COMPUTATIONAL LINEAR ALGEBRA
Syllabus: Vector spaces: bases, inner product and norm. Linear operators: definition and matrix representation; similarity transformations; eigenvalue and eigenvector analysis. Singular value decomposition. Adjoint and projection operators. Floating-point arithmetic. Linear equations.
LINEAR SYSTEMS ANALYSIS
Syllabus: Fundamental concepts of systems. System dynamics. Linear systems and linearization. Mathematical modeling of dynamical systems. Linear systems and linearization. Fundamental system properties. Global behavior of continuous-time and discrete-time systems. Linear time-invariant systems. Controllability. Observability and stability of continuous-time and discrete-time systems.
ANALYSIS OF LINEAR PARAMETER-VARYING SYSTEMS
Syllabus: Linear parameter-varying (LPV) system models. Quasi-LPV models. Lyapunov stability theory. Linear matrix inequalities (LMIs). Stability analysis of LPV systems. Performance analysis of LPV systems based on extensions of the H-infinity and H2 norms.
ROBUST CONTROL
Syllabus: Convex optimization and linear matrix inequalities (LMIs): algorithms and software. Passivity and robustness using LMIs. Controller analysis and synthesis using LMIs: nonconvexity and bilinear matrix inequalities (BMIs). Combining time-domain and frequency-domain methods for the synthesis of reduced-order robust controllers.
OPTIMAL CONTROL
Syllabus: Fundamentals of state-feedback control. State estimators. Least-squares theory. Optimal observer design (continuous-time and discrete-time Kalman filters). Optimal state-feedback controller design (continuous-time and discrete-time). LQR and LQG regulators. The tracking problem with regulation. Parametric sensitivity.
SUPERVISORY CONTROL OF DISCRETE-EVENT SYSTEMS
Syllabus: Introduction to discrete-event systems (DES). Language and automata theory. Supervisory control of DES. Extensions of supervisory control of DES. Tools for supervisory control of DES. Applications of supervisory control of DES.
DISCRETE-TIME CONTROL SYSTEMS
Syllabus: Fourier analysis: series and transform. Sampling theory. A/D and D/A conversion. Analysis of discrete-time signals and systems. Fourier transform for discrete-time signals. Discrete sequences. Difference equations. Stability and causality in discrete-time systems. Z-transform: properties and inverse transform. Discrete Fourier transform. FFT. Discrete-time equivalents of systems: transfer-function and state-space approaches. Controller and observer design for discrete-time systems.
MULTIVARIABLE SYSTEMS
Syllabus: State-space representations of multivariable linear systems. Structural canonical forms. Compensator construction. Description using polynomial matrices and matrix fractions. Poles and zeros in multivariable systems. Youla–Kučera parameterization. Bézout identity. Decentralized control and simultaneous control.
NONLINEAR SYSTEMS
Syllabus: Analytical methods. Approximate methods: describing functions and Krylov–Bogoliubov methods. Topological methods. Stability analysis: Lyapunov and Popov. Applications of functional analysis to nonlinear systems.
CONTROL SYSTEMS THEORY
Syllabus: Review of classical control theory. Laplace transform and differential equations. Transfer functions and state-space realizations. Classical control-system analysis techniques: root locus and frequency response (Bode, Nyquist and Nichols plots). Classical compensator design techniques. PID and lead–lag controllers. Introduction to optimal control.
SPECIAL TOPICS IN ELECTRIC POWER SYSTEMS
Syllabus: Power-flow calculation: bus admittance (Y) and impedance (Z) matrices; formulation of the power-flow problem; solution methods (Jacobi, Gauss–Seidel, Newton–Raphson, decoupled, fast decoupled and linearized methods); controls and limits. Fundamentals of power-system stability: introduction to electromechanical stability analysis, introduction to voltage stability analysis, and automatic generation control (AGC).
SPECIAL TOPICS IN OVERVOLTAGES IN ELECTRIC POWER SYSTEMS
Syllabus: Induced voltages in parallel circuits. Resonance and ferroresonance. The Ferranti effect in transmission lines. Mitigation of temporary overvoltages. Types of switching operations. Equipment for switching-impulse testing under controlled conditions. Analysis of the effects of switching overvoltages on power-equipment specifications. General aspects of lightning. Lightning protection. Equipment for lightning-impulse testing under controlled conditions. Measurement techniques. Lightning strikes on transmission lines and substations. Effects on equipment and transmission-line specifications.
ANTENNAS
Syllabus: Fundamental parameters. Basic antenna measurements. Wire antennas. Antenna arrays. Numerical methods for antenna analysis and design. Practical antenna considerations: mutual coupling, feeding arrangements and imbalance. Broadband antennas. Microstrip antennas. Electrically short antennas. State-of-the-art antenna configurations for terrestrial wireless systems.
