Course abstract

• 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 inclusing convergence issues. • 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): regularized methods, reconstruction from projections, iterative methods such as projection onto convex sets