# Courses and Registration

## Courses Quick Links |

### Sakai: Duke ECE Graduate Program

Current Duke ECE graduate students can find the most up-to-date course requreiments, exam documents, and other helpful academic forms and resources on the Resources page of the ECE Graduate Program Sakai website. If you are a current student and do not have access to this site, please contact the Graduate Program Coordinator.

## ECE Course Offerings

Below is a list of current ECE courses approved for offering by the department. Please note that all courses are not offered each semester.

**Note:** Students may also take courses from other engineering departments within Duke's Pratt School of Engineering, and courses from other graduate schools at Duke with the permission of the adviser and the Director of Graduate Studies.

**ECE 511(310). Foundations of Nanoscale Science and Technology. **This course is the introductory course for the Graduate Certificate Program in Nanoscience (GPNANO) and is designed to introduce students to the interdisciplinary aspects of nanoscience by integrating important components of the broad research field together. This integrated approach will cross the traditional disciplines of biology, chemistry, electrical & computer engineering, computer science, and physics. Fundamental properties of materials at the nanoscale, synthesis of nanoparticles, characterization tools, and self-assembly. Prerequisites: Physics 152L(62L) and Chem 101DL(21L) or instructor approval. C-L: NANO 511; pending in COMPSCI, CHEM, and PHYS. Instructor: Dwyer. 3 units. C-L: Nanosciences 511(310).

**ECE 521(211). Quantum Mechanics.** Discussion of wave mechanics including elementary applications, free particle dynamics, Schrödinger equation including treatment of systems with exact solutions, and approximate methods for time-dependent quantum mechanical systems with emphasis on quantum phenomena underlying solid-state electronics and physics. Prerequisite: Mathematics 216(107) or equivalent. Instructor: Brady, Brown, or Stiff-Roberts. One course.

**ECE 522(212). Introduction to Micro-Electromechanical Systems (MEMS). **Design, simulation, fabrication, and characterization of micro-electromechanical systems (MEMS) devices. Integration of non-conventional devices into functional systems. Principles of fabrication, mechanics in micrometer scale, transducers and actuators, and issues in system design and integration. Topics presented in the context of example systems. Lab covers design, simulation, and realization of MEMS devices using commercially available foundry process. Prerequisite: ECE 230L(51L) or ME 344L(125L) or equivalent. Instructors: Kim. One course.

**ECE 523(227). Quantum Information Science.** Fundamental concepts and progress in quantum information science. Quantum circuits, quantum universality theorem, quantum algorithms, quantum operations and quantum error correction codes, fault-tolerant architectures, security in quantum communications, quantum key distribution, physical systems for realizing quantum logic, quantum repeaters and long-distance quantum communication. Prerequisites: ECE 521(211) or Physics 464(211) or equivalent. Instructor: Kim. One course. C-L: Physics 627(272)

**ECE 524(214). Introduction to Solid-State Physics.** Discussion of solid-state phenomena including crystalline structures, X-ray and particle diffraction in crystals, lattice dynamics, free electron theory of metals, energy bands, and superconductivity, with emphasis on understanding electrical and optical properties of solids. Prerequisite: quantum physics at the level of Physics 264(143L) or Electrical and Computer Engineering 521(211). Instructor: Staff. One course.

**ECE525(215). Semiconductor Physics.** A quantitative treatment of the physical processes that underlie semiconductor device operation. Topics include band theory and conduction phenomena; equilibrium and nonequilibrium charge carrier distributions; charge generation, injection, and recombination; drift and diffusion processes. Prerequisite: Electrical and Computer Engineering 521(211) or consent of instructor. Instructor: Staff. One course.**ECE 526(216). Semiconductor Devices for Integrated Circuits.** Basic semiconductor properties (energy-band structure, effective density of states, effective masses, carrier statistics, and carrier concentrations). Electron and hole behavior in semiconductors (generation, recombination, drift, diffusion, tunneling, and basic semiconductor equations). Current-voltage, capacitance-voltage, and static and dynamic models of PN Junctions, Schottky barriers, Metal/Semiconductor Contacts, Bipolar-Junction Transistors, MOS Capacitors, MOS-Gated Diodes, and MOS Field-Effect Transistors. SPICE models and model parameters. Prerequisites: ECE 330(162). Instructor: Massoud. One course.

