1 Introduction 1
1.1 Topical Outline 1
1.2 Possible Approaches 12
1.3 Organization 15
2 Classical Detection and Estimation Theory 19
2.1 Introduction 19
2.2 Simple Binary Hypothesis Tests 23
2.3 M Hypotheses 46
2.4 Estimation Theory 52
2.5 Composite Hypotheses 86
2.6 The General Gaussian Problem 96
2.7 Performance Bounds and Approximations 116
2.8 Summary 133
2.9 Problems 133
References 163
3 Representations of Random Processes 166
3.1 Introduction 166
3.2 Deterministic Functions:Orthogonal Representations 169
3.3 Random Process Characterization 174
3.4 Homogeneous Integral Equations and Eigenfunctions 186
3.5 Periodic Processes 209
3.6 Infinite Time Interval:Spectral Decomposition 212
3.7 Vector Random Processes 220
3.8 Summary 224
3.9 Problems 226
References 237
4 Detection of Signals-Estimation of Signal Parameters 239
4.1 Introduction 239
4.2 Detection and Estimation in White Gaussian Noise 246
4.3 Detection and Estimation in Nonwhite Gaussian Noise 287
4.4 Signals with Unwanted Parameters:The Composite Hypo-thesis Problem 333
4.5 Multiple Channels 366
4.6 Multiple Parameter Estimation 370
4.7 Summary and Omissions 374
4.8 Problems 377
References 418
5 Estimation of Continuous Waveforms 423
5.1 Introduction 423
5.2 Derivation of Estimator Equations 426
5.3 A Lower Bound on the Mean-Square Estimation Error 437
5.4 Multidimensional Waveform Estimation 446
5.5 Nonrandom Waveform Estimation 456
5.6 Summary 459
5.7 Problems 460
References 465
6 Linear Estimation 467
6.1 Properties of Optimum Processors 468
6.2 Realizable Linear Filters:Stationary Processes.Infinite Past:Wiener Filters 481
6.3 Kalman-Bucy Filters 515
6.4 Linear Modulation:Communications Context 575
6.5 The Fundamental Role of the Optimum Linear Filter 584
6.6 Comments 585
6.7 Problems 586
References 619
7 Discussion 623
7.1 Summary 623
7.2 Preview of Part Ⅱ 625
7.3 Unexplored Issues 627
References 629
Appendix:A Typical Course Outline 635
Glossary 671
Author Index 683
Subject Index 687