PROPAGATION CHANNEL
Syllabus: Fundamentals of propagation. Propagation in frequency bands used for mobile radio applications (VHF/UHF/SHF). Mobile radio propagation channels: large-scale path loss. Mobile radio propagation channels: multipath and small-scale fading. Channel-sounding techniques. Guided study of special topics related to the course.
PHYSICS OF MICROWAVE SEMICONDUCTOR DEVICES
Syllabus: Theoretical foundations. Concepts of quantum mechanics. Schrödinger equation. Fermi gas. Fundamentals of crystallography. Bloch theorem. Energy bands. Statistical distributions: Boltzmann and Fermi–Dirac. Intrinsic and doped semiconductors. Calculation of the Fermi level. Drift and diffusion. Mobility and resistivity. Recombination. Semiconductor properties. Basic equations governing semiconductor-device operation. PN junctions. Depletion region and capacitance. I–V characteristics. Junction breakdown. Heterojunctions. PN-junction devices: rectifier, voltage-regulator, fast-recovery varactor, PIN, tunnel, backward, IMPATT and point-contact diodes. Silicon bipolar transistors and heterojunction bipolar transistors (HBTs). JFETs. Metal–insulator and metal–semiconductor contacts. Schottky effect. Energy bands. Mott, rectifying (Schottky) and ohmic contacts. Devices with metal–insulator and metal–semiconductor contacts: MIM and Schottky diodes; MOSFET, MESFET and HERT transistors. Charge-transfer mechanisms controlled by intrinsic semiconductor properties (bulk effects). Gunn effect. Gunn diodes and applications.
HIGH-FREQUENCY MEASUREMENTS
Syllabus: Conventional measurements. Scalar measurements: frequency, voltage, power and characterization of discrete passive components (R, L, C and Q factor). Transistor parameters. Vector measurements: vector voltages, impedance, gain, phase and S-parameters. Reflectometry: reflection of guided waves at transmission-line discontinuities. Spectral analysis. Frequency response. Signal analysis: AM and FM modulation, modulation index and spurious signals. Measurement of harmonic distortion, intermodulation, parasitic signals and noise. Measurements on passive microwave devices. Insertion loss, return loss, directivity, isolation and bandwidth. Testing of filters, directional couplers, hybrid structures, circulators and isolators. Antenna characterization. Measurements on active microwave devices. Amplifier measurements: gain, bandwidth, S-matrix, noise figure and nonlinear behavior. Oscillator measurements: power, stability, frequency response and saturation. Mixer measurements: conversion loss, bandwidth, noise figure and nonlinear behavior. Measurements on AM, FM and PM modulators.
COMPUTATIONAL NUMERICAL METHODS IN ELECTROMAGNETICS
Syllabus: Errors inherent in numerical methods. Interpolation and extrapolation. Approximation functions. Curve fitting. Roots of polynomials and functions. Transcendental equations. Numerical differentiation and integration. Eigenvalue problems. Systems of linear and nonlinear equations. Sensitivity. Initial-value and boundary-value problems for ordinary differential equations. Introduction to finite-difference, finite-element and finite-volume methods. Optimization and minimization. Applications to specific problems in electromagnetics.
PASSIVE MICROWAVE MICROCIRCUITS
Syllabus: Theory, design and applications of passive microwave circuits. Technologies used and typical performance.
ELECTROMAGNETIC WAVE PROPAGATION
Syllabus: Free-space propagation. Propagation over a flat Earth: general solution, space waves and surface waves; diffraction and interference regions; applications. Propagation over a spherical Earth. Van der Pol–Bremmer and Fock solutions, mixed paths and applications. Propagation over irregular terrain: reflection from rough surfaces, knife-edge diffraction, diffraction by convex obstacles, empirical solutions and applications. Propagation in stratified media: geometrical optics, WKB approximation, reflection in tropospheric layers and propagation in tropospheric ducts.
OPTICAL COMMUNICATIONS SYSTEMS
Syllabus: Optical fibers. Modes in optical fibers. Attenuation. Dispersion. Optical sources. Absorption and emission (spontaneous and stimulated) in semiconductors. LEDs. Lasers. Photodetectors. Efficiency. Noise. Responsivity. PN, PIN and APD diodes. Optical receivers. Sensitivity. Signal-to-noise ratio. Configurations. Optical amplifiers. Gain and amplification mechanisms. Modulation types. Multiplexing types and distribution networks. Digital and analog optical communications systems. CATV.