**ECE 527(217). Analog Integrated Circuits.** Analysis and design of bipolar and CMOS analog integrated circuits. SPICE device models and circuit macromodels. Classical operational amplifier structures, current feedback amplifiers, and building blocks for analog signal processing, including operational transconductance amplifiers and current conveyors. Biasing issues, gain and bandwidth, compensation, and noise. Influence of technology and device structure on circuit performance. Extensive use of industry-standard CAD tools, such as Analog Workbench. Prerequisite: Electrical Engineering 526(216). Instructor: Richards. One course.

**ECE 528(218). Integrated Circuit Engineering.** Basic processing techniques and layout technology for integrated circuits. Photolithography, diffusion, oxidation, ion implantation, and metallization. Design, fabrication, and testing of integrated circuits. Prerequisite: Electrical and Computer Engineering 330(162) or 331L(163L). Instructor: Fair. One course.

**ECE 529(219). Digital Integrated Circuits.** Analysis and design of digital integrated circuits. IC technology. Switching characteristics and power consumption in MOS devices, bipolar devices, and interconnects. Analysis of digital circuits implemented in NMOS, CMOS, TTL, ECL, and BiCMOS. Propagation delay modeling. Analysis of logic (inverters, gates) and memory (SRAM, DRAM) circuits. Influence of technology and device structure on performance and reliability of digital ICs. SPICE modeling. Prerequisites: Electrical and Computer Engineering 330(162) and 331L(163L). Instructor: Massoud. One course.

**ECE 531(298). Advanced Topics in Electrical and Computer Engineering.** Opportunity for study of advanced subjects in electrical and computer engineering. Instructor: Staff.**ECE 532(262). Analog Integrated Circuit Design.** Design and layout of CMOS analog integrated circuits. Qualitative review of the theory of pn junctions, bipolar and MOS devices, and large and small signal models. Emphasis on MOS technology. Continuous time operational amplifiers. Frequency response, stability and compensation. Complex analog subsystems including phase-locked loops, A/D and D/A converters, switched capacitor simulation, layout, extraction, verification, and MATLAB modeling. Projects make extensive use of full custom VLSI CAD software. Prerequisite: Electrical and Computer Engineering 330(162) or 331L(163L). Instructor: Morizio. One course.

**ECE 533. Biochip Engineering.** A problem-solving course in which students consider technology options for a complete lab-on-a-chip design. Lectures cover the basics of analog flow microfluidic devices, digital microfluidic devices, fabrication technologies for discrete devices, system integration issues, and a significant emphasis on biological applications for analysis, sample preparation, and detection issues. Technologies covered will include microfluidic devices, electrophoresis, analytical methods used in genetics, sample preparation methods, and analyte detection. Prerequisites: Biology 201L, Chem 101DL, and Physics 152L (or equivalents). Instructor: Fair. 3 units.

**ECE 534(264). CAD For Mixed-Signal Circuits.** The course focuses on various aspects of design automation for mixed-signal circuits. Circuit simulation methods including graph-based circuit representation, automated derivation and solving of nodal equations, and DC analysis, test automation approaches including test equipments, test generation, fault simulation, and built-in-self-test, and automated circuit synthesis including architecture generation, circuit synthesis, tack generation, placement and routing are the major topics. The course will have one major project, 4-6 homework assignments, one midterm, and one final. Prerequisites: ECE 331L(163L). Permission of instructor required. Instructor: Ozev. One course.**ECE 536(266). Synthesis and Verification of VLSI Systems.** Algorithms and CAD tools for VLSI synthesis and design verification, logic synthesis, multi-level logic optimization, high-level synthesis, logic simulation, timing analysis, formal verification. Prerequisite: Electrical and Computer Engineering 250L(52L) or equivalent. Instructor: Chakrabarty. One course.

