ECE 513 - Vector Space Signal Processing

Summer 2009 | Fall 2009 | Spring 2010 | Summer 2010
Web Page http://courses.ece.uiuc.edu/ece513/
Subject Area Signal Processing
Course Prerequisites Credit in ECE 313
Credit in ECE 410
Credit in MATH 415
Course Directors Yoram Bresler
Description Fundamentals of linear least squares estimation of discrete-time signals and their spectra: minimum-norm least squares and total least squares solutions; singular value decomposition; Wiener and Kalman filtering; autoregressive spectral analysis; and the maximum entropy method.
Credit 4 hours
Topics
  • Matrix inversion: orthogonal projections; left and right inverses; minimum-norm least squares solutions; Moore-Penrose pseudoinverse; reularization; singular value decomposition; Eckart and Young theorem; total least squares; principal components analysis
  • Projections in Hilbert space: Hilbert space; projection theorem; normal equations, approximation and Fourier series; pseudoinverse operators, application to extrapolation of bandlimited sequences
  • Hilbert space of random variables: spectral representation of discrete-time stochastic processes; spectral factorization; linear minimum-variance estimation; discrete-time Wiener filter; innovations representation; Wold decomposition; Gauss Markov theorem; sequential least squares; discrete-time Kalman filter
  • Power spectrum estimation: system identification; Prony's linear prediction method; Fourier and other nonparametric methods of spectrum estimation; resolution limits and model based methods; autoregressive models and the maximum entropy method; Levinson's algorithm; lattice filters; harmonic retrieval by Pisarenko's method; direction finding with passive multi-sensor arrays
Course Prerequisites ECE 313, ECE 410, and MATH 415.
Texts Class notes.

Recommended:
B. Porat, Digital Processing of Random Signals, Prentice-Hall, 1994.