ECE 513: Vector Space Signal Processing (Spring 2024)

Course Information

  • Lectures: Tuesdays-Thursdays, 9:30-10:50 AM, ECEB 3015. 

  • Instructor: Prof. Minh N. Do.

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

  • Teaching Assistant: Renán A. Rojas-Gómez.

    • Office hours: Wednesdays 9-10 AM, 221 CSL.


Grading Policy

Gradescope code: YDNXVY.
  • Homeworks: 25%

  • Exam 1: 25%

  • Exam 2: 25%

  • Project: 25%


  • 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.

  • S. Axler, Linear Algebra Done Right (4th edition), Springer. PDF Link.

  • S. Damelin and W. Miller, Jr, The Mathematics of Signal Processing, Cambridge University Press. PDF Link.

  • C.L. Byrne, Signal Processing: A Mathematical Approach, (2nd edition). Chapman and Hall/CRC. PDF Link.