Representation of signals and systems; system properties; sampling; Laplace and z-transforms; transfer functions and frequency response; convolution; stability; Fourier series; Fourier transform; AM/FM modulation; applications.

# Courses

### Course Level: Undergraduate

Introduction to electrostatics and magnetostatics; properties of conductive, dielectric, and magnetic materials; solutions of Maxwell's equations; frequency- and time-domain analysis transmission lines; uniform plane wave applications.

Solutions of time-varying Maxwell's equations with application to antennas and wireless propagation; antenna theory and design; array synthesis; electromagnetic wave propagation, scattering and diffraction; numerical methods for solving Maxwell's equations.

Probability, random variables, statistics, and random processes including counting, independence, conditioning, expectation, density functions, distributions, law of large numbers, central limit theorem, confidence intervals, hypothesis testing, statistical estimation, stationary processes, Markov chains, and ergodicity. In most sections, examinations are given on Wednesday nights; see the Course Schedule for more information.

Sampling, aliasing, truncation effects; discrete and fast Fourier transform methods; convolution and deconvolution; finite and infinite impulse response filter design methods; Wiener, Kalman, non-causal, linear phase, median, and prediction filters; spectral estimation.

Communication channels and their impairments; modulation; demodulation; probability of error analysis; source coding; error control coding; link budget analysis; equalization; synchronization and multiple access; spread spectrum; applications in wireline and wireless communication systems.

The concept of feedback is central in the study of systems and control. Feedback loops naturally appear in the most basic biological phenomena, including macroscopic scale (population evolution, extinction, etc.) but also physiological function, for example, regulation of glucose level in the blood. In Engineering, feedback has long played an important role in mechanical, electronic, and now also digital systems.

Digital image acquisition, processing, and analysis; algebraic and geometric image transformations; two-dimensional Fourier analysis; image filtering and coding.

Circuit and packet-switched networks; local area networks; protocol stacks; ATM and broadband ISDN; Internet; routing, congestion control, and performance evaluation; multimedia applications.

Distributed information system security; cryptographic tools; authentication; message security; system management.

Local, metropolitan, and wide-area operations; telecommunication common carrier organization and services; economic, administrative, and political considerations; premise distribution systems; name resolution, address assignment, and mail; datagrams, packets, frames, and cells; addressing and network-level interconnection; inter-network architecture; TCP/IP protocol suite (version 4 and 6); Ethernet and IEEE 802.3 standards; repeaters, hubs, bridges, routers; local area network emulation; public switched network access through POTS and ISDN; intra-domain and inter-domain routing; routing pr

System-level design tradeoffs in signal quality vs. implementation complexity; prototyping of baseband transceivers in real-time embedded software; addressing nodes, parallel instructions, pipelining, and interfacing in digital signal processors; sampling, filtering, quantization, and data conversion; modulation, pulse shaping, pseudo-noise sequences, carrier recovery, and equalization; and desktop simulation of digital communication systems.

### Course Level: Graduate

This class is one of our core classes, and it serves as an introduction to concepts and tools from system theory. It covers: Advanced linear algebra, including matrix algebra and analysis, and theory of linear operators. The first part of the course is primarily concerned with developing these important tools. It forms the technical bulk of the class, and developing this direction is as much a focus and goal of the course as anything else.

Analyzing large data sets for interesting and useful information. Includes online analytical processing, finding association rules, clustering, classification, and function approximations. Scalability of algorithms and real-life applications.

Analysis of data and information available from the World Wide Web. Exploiting the hyperlink structure of the Web for developing better search engines. Content analysis, information retrieval, clustering, and hierarchical categorization of Web documents. Web usage mining. Collaborative filtering and personalizing the Web. Additional prerequisite: Electrical Engineering 380L (Topic 10: Data Mining) or Computer Sciences 391L.

Higher-level languages for engineering design and problem solving; object-oriented programming in C++ and Unix systems programming.

Input/output systems calls, drivers and descriptors, and integrated circuits. Design and implementation of hardware and software for a Unix-like operating system.

Pattern recognition topics, including Bayesian decision theory, maximum likelihood and estimation, nonparametric techniques, and linear discriminant functions. Computer vision topics, including geometric camera models and calibration, geometry of multiple views and stereopsis, structure from motion, and tracking. Emphasis varies each semester.

Discussion of current research results and exploration of new directions in computer vision systems. Includes linear discriminant functions, nonmetric methods, unsupervised learning and clustering, model-based vision, segmentation using probabilistic methods, and content-based image and video analysis. Application of the techniques to real-world vision systems. Emphasis varies each semester.

Feed-forward networks, distributed associative memory, recurrent networks, self-organization, parallel implementation, and applications.

Probability spaces, random variables, expectation, conditional expectation, stochastic convergence, characteristic functions, and limit theorems. Introduction to Markov and Gaussian processes, stationary processes, spectral representation, ergodicity, renewal processes, martingales, and applications to estimation, prediction, and queueing theory.

Introduction to fundamental aspects of wireless communications. Channel modeling, radio propagation, cellular concepts, fading and multipath countermeasures (equalization, diversity, channel coding), spread spectrum, and basic multiple access techniques. Additional prerequisite: Electrical Engineering 351K and 371M, or their equivalents.

