Detection Theory : Applications and Digital Signal Processing

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Detection Theory : Applications and Digital Signal Processing

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  • 製本 Hardcover:ハードカバー版/ページ数 325 p.
  • 言語 ENG,ENG
  • 商品コード 9780849304347
  • DDC分類 621.3822

Table of Contents

  Introduction                                     1  (12)
General Philosophy 1 (2)
Detection and Estimation Philosophy 3 (3)
Detection 3 (2)
Estimation 5 (1)
Description of Spaces Involved in the 6 (4)
Decision
Summary 10 (3)
Review of Deterministic and Random System and 13 (24)
Signal Concepts
Some Mathematical and Statistical Background 13 (3)
Systems and Signals (Deterministic and 16 (2)
Random)
Transformation of Random Variables 18 (13)
Gaussian Density 19 (2)
Rayleigh Density 21 (1)
Cauchy Density 22 (2)
Uniform Density 24 (1)
Chi-Squared Density 25 (4)
Rician Density (Non-Central Rayleigh) 29 (1)
Non-Central Chi-Squared Density 29 (2)
Summary 31 (1)
Problems 32 (5)
Introduction to Signal Processing 37 (26)
Introduction 37 (1)
Data Structure and Sampling 37 (2)
Discrete-Time Transformations 39 (1)
Filtering 40 (1)
Finite Impulse Response Filter 41 (2)
The Fast Fourier Transform 43 (6)
FIR Filter with Complex Valued Weights 44 (1)
Interpretation
Complex Demodulator Interpretation 45 (1)
I-Q Demodulator (In-Phase Quadrature 46 (1)
Demodulator) Interpretation
Correlator Interpretation 46 (1)
Convolver Interpretation 47 (1)
Matched Filter Interpretation 48 (1)
Coordinate Transformation Interpretation 48 (1)
Fast Correlation 49 (1)
Periodogram (Power Spectral Density 50 (1)
Estimate)
Wavelets 50 (10)
Introduction 50 (1)
Revisiting FIR Filters and the DFT/FFT 51 (2)
FIR Filters and Wavelet Transforms 53 (5)
Mallat's Algorithm 58 (2)
Summary 60 (3)
Hypothesis Testing 63 (54)
Introduction 63 (4)
Bayes' Detection 67 (15)
Maximum a Posteriori (Map) Detection 82 (1)
Maximum Likelihood (ML) Criterion 83 (1)
Minimum Probability of Error Criterion 84 (4)
Min-Max Criterion 88 (2)
Neyman-Pearson Criterion 90 (6)
Introduction 90 (1)
Optimization and Lagrange Multipliers 90 (2)
Neyman-Pearson Approach 92 (4)
Multiple Hypotheses 96 (6)
Composite Hypothesis Testing 102(5)
Nuisance Parameters with Known or Unknown 103(4)
Probability Density Function or with
Unknown but Fixed Values
Receiver Operator Characteristic Curves and 107(4)
Performance
General Background 107(1)
ROC Curves 108(3)
Summary 111(1)
Problems 111(6)
Non-Parametric and Sequential Likelihood 117(12)
Ratio Detectors
Introduction 117(1)
Non-Parametric Detection 117(5)
Sign Detector 118(1)
Performance Analysis of the Sign Detector 119(3)
Wilcoxon Detector 122(1)
Sequential Detection 123(4)
Summary 127(1)
Problems 127(2)
Detection of Dynamic Signals in White 129(36)
Gaussian Noise
Introduction 129(1)
The Binary Detection Problem 130(13)
Performance Analysis 135(8)
Matched Filters 143(3)
Matched Filter Approach (maximizing the 146(1)
output SNR)
M-Ary Communication Systems 147(1)
Detection of Signals With Random Parameters 148(8)
Likelihood Functions 149(1)
Random Phase 150(2)
Random Amplitude 152(2)
Random Amplitude and Phase 154(1)
Random Frequency 154(1)
Random Arrival Time 154(1)
Summary 155(1)
Multiple Pulse Detection 156(3)
Incoherent Averaging 156(2)
Coherent Versus Incoherent Integration 158(1)
(Averaging)
Summary 159(1)
Problems 159(6)
Detection of Signals in Colored Gaussian Noise 165(52)
Introduction 165(1)
Series Representations 166(3)
Derivation of the Correlator Structure 169(5)
Using an Arbitrary Complete Ortho-Normal
(C.O.N.) Set
Gram-Schmidt Procedure 174(3)
Detection of a Known Signal in Additive 177(4)
White Gaussian Noise Using the Gram-Schmidt
Procedure
Series Expansion for Continuous Time 181(2)
Detection for Colored Gaussian Noise
Introduction 181(1)
Mercer's Theorem 181(1)
Karhunen-Loeve Expansion 182(1)
Detection of Known Signals in Additive 183(17)
Colored Gaussian Noise
Bilateral Laplace Transform 188(4)
Integral Equations 192(6)
Performance of the Optimum Receiver for 198(1)
Known Signals in Colored Gaussian Noise
Whitening Filter 199(1)
Discrete-Time Detection --- Known Signals 200(13)
Embedded in Colored Gaussian Noise
Introduction 200(2)
Whitening via Spectral Factorization 202(3)
Whitening Using Correlation Domain 205(3)
Information
Whitening via Auto-Regressive Modeling 208(3)
Whitening by Discretizing the Continuous 211(2)
Time Karhunen-Loeve Equations
Matched Filtering 213(1)
Summary 213(1)
Problems 214(3)
Estimation 217(26)
Introduction 217(1)
Basic Estimation Schemes 217(7)
MAP Estimation 218(2)
ML Estimation 220(1)
Bayes' Estimator 221(3)
Properties of Estimators 224(4)
Cramer-Rao Bound 228(1)
Waveform Estimation 229(11)
Wiener Filtering 232(5)
Discrete-Time Waveform Estimation 237(3)
Summary 240(1)
Problems 240(3)
Applications to Detection, Parameter 243(30)
Estimation, and Classification
Introduction 243(1)
The Periodogram and the Spectrogram 244(5)
Periodogram 244(1)
Spectrogram 245(4)
Correlation 249(1)
Instantaneous Correlation Function, 249(3)
Wignerville Distribution, Spectral
Correlation, and the Ambiguity Function
Wigner-Ville Distribution (WVD) 249(1)
Spectral Correlation 250(1)
Ambiguity Function 251(1)
Cyclo-Stationary Processing 252(5)
Higher Order Moments and Poly-Spectra 257(4)
Cumulant Spectrum 259(1)
Bi-Spectrum 259(1)
Tri-Spectrum 260(1)
Poly-Spectrum 260(1)
Coherence Processing 261(2)
Wavelet Processing 263(2)
Adaptive Techniques 265(2)
Summary 267(6)
Appendix A: Probability, Random Processes, and 273(20)
Systems
Appendix B: Signals and Transforms 293(10)
Appendix C: Mathematical Structures 303(4)
Appendix D: Some Mathematical Expressions and 307(8)
Moments of Probability Density Function
Appendix E: Wavelet Transforms 315(6)
Index 321