**ECE 537(267). Radiofrequency (RF) Transceiver Design.** Design of wireless radiofrequency transceivers. Analog and digital modulation, digital modulation schemes, system level design for receiver and transmitter path, wireless communication standards and determining system parameters for standard compliance, fundamentals of synthesizer design, and circuit level design of low-noise amplifiers and mixers. Prerequisites: Electrical and Computer Engineering 280L(54L) and Electrical and Computer Engineering 331L(163L) or equivalent. Instructor: Ozev. One course.

**ECE 538(269). VLSI System Testing.** Fault modeling, fault simulation, test generation algorithms, testability measures, design for testability, scan design, built-in self-test, system-on-a-chip testing, memory testing. Prerequisite: Electrical and Computer Engineering 250L(52L) or equivalent. Instructor: Chakrabarty. One course.

**ECE 539(261). CMOS VLSI Design Methodologies.** Emphasis on full-custom chip design. Extensive use of CAD tools for IC design, simulation, and layout verification. Techniques for designing high-speed, low-power, and easily-testable circuits. Semester design project: Groups of four students design and simulate a simple custom IC using Mentor Graphics CAD tools. Teams and project scope are multidisciplinary; each team includes students with interests in several of the following areas: analog design, digital design, computer science, computer engineering, signal processing, biomedical engineering, electronics, photonics. A formal project proposal, a written project report, and a formal project presentation are also required. The chip design incorporates considerations such as cost, economic viability, environmental impact, ethical issues, manufacturability, and social and political impact. Prerequisites: Electrical and Computer Engineering 250L(52L) and Electrical and Computer Engineering 331L(163L). Some background in computer organization is helpful but not required. Instructor: Chakrabarty. One course.

**ECE 541. Advanced Optics. **3 units. C-L: see Physics 621; also C-L: Biomedical Engineering 552

**ECE 545(225). Nanophotonics.** Theory and applications of nanophotonics and sub-wavelength optics. Photonic crystals, near-field optics, surface-plasmon optics, microcavities, and nanoscale light emitters. Prerequisite: Electrical and Computer Engineering 270L(53L) or equivalent. Instructor: Staff. One course.

**ECE 546(226). Optoelectronic Devices.** Devices for conversion of electrons to photons and photons to electrons. Optical processes in semiconductors: absorption, spontaneous emission and stimulated emission. Light-emitting diodes (LEDs), semiconductor lasers, quantum-well emitters, photodetectors, modulators and optical fiber networks. Prerequisite: Electrical and Computer Engineering 526(216) or equivalent. Instructor: Stiff-Roberts. One course.

**ECE 549. Optics and Photonics Seminar Series. **Weekly seminar on the current research topics in the field of optics and photonics. Instructor: Staff. 1 unit. C-L: Biomedical Engineering 609, Physics 549

**ECE 552(252). Advanced Computer Architecture I.** QS, R One course. C-L: see Computer Science 550(220); also C-L: Modeling Biological Systems ** **

**ECE 550D. Fundamentals of Computer Systems and Engineering. **Fundamentals of computer systems and engineering for Master's students whose undergraduate background did not cover this material. Topics covered include: Digital logic, assembly programming, computer architecture, memory hierarchies and technologies, IO, hardware implementation in VHDL, operating systems, and networking. Undergraduates may not take this course, and should take ECE 250, ECE 253, and/or ECE 356 instead. Instructor: Hilton. 3 units.

**ECE 551D. Programming, Data Structures, and Algorithms in C++.** Students learn to program in C and C++ with coverage of data structures (linked lists, binary trees, hash tables, graphs), Abstract Data Types (Stacks, Queues, Maps, Sets), and algorithms (sorting, graph search, minimal spanning tree). Efficiency of these structures and algorithms is compared via Big-O analysis. Brief coverage of concurrent (multi-threaded) programming. Emphasis is placed on defensive coding, and use of standard UNIX development tools in preparation for students' entry into real world software development jobs. Not open to undergraduates. Instructor: Hilton. 3 units.

