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# Mathematical methods and techniques in signal processing [E9 252 (3:0) – Fall 2017]

Instructor:
Shayan G. Srinivasa,

[Monday, Wednesday 3:30 pm – 5:00 pm, Video Studio (NPTEL, Room no. 203)]

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

• Homeworks : 25%
• Mid Term Exams : 25%
• Project : 25%
• Final Exam : 25%

Homeworks:

Exams:

Lecture Notes:

Announcements:

Exam #2 is on 2nd November 2017 from 6 pm to 9 pm.

Final Exam is on 11th December from 2 pm to 5 pm