATIONS
    9.1 Fourièr Transform Applications
    9.2 FFT Data-Weighting Functions
    9.3 FFT Algorithms for Real Data
    9.4 Inverse Fourier Transform Applications
    9.5 Laplace Transform Applications
    CHAPTER 10 FFT CONVOlUTION AND CORREιATION
    10.1 FFT Convolution of Finite-Duration Waveforms
    10.2 FFT Convolution of Infinite- and Finite-Duration Waveforms
    10.3 Efficient FFT Convolution
    10.4 FFT Correlation of Finite-Duration Waveforms
    CHAPTER 11 TWO-DIMENSIONAL FFT ANALYSIS
    11.1 Two-Dimensional Fourier Transforms
    11.2 Two-Dimensional FFTs
    11.3 Two-Dimensional Convolution and Correlation
    11.4 Two-Dimensional FFT Convolution and Correlation
    CHAPTER 12 FFT DIGITAL FIL TER DESIGN
    12.1 FFT Time-Domain Digital Filter Design
    12.2 FFT Frequ巳ncy-Domain Digital Filter Design
    CHAPTER 13 FFT MULTICHANNEL BAND-PASS FILTERING
    13.1 FFT Band-Pass Integrate and Sample Filters
    13.2 FFT Band-Pass Filter FrequencyResponse Characteristics
    13.3 Multichannel Band-Pass Filtering by Shifted FFTs
    13.4 Sample Rate Considerations in FFT Multichannel Filtering
    13.5 FFT Multichannel Denmltiplexing
    CHAPTER 14 FFT SIGNAL PROCESSING AND SYSTEM APPLICATIONS
    14.1 Sampling Band-Pass Signals
    14.2 Quadrature Sampling
    14.3 FFT Signal Detection
    14.4 FFT Cepstrum Analysis: Echo and Multipath Removal
    14.5 FFT Deconvolution
    14.6 FFT Antenna Design Analysis
    14.7 FFT Phase-Interferometer Measurement System
    14.8 FFT Time-Difference-of-Arrival Measurement System
    14.9 FFT System Simulation
    14.10 FFT Power-Spectrum Analysis
    14.11 FFT Beamforming
    Appendix A The Impulse Function: A Distribution
    Al Impulse-Function Definitions
    A2 Distribution Concepts
    A3 Properties of Impulse Functions
    A4 Two-DimensionalImpulse Functions
    BIBLIOGRAPHY
    INDEX
    CONTENTS PREFACE CHAPTER 1 INTRODUCTION I.I 1.2 1.3 The Ubiquitous FFT 1 Iuterpreting the Fourier Transfonn 4 Dig才tal Fourier Analysis 7 CHAPTER 2 THE FOURIER TRANSFORM 2.1 2.2 2.3 2.4 2.5 The Fourier Integral 9 The Inverse Fourier Transform Existence of the Fourier Integral 13 A1ternate Fourier Transform Definitions 22 Fourier Transform Pairs 23 11 CHAPTER 3 FOU FlIER TRANSFORM PROPERTIES 3.1 3.2 3.3 3.4 Linearity 30 Symmetry 32 Time and Frequency Sca1ing 32 Time and Frequency Shifting 35 xiii 9 30
    viii Contents 3.5 3.6 3.7 3.8 3.9 Alternate lnversion Formula 40 Even and Odd Functions 40 Waveform Decomposition 42 Complex Time Functions 44 Summary Table of Fourier Transform Properties 46 CHAPTER 4 CONVOLUTION AND CORRELATION 50 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Convolution lntegral 50 Graphical Evaluation of the Convolution lntegral 51 Alternat巳 Form of the Convolution lntegral 54 Convolution lnvolving lmpulse Functions 57 Time-Convolution Theorem 60 Frequency-Convolution Theorem 64 Correlation Theorem 65 CHAPTER 5 FOURIER SERIES AND SAMPLED WAVEFORMS 74 5.1 5.2 5.3 5.4 Fourier Series 74 Fourier Series as a Special Case of th巳 Fourier lntegral 77 Waveform Sampling 79 Sampling Theorems 83 CHAPTER 6 THE DISCRETE FOURIER TRANSFORM 89 6.1 6.2 6.3 6.4 6.5 A Graphical Development 90 Theoretical Development 92 Discrete lnv巳rse Fourier Transform 97 Relationship Between the Discrete and Continuous Fourier Transform 98 Discrete Fourier Transform Properties 107
    Con~n~ CHAPTER 7 DISCRETE CONVOlUTION AND CORRElATION ~ 118 7.1 7.2 7.3 7.4 Discrete Convolution 118 Graphical Interpretation of Discrete Convolution 119 Relationship Between Discrete and Continuous Convolution 121 Graphical Interpretation of Discrete Correlation 127 CHAPTER 8 THE FAST FOURIER TRANSFORM (FFT) 131 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 Matrix Formulation 131 Intuitive Development 132 Signal Flow Graph 136 Dual Nodes 138 WP Determination 140 Unscrambling the FFT 141 FFT Computation FlowChart 141 FFT BASIC and PASCAL Computer Programs 145 Theoretical Development of the Base-2 FFT Algorithm 148 FFT Algorithms for Arbitrary Factors 156 CHAPTER 9 FFT TRANSFORM APPlICATIONS 167 9.1 9.2 9.3 9.4 9.5 。 Fourièr Transform Applications 167 FFT Data-Weighting Functions 178 FFT Algorithms for Real Data 188 Inverse Fourier Transform Applications 195 Laplace Transform Applications 199 CHAPTER 10 FFT CONVOlUTION AND CORREιATION 204 10.1 FFT Convolution of Finite-Duration Waveforms 204
    x Contents 10.2 10.3 10.4 FFT Convolution of Infinite- and Finite-Duration Waveforms 211 Efficient FFT Convolution 223 FFT Correlation of Finite-Duration Waveforms 225 CHAPTER 11 TWO-DIMENSIONAL FFT ANALYSIS 232 11.1 11.2 11.3 11 .4 Two-Dimensional Fourier Transforms 232 Two-Dim巳nsional FFTs 240 Two-Dimensional Convolution and Correlation 255 Two-Dimensional FFT Convolution and Correlation 260 CHAPTER 12 FFT DIGITAL FIL TER DESIGN 272 12.1 12.2 FFT Time-Domain Digital Filter Design 273 FFT Frequ巳ncy-Domain Digital Filter Design 280 CHAPTER 13 FFT MULTICHANNEL BAND-PASS FILTERING 291 13.1 13.2 13.3 13 .4 13.5 FFT Band-Pass Integrate and Sample Filters 291 FFT Band-Pass Filter Frequency Response Characteristics 299 Multichannel Band-Pass Filtering by Shifted FFTs 303 Sample Rate Considerations in FFT Multichannel Filtering 313 FFT Multichannel Denmltiplexing 315 CHAPTER 14 FFT SIGNAL PROCESSING AND SYSTEM APPLICATIONS 320 14.1 14.2 14.3 Sampling Band-Pass Signals 320 Quadrature Sampling 327 FFT Signal Detection 337
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