**Probability and Statistics (ENGR 3341)**

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 Optimization (EEGR 6397)**

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.

**Random Processes**

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

**Digital Communications**

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.