1 Introduction 1.1 Topical Outline 1.2 Possible Approaches 1.3 Organization 2 Classical Detection and Estimation Theory 2.1 Introduction 2.2 Simple Binary Hypothesis Tests Decision Criteria.Performance:Receiver Operating Characteristic 2.3 M Hypotheses 2.4 Estimation Theory Random Parameters:Bayes Estimation.Real(Nonrandom)Parameter Estimation.Multiple Parameter Estimation.Summary of Estimation Theory. 2.5 Composite Hypotheses 2.6 The General Gaussian Problem Equal Covariance Matrices.Equal Mean Vectors.Summary. 2.7 Performance Bounds and Approximations 2.8 Summary 2.9 Problems Referecnces 3 Representations of Random Processes 3.1 Introduction 3.2 Deterministic Functions:Orthogonal Representations 3.3 Random Process Characterization Random Processes:Conventional Characterizations.Series Representation of Sample Functions of Random Processes.Gaussian Processes. 3.4 Homogeneous Integral Equations and Eigenfunctions Rational Spectra.Bandlimited Spectra.Nonstationary Processes.White Noise Processes.The Optimum Linear Filler.Properties of Eigenfunctions and Eigenvalues. 3.5 Periodic Processes 3.6 Infinite Time Interval:Spectral Decomposition Spectral Decomposition.An Application of Spectral Decomposition:MAP Estimation of a Gaussian Process. 3.7 Vector Random Processes 3.8 Summary 3.9 Problems Referecnces 4 Detection of Signals-Estimation of Signal Parameters 4.1 Introduction Models.Format. 4.2 Detection and Estimation in White Gaussian Noise Detection of Signals in Additive White Gaussian Noise.Linear Estimation.Nonlinear Estimation.Summary:Known Signals in White Gaussian Noise 4.3 Detection and Estimation in Nonwhite Gaussian Noise “Whitening”Approach.A Direct Derivation Using the Karhunen-Loeve Expansion.A Direct Derivation Using the Suffcient Statistic.Detection Performance.Estimation.Solution Techniques for Integral Equations.Sensitivity.Known Linear Channels 4.4 Signals with Unwanted Parameters:The Composite Hypothesis Problem Random Phase angles.Random Amplitude and Phase. 4.5 Multiple Channels Formulation.Application. 4.6 Multiple Parameter Estimation Additive White Gaussian Noise Channel.Extensions. 4.7 Summary and Omissions Summary.Topics Omitted. 4.8 Problems Referecnces 5 Estimation of Continuous Waveforms 5.1 Introduction 5.2 Derivation of Estimator Equations No-Memory Modulation Systems.Modulation Systems with Memory. 5.3 A Lower Bound on the Mean-Square Estimation Error 5.4 Multidimensional Waveform Estimation Examples of Multidimensional Problems.Problem Formulation.Derivation of Estimator Equations.Lower Bound on the Error Matrix.Colored Noise Estimation. 5.5 Nonrandom Waveform Estimation 5.6 Summary 5.7 Problems Referecnces 6 Linear Estimation 6.1 Properties of Optimum Processors 6.2 Realizable Linear Filters:Stationary Processes,Infinite Past:Wiener Filters solution of Wiener-Hopf Equation.Errors in Optimum Systems.Unrealizable Filters.Closed-Form Error Expressions.Optimum Feedback Systems.Comments. 6.3 Kalman-Bucy Filters Differential Equation Representation of Linear Systems and Random Process Generation.Derivation of Estimator Equations.Applications.Generalizations. 6.4 Linear Modulation:Communications Context DSB-AM:Realizable Demodulation.DSB-AM:Demodulation with delay.Amplitude Modulation:Generalized Carriers.Amplitude Modulation:Single-Sideband Suppressed-Carrier. 6.5 The Fundamental Role of the Optimum Linear Filter 6.6 Comments 6.7 Problems Referecnces 7 Discussion 7.1 Summary 7.2 Preview of Part II 7.3 Unexplored Issues References Appendix:A Typical Course Outline Glossary Author Index Subject Index
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