Advanced DSP

In Brief: Linearity and Time Invariance are universally applicable approximations. A large number of physical phenomena are thus modelable as an LTI system. We start with the question, “If we know the output of an LTI system, can we find the input?” This simple question will take us on a long and winding journey through advanced topics of signal processing and statistical signal processing. Along the way, we will meet the least squares method, many problems in linear algebra, and the fundamentals of statistical signal processing.

Target Audience: The subject matter should be of maximum interest to electrical, electronics, computer and instrumentation engineers and people interested in scientific computation. Also serves as a good applied introduction to DSP, linear (matrix) algebra, and probability and statistics; thus, should be relevant to all engineers and applied mathematicians.

Course Topics: Convolution, deconvolution, least squares problems and algorithms, system models and identification. Random processes, their spectra, whitening, spectrum estimation, Weiner filtering.

Prerequisites: A basic course in DSP would be beneficial, but not necessary. All we will use is the idea of convolution, transform theory (Fourier, Laplace, z) not required. Basic knowledge of probability (balls and urns) would be beneficial. Calculus, as required, will be developed.

Teacher's Introduction: Udayan Kanade did his MS in CS with the specialization "Optimization and Signal Processing" from Stanford. He led the DSP team at Codito for three years, and currently works for Oneirix Labs, a DSP research firm. Udayan has taught Advanced DSP four times, and also basic DSP thrice.