Syllabus: 36 hour Graduate Lecture Module on

**Adaptive Signal Processing**

University of Strathclyde, Glasgow, UK.

The aim of the Adaptive Signal Processing course is to present its algorithms and architectures and explain their use in real world applications. As prerequisites it is assumed that students have studied discrete and continuous signals and systems, and introductory linear algebra.

The syllabus of the course can be summarized as:

**Introduction to Adaptive Filtering:**a historical perspective; a state of the art perspective.**Statistical Signal Processing Revision:**correlation; ergodicity; means, variances; stationarity; wide sense stationarity; periodogramme; frequency response vs.~power spectrum.**Matrix Algebra Revision:**addition, multiplication and matrix inverses; properties of the correlation/covariance matrix; eigenvalues and eigenvectors; QR algorithm.**Wiener Filter Theory:**normal equations; error performance surfaces; orthogonality; minimum mean square errors.**The Least Mean Squares (LMS) algorithm:**formulation; convergence; stability criteria. Algorithm variations: normalized algorithm, sign error algorithm, sign data algorithm, leaky algorithm, filtered-X algorithm, variable step-size algorithm.

**Applications of the LMS:**System identification; room acoustics, control systems; inverse system modeling; modems, telecommunications adaptive equalization, echo cancelation; adaptive beamforming (radar, sonar, hearing aids, listening devices); active noise cancelation systems in cars, airplanes, medical systems, communication systems.**Recursive LMS-IIR Algorithms:**output error formulation; equation error formulation; full gradient, simplified gradient, SHARF, Feintuch's algorithm; applications of recursive LMS algorithms.**Frequency Domain Adaptive LMS:**Architectures, advantages, and disadvantages.**General Least Squares Solution:**Least squares solution of general adaptive system; QR algorithm solution.**Recursive Least Squares (RLS) algorithm:**RLS formulation; forgetting factors; practical implementations; QR based RLS; numerical stability and integrity issues.**Adaptive Lattice Filters:**gradient lattice, RLS lattice.**Non Linear Adaptive Filters:**simple LMS neuron, adaptive polynomial filters (Volterra).**Comparative Analysis:**Wiener; LMS-FIR, LMS-IIR; RLS, lattice; frequency domain and neural networks for adaptive signal processing applications**Implementation of Adaptive Filters:**DSP microprocessor implementation; software; custom hardware.**Application Examples:**Examples for the use and performance of adaptive filters are given and demonstrated by audio demonstrations.