ADVANCED ELECTROMAGNETIC THEORY
Syllabus: Introduction to electromagnetic waves. Theorems and concepts in electromagnetics. Plane-wave functions. Cylindrical-wave functions. Spherical-wave functions. Green’s functions. Perturbation and variational techniques.
THEORY AND DESIGN OF LINEAR ACTIVE MICROWAVE CIRCUITS
Syllabus: Two-port parameters used in high-frequency design. Negative resistance. Unconditional stability and potential instability. Smith chart. Power-gain and stability circles. Impedance matching and common structures. Noise characterization. Noise-figure circles. Planar and monolithic technologies: differences and limitations. Bias circuits. Unilateral amplifiers. Potentially unstable amplifiers. Optimization. Low-noise amplifiers. Characterization of nonlinear behavior. Broadband amplifiers. Power amplifiers. Computer-aided design. Software for synthesis, optimization, simulation and nonlinear analysis. Available commercial software.
COMPUTATIONAL LINEAR ALGEBRA
Syllabus: Vector spaces: bases, inner product and norm. Linear operators: definition and matrix representation; similarity transformations; eigenvalue and eigenvector analysis. Singular value decomposition. Adjoint and projection operators. Floating-point arithmetic. Linear equations.
CLASSICAL DETECTION AND ESTIMATION
Syllabus: Basic detection theory: binary hypothesis testing; Bayes, minimax and Neyman–Pearson criteria; detector performance; multiple-hypothesis testing. Basic estimation theory: Bayesian estimation; minimum mean-square-error estimation; maximum-likelihood estimation; Cramér–Rao bound; multiparameter estimation; Kalman filtering. Composite hypothesis testing. Representation of finite-energy signals using an orthonormal function basis. Signal detection in additive white Gaussian noise.
ADAPTIVE FILTERING
Syllabus: Introduction. Fundamentals of adaptive filtering. LMS algorithm. LMS-based algorithms. Conventional RLS algorithm. Lattice-RLS algorithms. Fast transversal RLS algorithms. QR-RLS algorithms. Constrained adaptive filtering.
DIGITAL SIGNAL PROCESSING
Syllabus: Signals and systems. Digital signals and systems: sequences, linear shift-invariant systems, convolution, frequency-domain representation, spectra and sampling of continuous-time signals. Z-transform: principal properties and theorems. Transfer function. Discrete Fourier series. Circular convolution. Linear convolution using the discrete Fourier transform. Digital-filter design using various methods (impulse invariance and bilinear transformation). Finite impulse response (FIR) filters. Infinite impulse response (IIR) filters.
STOCHASTIC PROCESSES I
Syllabus: Introduction to probability. Random variables and vectors. Functions of random variables. Expected value. Moments. Characteristic function. Power spectral density. Stochastic processes. Stationarity and ergodicity. Gaussian and Wiener processes. Markov processes. Markov chains. Introduction to Markovian queueing theory.
STOCHASTIC PROCESSES II
Syllabus: Introduction to stochastic processes. Markov chains. Poisson process. Basic concepts of queueing theory. Queue performance measures. Queueing theory (M/M/1, M/M/C, M/M/1/K, M/M/C/C, M/D/1/K, M/G/1 and M/G/∞). Dependent stochastic processes: temporal dependence and self-similarity, fBm, fGn, fARIMA and estimation of temporal dependence.
IMAGE PROCESSING
Syllabus: Two-dimensional signals, systems and Fourier transform. Two-dimensional discrete Fourier transform. Two-dimensional FIR filters. Principles of photometry, colorimetry and visual perception. Geometric models of image acquisition. Image sampling and quantization. Image transforms. Fundamentals of image coding. Image enhancement. Edge extraction, morphology, segmentation and texture. Fundamentals of image restoration and computer vision.
VIDEO CODING TECHNIQUES AND STANDARDS
Syllabus: Introduction to image and video fundamentals. Principles of image and video compression. History of video coding standards. Motion-estimation techniques. Still-image coding (JPEG). Video coding for videoconferencing (H.261). Video coding for digital storage (MPEG-1). Generic video coding (MPEG-2). Low-bit-rate video coding (H.263). Video coding using the H.264 standard.
INFORMATION THEORY
Syllabus: Communications systems and information theory. Measures of information; mutual information and entropy. Discrete-source coding and the source coding theorem. Memoryless channels. Channel capacity. Differential entropy. The Gaussian channel. Introduction to rate–distortion theory.
DIGITAL TRANSMISSION
Syllabus: Representation of bandpass signals and systems. Representation of digitally modulated signals. Power spectra of digitally modulated signals. Digital modulation techniques with coherent detection. Noncoherent detection of digitally modulated signals. Performance comparison of digital modulation techniques. Band-limited channels: intersymbol interference and the Nyquist criterion. Equalizers.