ECE 513
Home
Syllabus
Lectures
Homeworks
Exams
Projects

ECE 513: Vector Space Signal Processing (Spring 2020)

Course Information

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

  • LINK SAME AS INSTRUCTOR OFFICE HOURS

  • Instructor: Prof Minh N. Do

    • Office hours: Tuesdays, 4-5 PM,

    • Zoom: Link, Meeting ID: 217 244 4782

  • Teaching Assistant: Vaishnavi Subramanian

    • Feel free to email TA for any questions. Office hours cancelled.

Announcements

  • We will be having online instructions starting March 23rd.

  • All homeworks will need to be uploaded on Compass. The LaTex files for the homeworks will henceforth be shared to help you typset your solutions. Typesetting is not required but well appreciated!

  • TA and instructor office hours will be conducting via Zoom at the regular times.

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.