Monographs in Computer Science

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.