Probability axioms, conditioning and independence, combinatorics, random variables and distributions, averages and moments, functions of a random variable, joint distributions and densities, limits, moment generating function, the central limit theorem, sample mean and variance, regression techniques, empirical distributions, law of large numbers.
Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, communications, as well as other engineering applications.
Signal Theory (EESC 6350)
Basic overview of matrix and vector analysis, vector representation of signals, least squares (LS) approximation and the orthogonality principle, Minimum-norm and MNLS solutions, psuedo-inverses, eigen-value and singluar-value decompositions. Time permitting, additional advanced topics will also be visited.
Coding Theory (EESC 6344)
Theory and practice of error-control coding; Linear block codes, LDPC Codes cyclic codes, BCH codes, Reed-Solomon codes, convolutional codes, trellis coded modulation, Turbo Codes.
Information Theory (EESC 6341)
Probability review, Entropy, mutual information, the asymptotic equipartition property. Lossless compression: Huffman, Shannon, Elias, and arithmetic coding. Channel capacity: Shannon’s channel coding theorem, discrete channels, Gaussian channels, waveform channels, elements of rate-distortion theory.
Probability review, sequences of random variables, convergence, random processes, continuity, Markov processes, Wiener and Poisson processes, random signals and linear systems, filtering, prediction and smoothing
Baseband signal analysis, PCM, Channel effects: noise and distortion, Detection of binary signals in noise, Matched filter and correlation receiver, Intersymbol interference and equalization, ASK, PSK, FSK, Coherent and non-coherent detection, Error performance, M-ary signaling, Elements of coding: block codes and their decoding, convolutional codes.
Source Coding and Compression
Lossless and lossy compression of signals. Review of Huffman, arithmetic and Lempel-Ziv coding. Overview of linear estimation and prediction, the Levinson-Durbin algorithm. Scalar quantization, optimality conditions and the Lloyd-Max algorithm. Vector quantization, optimality and the generalized Lloyd algorithm. Predictive quantization and performance bounds. Bit allocation and transform coding. Tree-structured VQ, hierarchical VQ. Advanced topics: trellis coded quantization (TCQ).
Digital Signal Processing
Digital signals and systems, digital filter design, the FFT and its variations, multirate signal processing and wavelets
Image and Video Communications
Signals and Systems (undergraduate)
Continuous- and discrete-time linear time-invariant systems; time domain analysis, Fourier and Laplace frequency domain analysis, stability, Nyquist sampling.