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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.

Week

Topics

1.

Review of vector  spaces, inner product spaces, orthogonal projections, state variable representation

2.

Review of probability and random processes

3.

Signal geometry and applications

4.

Sampling theorems multirate signal processing  decimation and expansion (time and frequency domain effects)

5.

Sampling rate conversion and efficient architectures, design of high decimation and interpolation filters, Multistage designs.

6.

Introduction to 2 channel QMF filter bank, M-channel filter banks, overcoming aliasing, amplitude and phase distortions.

7.

Subband  coding and Filter Designs: Applications to Signal Compression

8.

Introduction to multiresolution analysis and wavelets, wavelet properties

9.

Wavelet decomposition and reconstruction, applications to denoising

10.

Derivation of the KL Transform, properties and applications.

11.

Topics on matrix calculus and constrained optimization relevant to KL Transform derivations.

12.

Fourier expansion, properties, various notions of convergence and applications.
  1. UG in Digital Signal Processing, familiarity with probability and linear algebra

  • 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

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