1 Introduction.- 1.1 Signal Processing in Unknown Environments.- 1.2 Two Examples.- 1.3 Outline of the Text.- References.- 2 The Mean Square Error (MSE) Performance Criteria.- 2.1 Introduction.- 2.2 Mean Square Error (MSE) and MSE Surface.- 2.3 Properties of the MSE Surface.- 2.4 The Normal Equations.- 2.5 Further Geometrical Properties of the Error Surfaces.- Problems.- References.- 3 Linear Prediction and the Lattice Structure.- 3.1 Introduction.- 3.2 Durbin's Algorithm.- 3.3 Lattice Derivation.- Problems.- References.- 4 The Method of Steepest Descent.- 4.1 Introduction.- 4.2 Iterative Solution of the Normal Equations.- 4.3 Weight Vector Solutions.- 4.4 Convergence Properties of Steepest Descent.- 4.5 Mean Square Error Propagation.- Problems.- References.- 5 The Least Mean Squares (LMS) Algorithm.- 5.1 Introduction.- 5.2 Effects of Unknown Signal Statistics.- 5.3 Derivation of the LMS Algorithm.- 5.4 Convergence of the LMS Algorithm.- 5.5 LMS Mean Square Error Propagation.- Problems.- References.- 6 Applications of the LMS Algorithm.- 6.1 Introduction.- 6.2 Echo Cancellation.- 6.3 Adaptive Waveform Coding.- 6.4 Adaptive Spectrum Analysis.- References.- 7 Gradient Adaptive Lattice Methods.- 7.1 Introduction.- 7.2 Lattice Reflection Coefficient Computation.- 7.3 Adaptive Lattice Derivations.- 7.4 Performance Example.- Problems.- References.- 8 Recursive Least Squares Signal Processing.- 8.1 Introduction.- 8.2 The Recursive Least Squares Filter.- 8.3 Computational Complexity.- Problems.- References.- 9 Vector Spaces for RLS Filters.- 9.1 Introduction.- 9.2 Linear Vector Spaces.- 9.3 The Least Squares Filter and Projection Matrices.- 9.4 Least Squares Update Relations.- 9.5 Projection Matrix Time Update.- Problems.- References.- 10 The Least Squares Lattice Algorithm.- 10.1 Introduction.- 10.2 Forward and Backward Prediction Filters.- 10.3 The LS Lattice Structure.- 10.4 Lattice Order and Time Updates.- 10.5 Examples of LS Lattice Performance.- Problems.- References.- 11 Fast Transversal Filters.- 11.1 Introduction.- 11.2 Additional Vector Space Relations.- 11.3 The Transversal Filter Operator Update.- 11.4 The FTF Time Updates.- 11.5 Further Computational Reductions.- Problems.- References.
The creation of the text really began in 1976 with the author being involved with a group of researchers at Stanford University and the Naval Ocean Systems Center, San Diego. At that time, adaptive techniques were more laboratory (and mental) curiosities than the accepted and pervasive categories of signal processing that they have become. Over the lasl 10 years, adaptive filters have become standard components in telephony, data communications, and signal detection and tracking systems. Their use and consumer acceptance will undoubtedly only increase in the future. The mathematical principles underlying adaptive signal processing were initially fascinating and were my first experience in seeing applied mathematics work for a paycheck. Since that time, the application of even more advanced mathematical techniques have kept the area of adaptive signal processing as exciting as those initial days. The text seeks to be a bridge between the open literature in the professional journals, which is usually quite concentrated, concise, and advanced, and the graduate classroom and research environment where underlying principles are often more important.
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