Topics include probability spaces; random variables and vectors; and random sequences and processes; especially specification and classification. Includes detailed discussion of second-order stationary processes and Markov processes; inequalities, convergence, laws of large numbers, central limit theorem, ergodic, theorems; and MS estimation, Linear MS estimation, and the Orthogonality Principle. Prerequisite: APMA 3100, MATH 3100, or equivalent.

Covers foundations of estimation theory and machine learning in a probabilistic modeling framework. Topics include frequentist and Bayesian estimation, analysis of estimators, linear regression, linear classification, graphical models, Markov models, sampling methods, and variational inference. Requires APMA 3100 or an equivalent course on Probability, familiarity with linear algebra, and Python programming.

A first graduate course in digital signal processing. Topics include discrete-time signals and systems, application of z-transforms, the discrete-time Fourier transform, sampling, digital filter design, the discrete Fourier transform, the fast Fourier transform, quantization effects and nonlinear filters. Additional topics can include signal compression and multi-resolution processing.

This course focuses on an in-depth study of advanced topics and interests in image data analysis. Students will learn practical image techniques and gain mathematical fundamentals in machine learning needed to build their own models for effective problem solving. The graduate students (ECE/CS 6501) will be given additional programming tasks and more advanced theoretical questions.

This is an entry-level course on wireless communications, especially we will discuss how machine learning impacts the design of wireless systems. The goal is to teach fundamental and core techniques that enable physical layer wireless communications.

This course aims to provide an instruction to basic principles and tools for the analysis and design of control systems. It is intended for general graduate students in engineering and science. Topics to be covered include concepts, examples and designs of feedback, system modeling, linear and nonlinear dynamic behaviors, stability analysis, frequency domain analysis and design, transfer functions, PID control, and robustness of control systems.

Detailed study of graduate course material on an independent basis under the guidance of a faculty member.

Formal record of student commitment to project research under the guidance of a faculty advisor. A project report is required at the completion of each semester. May be repeated as necessary.

A guided teaching experience for Ph.D. students, with selected teaching assignments and directed performance evaluation, under the supervision of a faculty member, as a part of Ph.D. training designed for students' development of independent teaching skills.

An in-depth treatment of digital communications techniques and performance. Topics include performance of uncoded systems such as Mary, PSK, FSK, and multi-level signaling; orthogonal and bi-orthogonal codes; block and convolutional coding with algebraic and maximum likelihood decoding; burst correcting codes; efficiency and bandwidth; synchronization for carrier reference and bit timing; baseband signaling techniques; intersymbol interference; and equalization. Prerequisite: ECE 6711.