**ECE 553. Compiler Construction. Covers the fundamentals of compiler design. **Students will develop a working compiler, writing all stages required to take source code as input and produce working assembly as output: lexical analysis, parsing, type checking, translation to intermediate representation, instruction selection, liveness analysis, and register allocation. Students are expected to have a strong programming background prior to taking this course, as writing a compiler is a significant programming task. Prerequisites: Electrical and Computer Engineering 250L or Computer Science 250 or (ECE 550D and ECE 551D). Instructor: Hilton. 3 units. C-L: Computer Science 553

**ECE 554(254). Fault-Tolerant and Testable Computer Systems.** Technological reasons for faults, fault models, information redundancy, spatial redundancy, backward and forward error recovery, fault-tolerant hardware and software, modeling and analysis, testing, and design for test. Prerequisite: Electrical and Computer Engineering 350(152) or equivalent. Instructor: Sorin. One course. C-L: Computer Science 554(225)

**ECE 555(255). Probability for Electrical and Computer Engineers.** Basic concepts and techniques used stochastic modeling of systems with applications to performance and reliability of computer and communications system. Elements of probability, random variables (discrete and continuous), expectation, conditional distributions, stochastic processes, discrete and continuous time Markov chains, introduction to queuing systems and networks. Prerequisite: Mathematics 216(107). Instructor: Trivedi. One course. C-L: Computer Science 555(226), Information Science and Information Studies, Modeling Biological Systems

**ECE 556(256). Wireless Networking and Mobile Computing.** Theory, design, and implementation of mobile wireless networking systems. Fundamentals of wireless networking and key research challenges. Students review pertinent journal papers. Significant, semester-long research project. Networking protocols (Physical and MAC, multi-hop routing, wireless TCP, applications), mobility management, security, and sensor networking. Prerequisites: Electrical and Computer Engineering 356(156) or Computer Science 310(114). Instructor: Staff. One course. C-L: Computer Science 515(215)**ECE 557(257). Performance and Reliability of Computer Networks**. Methods for performance and reliability analysis of local area networks as well as wide area networks. Probabilistic analysis using Markov models, stochastic Petri nets, queuing networks, and hierarchical models. Statistical analysis of measured data and optimization of network structures. Prerequisites: Electrical and Computer Engineering 356(156) and 555(255). Instructor: Trivedi. One course. C-L: Information Science and Information Studies.

**ECE 558. Computer Networks and Distributed Systems.** 3 units. C-L: see Computer Science 514

**ECE 559(251). Advanced Digital System Design.** This course covers the fundamentals of advanced digital system design, and the use of a hardware description language, VHDL, for their synthesis and simulation. Examples of systems considered include the arithmetic/logic unit, memory, and microcontrollers. The course includes an appropriate capstone design project that incorporates engineering standards and realistic constraints in the outcome of the design process. Additionally, the designer must consider most of the following: Cost, environmental impact, manufacturability, health and safety, ethics, social and political impact. Each design project is executed by a team of 4 or 5 students who are responsible for generating a final written project report and making an appropriate presentation of their results to the class. Prerequisite: Electrical and Computer Engineering 250L(52L) and Senior/graduate student standing. Instructor: Derby. One course.

**ECE 571(271). Electromagnetic Theory.** The classical theory of Maxwell's equations; electrostatics, magnetostatics, boundary value problems including numerical solutions, currents and their interactions, and force and energy relations. Three class sessions. Prerequisite: Electrical and Computer Engineering 270L(53L). Instructor: Carin, Cummer, Joines, Liu, or Smith. One course.

**ECE 572(272). Electromagnetic Communication Systems.** Review of fundamental laws of Maxwell, Gauss, Ampere, and Faraday. Elements of waveguide propagation and antenna radiation. Analysis of antenna arrays by images. Determination of gain, loss, and noise temperature parameters for terrestrial and satellite electromagnetic communication systems. Prerequisite: Electrical and Computer Engineering 270L(53L) or ECE 571(271). Instructor: Joines. One course.**ECE 573(273). Optical Communication Systems.** Mathematical methods, physical ideas, and device concepts of optoelectronics. Maxwell's equations, and definitions of energy density and power flow. Transmission and reflection of plane waves at interfaces. Optical resonators, waveguides, fibers, and detectors are also presented. Prerequisite: Electrical and Computer Engineering 270L(53L) or equivalent. Instructor: Joines. One course.

