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Mathematical Methods and Techniques in Signal Processing

Indian Institute of Science Bangalore via NPTEL

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Overview

  • 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.

Syllabus

Week 1 : Review of vector spaces, inner product spaces, orthogonal projections, state variable representation
Week 2 : Review of probability and random processes
Week 3 : Signal geometry and applications
Week 4 : Sampling theorems multirate signal processing decimation and expansion (time and frequency domain effects)
Week 5 : Sampling rate conversion and efficient architectures, design of high decimation and interpolation filters, Multistage designs.
Week 6 : Introduction to 2 channel QMF filter bank, M-channel filter banks, overcoming aliasing, amplitude and phase distortions.
Week 7 : Subband coding and Filter Designs: Applications to Signal Compression
Week 8 : Introduction to multiresolution analysis and wavelets, wavelet properties
Week 9 : Wavelet decomposition and reconstruction, applications to denoising
Week 10 : Derivation of the KL Transform, properties and applications.
Week 11 : Topics on matrix calculus and constrained optimization relevant to KL Transform derivations.
Week 12 : Fourier expansion, properties, various notions of convergence and applications.

Taught by

Shayan Garani Srinivasa

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