MOOC: Mathematical methods and techniques in signal processing [Spring 2018]

Shayan G. Srinivasa

Link to the online course

UG in Digital Signal Processing, familiarity with Probability and Linear Algebra

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.
  • Sampling theorems (a peek into Shannon and compressive sampling), 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 including convergence issues.
  • Wavelets: Characterization of wavelets, wavelet transform, multi-resolution analysis.

Reference Books:

  • Moon & Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice Hall, 2000. (required)
  • P. P. Vaidyanathan, Multirate systems and filter banks, Prentice Hall, 2000. (required)
  • A. Boggess & F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall, 2001.
  • G. Strang, Introduction to Linear Algebra, 2016.
  • H. Stark & J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 2014.
  • Class notes

Grading Policy:

Assignments:      25%
Final exam:         75%