**Analysis of wave phenomena that occur in materials based on fundamental formulations for electromagnetic and elastic waves. Examples from these and other classes of waves are used to demonstrate general wave phenomena such as dispersion, anisotropy, and causality; phase, group, and energy propagation velocities and directions; propagation and excitation of surface waves; propagation in inhomogeneous media; and nonlinearity and instability. Applications that exploit these wave phenomena in general sensing applications are explored. Prerequisites: Electrical and Computer Engineering 270L(53L). Instructor: Cummer. One course.**

ECE 574(279). Waves in Matter.

ECE 574(279). Waves in Matter.

**Microwave circuit analysis and design techniques. Properties of planar transmission lines for integrated circuits. Matrix and computer-aided methods for analysis and design of circuit components. Analysis and design of input, output, and interstage networks for microwave transistor amplifiers and oscillators. Topics on stability, noise, and signal distortion. Prerequisite: Electrical and Computer Engineering 270L(53L) or equivalent. Instructor: Joines. One course.**

ECE 575(275). Microwave Electronic Circuits.

ECE 575(275). Microwave Electronic Circuits.

**ECE 577(277). Computational Electromagnetics.**Systematic discussion of useful numerical methods in computational electromagnetics including integral equation techniques and differential equation techniques, both in the frequency and time domains. Hands-on experience with numerical techniques, including the method of moments, finite element and finite-difference time-domain methods, and modern high order and spectral domain methods. Prerequisite: Electrical and Computer Engineering 571(271) or consent of instructor. Instructor: Carin or Liu. One course.

**Systematic discussion of practical inverse problems in electromagnetics and acoustics. Hands-on experience with numerical solution of inverse problems, both linear and nonlinear in nature. Comprehensive study includes: discrete linear and nonlinear inverse methods, origin and solution of nonuniqueness, tomography, wave-equation based linear inverse methods, and nonlinear inverse scattering methods. Assignments are project oriented using MATLAB. Prerequisites: Graduate level acoustics or electromagnetics (Electrical and Computer Engineering 571(271)), or consent of instructor. Instructor: Liu. One course.**

ECE 578S(278). Inverse Problems in Electromagnetics and Acoustics.

ECE 578S(278). Inverse Problems in Electromagnetics and Acoustics.

**ECE 581(281). Random Signals and Noise.** Introduction to mathematical methods of describing and analyzing random signals and noise. Review of basic probability theory; joint, conditional, and marginal distributions; random processes. Time and ensemble averages, correlation, and power spectra. Optimum linear smoothing and predicting filters. Introduction to optimum signal detection, parameter estimation, and statistical signal processing. Prerequisite: Mathematics 230(135) or Statistics 130(113). Instructor: Collins or Nolte. One course.

**ECE 582(282). Digital Signal Processing.** Introduction to fundamental algorithms used to process digital signals. Basic discrete time system theory, the discrete Fourier transform, the FFT algorithm, linear filtering using the FFT, linear production and the Wierner filter, adaptive filters and applications, the LMS algorithm and its convergence, recursive least-squares filters, nonparametric and parametric power spectrum estimation minimum variance and eigenanalysis algorithms for spectrum estimation. Prerequisite: Electrical and Computer Engineering 581(281) or equivalent with consent of the instructor. Instructor: Collins, Krolik, Nolte, Tantum, or Willett. One course. One course.

**ECE 584(284). Acoustics and Hearing (GE, IM).** One course. C-L: see Biomedical Engineering 545(235)

**Introduction to signal detection and information extraction theory from a statistical decision theory viewpoint. Subject areas covered within the context of a digital environment are decision theory, detection and estimation of known and random signals in noise, estimation of parameters and adaptive recursive digital filtering, and decision processes with finite memory. Applications to problems in communication theory. Prerequisite: Electrical and Computer Engineering 581(281) or consent of instructor. Instructor: Nolte. One course.**

ECE 585(285). Signal Detection and Extraction Theory.

