1. 12/03Page1 Course Description Emphasis: adaptive digital (discrete-time) filters Secondary emphasis (application): digital data communications Course goals: Enable students to –Design/select adaptive filters for different applications –Read the literature associated with adaptive filters/signal processing Prereqs: 359 (DSP), 422 (random processes)

2. 12/03Page2 Course Topics Description of AF’s, applications Linear prediction, discrete-time Wiener or Minimum Mean Squared Error filtering Lattice filters Stochastic gradient algorithms Least squares filtering Performance (convergence, misadjustment) Additional topics to be selected depending on available time

3. 12/03Page3 Course Information Text: Haykin, “Adaptive Filters (4 th Ed)”, Prentice-Hall 2002 Grading: homework (20%), test (30%), project (50%) One midterm exam (probably around the 8 th week) Project: –Report on some aspect of adaptive filtering (suggestions will be given) –Due last day of class

4. 12/03Page4 Course Information Text: Haykin, “Adaptive Filters (4 th Ed)”, Prentice-Hall 2002 Grading: homework (20%), test (30%), project (50%) One midterm exam (probably around the 8 th week) Project: –Report on some aspect of adaptive filtering (suggestions will be given) –Due last day of class

5. 12/03Page5 Historical Notes Linear estimation theory was first motivated by astronomical studies (motion of planets and comets using telescopic measurements). –Galileo Galilei (1632): minimized various error functions –Gauss (1795, published 1809): introduced method of least squares –Legendre (1810) Minimum Mean Square Error (MMSE) estimation was applied to stochastic processes in the 1930’s and 40’s. –Kolmogorov: comprehensive treatment of linear prediction for discrete-time stochastic processes –Krein: extended to continuous-time via bilinear transformation –Wiener: independently derived continuous-time MMSE linear predictor Kalman filter for dynamic estimation was introduced in 1960 (discrete- time) and 1961 (continuous-time with Bucy).

6. 12/03Page6 Historical Notes: Adaptive Filters Stochastic gradient, or Least Mean Square (LMS) algorithm introduced by Widrow, Hoff in 1959 for a pattern recognition application. Zero-forcing adaptive filter for equalization in data transmission introduced by Lucky in 1965. –Motivated further work on applications of adaptive filters to data communications in 1960’s, 70’s, 80’s Linear prediction for speech modeling introduced by Itakura and Saito in 1966. –Motivated further work on speech modeling and compression from 70’s onward. –Lattice predictor introduced by Itakura and Saito in 1972. –Parallel work on waveform coding methods for speech compression in 60’s, 70s.

7. 12/03Page7 Historical Notes: Additional Applications Spectral analysis of time series based on autoregressive model introduced by Yule in 1927. (Applied to investigate periodicities in time series, i.e., sunspot numbers.) –Maximum entropy spectral estimation introduced by Burg in 1967. Adaptive noise cancellation introduced in 60’s and 70’s. –Echo cancellation (Kelly, Sondhi) –Adaptive line enhancer for cancelling sinusoidal interference (Widrow et al, 1975) Adaptive beamforming introduced by Howells (late 1950s), Applebaum (1966), Widrow et al (1967). Recursive least squares algorithms for adaptive filtering applications were developed by Godard, Kailath, Morf (and others) in the 70’s.