Stochastic and deterministic traffic and queueing models. Techniques for call admission, routing, flow control, network optimization, estimation, and decision making in uncertain environments. Additional prerequisite: Electrical Engineering 381J and 382N (Topic 5: Communication Networks: Technology, Architectures, and Protocols).

Multidimensional signals and systems, multidimensional discrete Fourier analysis, discrete cosine transform, two-dimensional filters, beamforming, seismic processing, tomography, multidimensional multirate systems, image halftoning, and video processing. Additional prerequisite: Electrical Engineering 380K, 381K (Topic 8), or 383P (Topic 1: Fourier Optics).

Characterization of communication signals and systems (bandpass signals and systems, signal space representation, digitally modulated signals, and spectral characteristics), optimum receivers for additive white Gaussian noise (correlation demodulator, matched-filter demodulator, performance for binary and M-ary modulation, and noncoherent receivers), error control codes (block and convolutional), and bandlimited channels (ISI and equalization, MLSE, and OFDM). Additional prerequisite: Electrical Engineering 351K, 351M, and 360K.

Methods and research issues in the performance evaluation and management of high-speed and mobile communication networks. Additional prerequisite: Electrical Engineering 380N (Topic 11: Optimization in Engineering Systems), 381J, and 381K (Topic 13).

Introduction to the fundamentals of estimation theory, with applications to stochastic and adaptive signal processing. Topics include deterministic and stochastic least-squares estimation; the innovation process; spectral factorization and Wiener filtering; state-space structure and Kalman filters; array and fast array algorithms; LMS and RLS adaptive filters; Markov chain Monte Carlo methods; Bayesian filtering and particle filters; parameter estimation; expectation-maximization algorithm; Cramer-Rao bounds.

Source and channel coding theorems, Kolmogorov complexity, network information theory, and connections with large deviations. Additional prerequisite: Electrical Engineering 371M.

Signals and systems; generalized functions; z-transforms; Fourier series and transforms; fast Fourier transform; sampling, quantization, and aliasing; digital filter design; discrete-time random processes; multirate processing; filter banks and subband decomposition; nonlinear digital filters. Additional prerequisite: Electrical Engineering 351K and 351M.

Signal modeling; optimum filtering; spectral estimation; fast algorithms; and applications in array signal processing, speech coding, and digital communication. Additional prerequisite: Electrical Engineering 351K, 381K (Topic 8), and Mathematics 340L.

Multiple-input multiple-output (MIMO) wireless communication, including discrete-time signal models, equalization, and channel estimation; channel models; channel capacity; average probability of error in fading channels; channel coding; transmit and receive diversity; space-time codes; spatial multiplexing; precoding and limited feedback; space-time adaptation; multiuser communication; multiuser information theory; practical multiuser algorithms; and applications in recent standards. Three lecture hours a week for one semester.

This is part of a two-course sequence on Large Scale Optimization and Large Scale Learning. We focus on Convex Optimization including basic material from convex geometry, convex analysis and convex optimization. It will cover basic modeling, and understanding how to find and exploit convexity, both for theoretical analysis, and also for developing algorithms. This class is structured to be interesting and relevant to students who are using or plan to use optimization in their research, and are interested in solving large-scale optimization problems.

This is the second course in a two-course sequence on Large-Scale Optimization and Learning. While the first course (EE381V-11a) focused on convex optimization, with an emphasis on methods for large-scale problems, this course will focus on drawing inference from data - machine learning techniques, with a focus on methods for problems of large size and high dimensionality. Intended audience: This class is structured to be interesting and relevant to students who are using or plan to use machine learning in their research, and are interested in solving large-scale problems.

This is a research-level graduate class geared towards advanced graduate students. The topics change from year to year, to reflect latest developments in the field, exciting topics, and topics of most interest. In the past, the first half of the course has focused on Convex Analysis, developing the geometry of convexity and proving the basic duality results of convex sets and then convex functions. The goal is to impart an appreciation of the questions, tools, and techniques central to convex analysis, to enable the student to go on to read the foundational texts on the topic.

Study of parallel computing, including models, algorithms, languages, compilers, interconnection networks, and architectures.

Concurrent programming languages, distributed algorithms, distributed operating systems, distributed data, formal models of concurrency, protection and security in computer networks.

Models for discrete event systems, state machines, Petri nets, algebraic models, temporal logic, control of discrete event systems, observability, stability, simulation.

Design of computer arithmetic units: fast adders, fast multipliers, dividers, and floating-point arithmetic units.

Advanced topics in computer arithmetic, including error correcting coding, residue number systems, CORDIC arithmetic, and VLSI implementation. Additional prerequisite: Electrical Engineering 382N (Topic 14).

Hardware and software parallelism and locality mechanisms, and their impact on processor performance, bandwidth, and power requirements; architectures and microarchitectures of throughput-oriented processors that rely on parallelism, locality, and hierarchical control; parallel memory systems; and streaming and bulk execution and programming models. Includes programming and measuring performance on massively parallel processors. Electrical Engineering 382N (Topic 20) and 382V (Topic: Principles of Computer Architecture) may not both be counted.

Hardware and software design of microcontroller systems; applications, including communication systems; object-oriented and operating systems approaches to interfacing and resource management.

Network services and techniques, layered architectures, circuit and packet-switching networks, internetworking, switch architectures, control mechanisms, and economic issues.