ECE 585(285). Signal Detection and Extraction Theory.

**ECE 587. Information Theory.** Information theory is the science of processing, transmitting, storing, and using information. This course provides an introduction to mathematical measures of information and their connection to practical problems in communication, compression, and inference. Entropy, mutual information, lossless data compression, channel capacity, Gaussian channels, rate distortion theory, Fisher information. Useful for researchers in a variety of fields, including signal processing, machine learning, statistics, and neuroscience. Appropriate for beginning graduate students in electrical engineering, computer science, statistics, and math with a background in probability. Instructor: Reeves, Carin. 3 units. C-L: Statistical Science 563

**ECE 590(299). Advanced Topics in Electrical and Computer Engineering.** Opportunity for study of advanced subjects related to programs within the electrical and computer engineering department tailored to fit the requirements of a small group. Instructor: Staff. One course.

**ECE 611. Nanoscale and Molecular Scale Computing.** Students study the design and analysis of nanoscale computing systems. Topics include nanoelectronic devices (e.g., graphene and carbon nanotube transistors, quantum dots, etc.), computational paradigms (conventional von Neumann, quantum cellular automata, quantum computing, etc.), microarchitecture and instruction set design specific to nanoscale systems, defect and fault tolerance, fabrication techniques (e.g., self-assembly), modeling and simulation methods. This course relies on current literature and student discussion. Prerequisites: Electrical and Computer Engineering 350, Electrical and Computer Engineering 511. Instructor: Dwyer, Lebeck. 3 units. C-L: Computer Science 624

**ECE 631. Analog and RF Integrated Circuit Design, Fabrication, and Test. **For students who have some experience in analog circuit design and want to fabricate and test an IC under faculty supervision. Typically taken over three semesters (Fall, Spring, Summer, or Fall, Spring, Fall) to accommodate design-fabricate-test cycle. Design cycle: students use Cadence or Mentor IC layout tools, and HSPICE or ADS simulation tools. Fabrication cycle: a detailed test plan is developed. Test cycle: students access test facility appropriate for design and submit a report to the IC fabrication foundry. Co-requisite: ECE 539, or consent of instructor. Instructor: Brooke. Variable credit.

**ECE 650 - Systems Programming and Engineering. **Focuses on a range of topics that are central to both the design of operating systems and the programming system-level software. Students will apply knowledge of basic concepts in operating systems, networking, and programming towards these two areas. Topics covered will include concurrency, process management, hypervisors, networking, security, databases, and file systems. Students will be expected to demonstrate their understanding in these areas through a series of programming assignments covering these topics. Prerequisites: ECE 550D and ECE 551D. Instructor: Staff. 3 Units.

**ECE 651 - Software Engineering. **Teaches students about all steps of the software development lifecycle: requirements definition, design, development, testing, and maintenance. The course assumes students are skilled object-oriented programmers from prior courses, but will include a rapid introduction to Java. Students complete team-based semester-long software project which will progress through all phases of the software lifecycle. Prerequisite: ECE 551D. Instructor: Staff. 3 Units.

**ECE 652(259). Advanced Computer Architecture II.** QS One course. C-L: see Computer Science 650(221); also C-L: Modeling Biological Systems

**ECE 675(375). Optical Imaging and Spectroscopy.** Wave and coherence models for propagation and optical system analysis. Fourier optics and sampling theory. Focal plane arrays. Generalized and compressive sampling. Impulse response, modulation transfer function and instrument function analysis of imaging and spectroscopy. Code design for optical measurement. Dispersive and interferometric spectroscopy and spectral imaging. Performance metrics in optical imagine systems. Prerequisite: Electrical and Computer Engineering 270L(53L) and 280L(54L). Instructor: Brady. 3 units.

