ECE 513: Vector Space Signal Processing (Spring 2022)

Course Information

  • Lectures: Mon-Wed 9:30 - 10:50 AM 

  • Zoom: Link

  • Instructor: Prof. Zhizhen Zhao

    • Office hours: Thursdays, 4-5 PM,

    • Zoom: Link


  • Recorded videos of the lectures are available in the media space.

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

  • Homework 6 is posted, due 11:59pm Friday, April 15, 2022. (Update: the homework link is updated.)

  • Final projects deadlines are updated in Projects

Grading Policy

  • Homeworks: 10%

  • Exam 1: 25%

  • Exam 2: 25%

  • Project: 40%


  • 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


  • 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, - PDF Link.