Description
Apple Academic Press Inc. Adaptive Filteringfundamentals Of Least Mean Squares With Matlab 2014 Edition by Alexander D. Poularikas
Adaptive filters are used in many diverse applications, appearing in everything from military instruments to cellphones and home appliances. Adaptive Filtering: Fundamentals of Least Mean Squares with MATLAB (R) covers the core concepts of this important field, focusing on a vital part of the statistical signal processing area-the least mean square (LMS) adaptive filter. This largely self-contained text:Discusses random variables, stochastic processes, vectors, matrices, determinants, discrete random signals, and probability distributionsExplains how to find the eigenvalues and eigenvectors of a matrix and the properties of the error surfacesExplores the Wiener filter and its practical uses, details the steepest descent method, and develops the Newton's algorithmAddresses the basics of the LMS adaptive filter algorithm, considers LMS adaptive filter variants, and provides numerous examplesDelivers a concise introduction to MATLAB (R), supplying problems, computer experiments, and more than 110 functions and script filesFeaturing robust appendices complete with mathematical tables and formulas, Adaptive Filtering: Fundamentals of Least Mean Squares with MATLAB (R) clearly describes the key principles of adaptive filtering and effectively demonstrates how to apply them to solve real-world problems. PrefaceAuthor Abbreviations MATLAB (R) Functions Vectors IntroductionMultiplication by a Constant and Addition and Subtraction Unit Coordinate Vectors Inner Product Distance between Two Vectors Mean Value of a Vector Direction Cosines The Projection of a Vector Linear Transformations Linear Independence, Vector Spaces, and Basis Vectors Orthogonal Basis Vectors Problems Hints-Suggestions-Solutions Matrices Introduction General Types of Matrices Diagonal, Identity, and Scalar Matrices Upper and Lower Triangular Matrices Symmetric and Exchange Matrices Toeplitz Matrix Hankel and Hermitian Matrix Operations Determinant of a Matrix Definition and Expansion of a Matrix Trace of a Matrix Inverse of a Matrix Linear Equations Square Matrices (n x n) Rectangular Matrices (n < m) Rectangular Matrices (m < n) Quadratic and Hermitian Forms Eigenvalues and Eigenvectors Eigenvectors Properties of Eigenvalues and Eigenvectors Problems Hints-Suggestions-Solutions Processing of Discrete Deterministic Signals: Discrete Systems Discrete-Time Signals Time-Domain Representation of Basic Continuous and Discrete Signals Transform-Domain Representation of Discrete SignalsDiscrete-Time Fourier Transform The Discrete FT Properties of DFT The z-Transform Discrete-Time Systems Linearity and Shift Invariant Causality Stability Transform-Domain Representation Problems Hints-Suggestions-Solutions Discrete-Time Random Processes Discrete Random Signals, Probability Distributions, and Averages of Random Variables Stationary and Ergodic Processes Averages of RV Stationary Processes Autocorrelation MatrixPurely Random Process (White Noise) Random Walk Special Random Signals and pdf's White Noise Gaussian Distribution (Normal Distribution) Exponential Distribution Lognormal DistributionChi-Square Distribution Wiener-Khinchin Relations Filtering Random Processes Special Types of Random Processes Autoregressive Process Nonparametric Spectra Estimation Periodogram Correlogram Computation of Periodogram and Correlogram Using FFT General Remarks on the Periodogram Proposed Book Modified Method for Better Frequency Resolution Bartlett Periodogram The Welch Method Proposed Modified Welch Methods Problems Hints-Solutions-Suggestions The Wiener Filter Introduction The LS Technique Linear LS LS Formulation Statistical Properties of LSEs The LS Approach Orthogonality Principle Corollary Projection Operator LS Finite Impulse Response Filter The Mean-Square Error The FIR Wiener Filter The Wiener Solution Orthogonality Condition Normalized Performance Equation Canonical Form of the Error-Performance Surface Wiener Filtering Examples Minimum MSE Optimum Filter (wo) Linear Prediction Problems Additional Problems Hints-Solutions-Suggestions Additional Problems Eigenvalues of Rx: Properties of the Error Surface The Eigenvalues of the Correlation Matrix Karhunen-Loeve Transformation Geometrical Properties of the Error Surface Problems Hints-Solutions-Suggestions Newton's and Steepest Descent Methods One-Dimensional Gradient Search Method Gradient Search Algorithm Newton's Method in Gradient Search Steepest Descent Algorithm Steepest Descent Algorithm Applied to Wiener Filter Stability (Convergence) of the Algorithm Transient Behavior of MSE Learning Curve Newton's Method Solution of the Vector Difference Equation Problems Edition Problems Hints-Solutions-Suggestions Additional Problems The Least Mean-Square Algorithm Introduction The LMS Algorithm Examples Using the LMS Algorithm Performance Analysis of the LMS Algorithm Learning Curve The Coefficient-Error or Weighted-Error Correlation Matrix Excess MSE and Misadjustment Stability The LMS and Steepest Descent Methods Complex Representation of the LMS Algorithm Problems Hints-Solutions-Suggestions Variants of Least Mean-Square Algorithm The Normalized Least Mean-Square Algorithm Power NLMS Self-Correcting LMS Filter The Sign-Error LMS Algorithm The NLMS Sign-Error Algorithm The Sign-Regressor LMS Algorithm Self-Correcting Sign-Regressor LMS Algorithm The Normalized Sign-Regressor LMS Algorithm The Sign-Sign LMS Algorithm The Normalized Sign-Sign LMS Algorithm Variable Step-Size LMS The Leaky LMS Algorithm The Linearly Constrained LMS Algorithm The Least Mean Fourth Algorithm The Least Mean Mixed Norm LMS Algorithm Short-Length Signal of the LMS Algorithm The Transform Domain LMS Algorithm Convergence The Error Normalized Step-Size LMS Algorithm The Robust Variable Step-Size LMS Algorithm The Modified LMS Algorithm Momentum LMS The Block LMS Algorithm The Complex LMS Algorithm The Affine LMS Algorithm The Complex Affine LMS Algorithm Problems Hints-Solutions-Suggestions Appendix 1: Suggestions and Explanations for MATLAB Use Suggestions and Explanations for MATLAB Use Creating a Directory Help Save and Load MATLAB as Calculator Variable Names Complex Numbers Array Indexing Extracting and Inserting Numbers in Arrays Vectorization Windowing Matrices Producing a Periodic Function Script Files Functions Complex Expressions Axes 2D Graphics3D Plots General Purpose Commands Managing Commands and FunctionsManaging Variables and Workplace Operators and Special Characters Control Flow Elementary Matrices and Matrix ManipulationElementary Matrices and Arrays Matrix Manipulation Elementary Mathematical Functions Elementary FunctionsNumerical Linear Algebra Matrix Analysis Data Analysis Basic OperationsFiltering and Convolution Fourier Transforms 2D Plotting 2D Plots Appendix 2: Matrix Analysis Definitions Special Matrices Matrix Operation and Formulas Eigendecomposition of Matrices Matrix Expectations Differentiation of a Scalar Function with respect to a Vector Appendix 3: Mathematical Formulas Trigonometric Identities Orthogonality Summation of Trigonometric Forms Summation Formulas Finite Summation Formulas Infinite Summation Formulas Series Expansions Logarithms Some Definite Integrals Appendix 4: Lagrange Multiplier Method Bibliography Index