The Course Presents Fundamental Methods For Processing and Analyzing Signals and Data Sources, Using Both Deterministic and Stochastic Tools. The Topics Covered Are# Signals and Systems in Discrete Domain, Fourier Analysis For Linear Time Invariant Systems, Signal Processing and Representation in Algebraic Spaces, Statistical Estimation - Maximum Likelihood, Bayesian Methods, Fundamentals In Random Processes - Wiener, Poisson, and Markov Processes, Linear Filtering, Random Noise, Parametric Models For Random Processes And Their Estimation, The Cramer-rao Bound, Linear Prediction and Adaptive Filters. Proving Optimality and Uniqueness of The Truncated Fourier Basis in Representing Functions With Bounded Dirichlet Energy, 2-optimal Approximation For The Clustering Problem and Introduction To Functional Maps. Learning Outcomes# Graduates of This Course Will Be Able To# 1. Characterize Linear Time Invariant Systems, and Tie This Analysis To The Frequency Domain. 2. Transform Signals to Alternative Representations, Adopting a Matrix Form For The System and a Vector For The Signals 3. Apply Statistical Estimation Methods, Parametric And Direct, to a Variety of Basic Problems in Data Processing. 4. Apply Linear Filtering Methods Such As The Wiener Filter, To Stochastic Sources of Noisy Data. 5. Set Performance Bounds For Various Estimation Problems.

Faculty: Computer Science
|Undergraduate Studies |Graduate Studies

Pre-required courses

44131 - Signals and Systems or 104174 - Algebra Bm or 234125 - Numerical Algorithms

Course with no extra credit

236201 - Introduction to Data Processing And 236327 - Digital Image and Signal Processing

Semestrial Information