**ECE 676(376). Lens Design.** Paraxial and computational ray tracing. Merit functions. Wave and chromatic aberrations. Lenses in photography, microscopy and telescopy. Spectrograph design. Emerging trends in lens system design, including multiple aperture and catadioptric designs and nonimaging design for solar energy collection. Design project management. Each student must propose and complete a design study, including a written project report and a formal design review. Prerequisite: Electrical and Computer Engineering 340(122). Instructor: Brady. 3 units. One course.

**ECE 681(243). Pattern Classification and Recognition Technology.** Theory and practice of recognition technology: pattern classification, pattern recognition, automatic computer decision-making algorithms. Applications covered include medical diseases, severe weather, industrial parts, biometrics, bioinformation, animal behavior patterns, image processing, and human visual systems. Perception as an integral component of intelligent systems. This course prepares students for advanced study of data fusion, data mining, knowledge base construction, problem-solving methodologies of "intelligent agents" and the design of intelligent control systems. Prerequisites: Mathematics 216(107), Statistics 130(113) or Mathematics 230(135), Computer Science 101(6), or consent of instructor. Instructor: Collins. One course.** **

**ECE 683(283). Digital Communication Systems. **Digital modulation techniques. Coding theory. Transmission over bandwidth constrained channels. Signal fading and multipath effects. Spread spectrum. Optical transmission techniques. Prerequisite: Electrical and Computer Engineering 581(281) or consent of instructor. Instructor: Staff. One course.** **

**ECE 686(289). Adaptive Filters.** Adaptive digital signal processing with emphasis on the theory and design of finite-impulse response adaptive filters. Stationary discrete-time stochastic processes, Wiener filter theory, the method of steepest descent, adaptive transverse filters using gradient-vector estimation, analysis of the LMS algorithm, least-squares methods, recursive least squares and least squares lattic adaptive filters. Application examples in noise canceling, channel equalization, and array processing. Prerequisites: Electrical and Computer Engineering 581(281) and 582(282) or consent of instructor. Instructor: Krolik. One course.

**ECE 688(288). Sensor Array Signal Processing.** An in-depth treatment of the fundamental concepts, theory, and practice of sensor array processing of signals carried by propagating waves. Topics include: multidimensional frequency-domain representations of space-time signals and linear systems; apertures and sampling of space-time signals; beamforming and filtering in the space-time and frequency domains, discrete random fields; adaptive beamforming methods; high resolution spatial spectral estimation; optimal detection, estimation, and performance bounds for sensor arrays; wave propagation models used in sensor array processing; blind beamforming and source separation methods; multiple-input-multiple-output (MIMO) array processing; application examples from radar, sonar, and communications systems. Instructor: Staff. One course.

**ECE 722(322). Quantum Electronics. **Quantum theory of light-matter interaction. Laser physics (electron oscillator model, rate equations, gain, lasing condition, oscillation dynamics, modulation) and nonlinear optics (electro-optic effect, second harmonic generation, phase matching, optical parametric oscillation and amplification, third-order nonlinearity, optical bistability.) Prerequisite ECE 521(211), Physics 464(211), or equivalent. Instructors: Stiff-Roberts. One course. 3 units.

**ECE 781. Advanced Topics in Signal Processing.** Instructor: Staff. 3 units.

**ECE 784LA. Sound in the Sea: Introduction to Marine Bioacoustics.** 4 units. C-L: see Environment 784LA; also C-L: Biology 784LA

**ECE 891. Internship.** Student gains practical electrical and computer engineering experience by taking a job in industry, and writing a report about this experience. Requires prior consent from the student's advisor and from the Director of Graduate Studies. May be repeated with consent of the advisor and the director of graduate studies. Credit/no credit grading only. Instructor: Staff. 1 unit.

**ECE 899. Special Readings in Electrical Engineering.** Special individual readings in a specified area of study in electrical engineering. Approval of director of graduate studies required. 1 to 4 units. Instructor: Graduate staff. Variable credit.

All graduate-level courses are also listed on the Bulletin of the Duke University Graduate School.

The Registrar's Office also offers a real-time public view of the current Schedule of Classes.