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. Language: English