ECE 513: Vector Space Signal Processing (Spring 2021)

Course Information

  • Lectures: Mon-Wed 9:30 - 10:50 AM

  • LINK SAME AS INSTRUCTOR OFFICE HOURS

  • Instructor: Prof. Yoram Bresler

    • Office hours: Tuesdays, 4-5 PM,

    • Zoom: Link, Meeting ID: 895 8140 0620

  • Teaching Assistant: Yudu Li

    • Office hours: Mondays, 4-5 PM & Thursdays, 7-8 PM

    • Zoom: Link, Meeting ID: 897 4384 4706

    • Email: yuduli2@illinois.edu

Announcements

  • Recorded videos of the lectures are available from the "Lectures" tab.

  • Slides/classnotes  are available from the "Lectures" tab.

  •  Project Presentations scheduled

  • HW8 (our last one!) posted

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; regularization; singular value decomposition; Eckart and Young theorem; total least squares; principal components analysis. Applications in inverse problems and in various signal and image processing problems.

  • Projections in Hilbert space: Hilbert space; projection theorem; normal equations, approximation and Fourier series; pseudoinverse operators, application to extrapolation of bandlimited sequences, and to compressive sensing.

  • 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.

  • Damelin, S., & Miller, Jr, W. (2011). The Mathematics of Signal Processing (Cambridge Texts in Applied Mathematics). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139003896 PDF Link.

  • Byrne, C.L. (2014). Signal Processing: A Mathematical Approach, Second Edition. (2nd edition). Chapman and Hall/CRC, https://doi.org/10.1201/b17672 - PDF Link.