Mathematical methods and techniques in signal processing [E9 252 (3:0) – Fall 2015]

Instructor: 
Shayan G. Srinivasa,

[Monday, Wednesday 3:30 pm – 5:00 pm, Old Conference Hall]

Pre-requisities:

Digital signal processing at the undergrad level.

Course Syllabus:

  • Review of basic signals, systems and signal space: Review of 1-D signals and systems, review of random signals, multi-dimensional signals, review of vector spaces, inner product spaces, orthogonal projections and related concepts.
  • Basics of multi-rate signal processing: sampling, decimation and interpolation, sampling rate conversion (integer and rational sampling rates), oversampled processing (A/D and D/A conversion), and introduction to filter banks.
  • Signal representation: Transform theory and methods (FT and variations, KLT), other transform methods.
  • Wavelets: Characterization of wavelets, wavelet transform, multi-resolution analysis.
  • Statistical signal modeling: The least squares method, Pade’s approximation, Prony’s method, Shanks’ method, iterative pre-filtering, all-pole modeling and linear prediction, autocorrelation and covariance methods, FIR least squares inverse filter design, applications and examples.
  • Inverse problems (signal reconstruction): underdetermined least squares, pseudo-inverse (SVD), min-norm solutions, regularized methods, reconstruction from projections, iterative methods such as projection onto convex sets, expectation-maximization and simulated annealing.

Reference Books:

  • Moon & Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice Hall, 2000. (required)
  • Monson Hayes, Statistical Digital Signal Processing and Modeling, John Wiley and Sons, 1996. (optional)
  • Class notes

Grading Policy:

Homeworks:      25%

Mid-term exam: 25%

Project:                25%

Final exam:         25%

Homeworks

Exams

Project

Course announcements

  • Final exam: Assigned on 27th Nov, 2015. Submission due 4th Dec, 2015 in class.
  • Project report due date: 4th Dec, 2015 in class.
  • Project presentations and demos : 2:00PM – 5:00 PM, 4th Dec, 2015.