NEEC-8551 Adaptive Signal Processing (CC 766)

Note: The following provides a suggested course description, objectives, and an outline. These may be modified pending discussion with the Faculty Chairs, proposing faculty, and other curriculum reviewers.

Course Description: Wiener filtering, linear prediction, methods of steepest descent, stochastic gradient algorithms, recursive least-squares (RLS) algorithms, fast RLS methods, RLS with systolic arrays, QRD-least squares methods, blind deconvolution.

Course Objectives: Students will have a firm basis of adaptive signal processing algorithms and their theoretical foundation. The topics covered are now widely used in all aspects of signal processing in both academic and industrial environments.

Course Outline by Topical Areas:

• Introduction to Adaptive Filters
• Adaptive filters, filter structures, cost functions, applications and historical notes
• Stationary Processes and Models
• Mean ergodic theorem, correlation matrix and its properties, stochastic models, world decompositions, the eigenanalysis problem
• Wiener Filters
• Optimum linear filtering, principle of orthogonality, minimum mean-squared error (MMSE), Wiener-Hopy equations, MMSE cost function, linearly constrained minimum variance filters
• Linear Prediction
• Forward and backward linear prediction, Levinson algorithm, lattice filters and their properties, joint process estimation
• Method of Steepest Descent
• Steepest-descent algorithm, its stability and transient behavior, examples
• Stochastic Gradient Algorithms
• The LMS algorithm, its stability and transient behavior, convergence properties, applications examples
• Fast Kalman Algorithms
• Brief review of Kalman filtering, adaptive signal processing algorithms based on transversal filters and Kalman Theory equations, dynamic AR models, square-root Kalman filtering algorithms
• Recursive Least-Squares (RLS) Algorithms
• Linear least-squares estimation problem, its solution and properties; the matrix inversion lemma; the RLS algorithm, its stability and transient behavior; comparison of RLS and LMS algorithms
• Fast RLS Algorithms
• Background theory and classes of fast RLS algorithms; the FTF algorithm, its properties, initialization and complexity, modifications
• RLS Algorithms Based Lattice Filters
• Order-Update and Time-Update equations, Lattice Least-Squares (LLS) algorithms using a posteriori and a priori estimation errors, modified LSL algorithm; QRD-LSL algorithm
• Applications
• Echo cancellation, active noise control, adaptive arrays, blind equalization