ECE 513: Vector Space Signal Processing (Spring 2020)

Course Information

  • Lectures: Mon-Wed 9:30 - 10:50 AM, ECEB 4070

  • Instructor: Prof Minh N. Do

    • Office hours: Tuesdays, 4-5 PM, CSL 113

  • Teaching Assistant: Vaishnavi Subramanian

    • Office hours: Mondays 4-5 PM, CSL 114

Grading Policy

  • Homeworks: 20%

  • Exam 1: 25%

  • Exam 2: 25%

  • Project: 30%

Outline

  • 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

Reading

  • Class notes by Bresler, Basu and Couvreur (BBC) - Available on the lectures page