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.

Resources

Lectures are available on Media Space.
Discussion board available on Campuswire. Access code: 2832.

Grading Policy

Gradescope code: YDNXVY.

Homeworks: 25%
Exam 1: 25%
Exam 2: 25%
Project: 25%

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.
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.