Discrete and continuous random variables and processes, functions of random variables, independence of random variables. Central Limit Theorem. Discrete-time random processes, continuous-time random processes, stationary random processes, ergodicity, auto and cross correlation functions, power spectral density, spectral estimation, white noise processes, Markov chains.

Linear Algebra Review, Normal Matrices, Quadratic Forms and Semidefinite Matrices, Inner Product and Norm Spaces, State Space Descriptions for Continuous and Discrete Time Systems, Controllability, Observability, Stability, Realization Theory.

Entropy, Relative Entropy and Mutual Information; Asymptotic Equipartition Theory; Entropy Rates of a Stochastic Process; Data Compression; Kolmogorov Complexity; Channel Capacity; Differential Entropy; The Gaussian Channel; Maximum Entropy and Spectral Estimation; Rate Distortion Theory, Network Information Theory.

Probability theory, stochastic processes, characterization of digital communication signals and systems, digital modulation schemes, optimum receivers for additive white gaussian noise (AWGN) channels, signal design for band-limited channels, inter-symbol interference (ISI), optimum reception for channels with ISI and AWGN, linear equalization, adaptive equalization, entropy and source coding, channel capacity and coding.

The cellular concept, channel assignment strategies, frequency reuse, handoff strategies, interference sources, mobile radio propagation, large-scale path loss, small-scale fading and multipath, modulation techniques for mobile radio, diversity combining, transmit and receive antennas for wireless communication systems, multiple access techniques in wireless, error correction codes and ARQ schemes, wireless networking, OFDM and multiple-input multiple-output systems, wireless systems & standards: GSM, IS-95, cdma2000, W-CDMA, LTE (4G), LTE-Advanced and 5G New Radio, advanced topics and current trends in wireless communications,design oriented exercises using MATLAB aids.

Principles of computer networks and network protocols; Internet protocol stack with emphasis on application, transport, network and link layers; network edge and network core; client/server and peer-to-peer models; routing algorithms; reliable data transfer; flow and congestion control; protocol design and analysis; network performance metrics; software-defined networks; network programming and distributed applications.

Introduction to mathematical formulations and computational techniques for the modeling and simulation of engineering and other kinds of systems, including electronic, mechanical, biological, biochemical, virtual, abstract and multi-domain dynamical systems. Applications from various engineering disciplines and the sciences. Matrix formulation of equations for linear problems. Formulation of equations for nonlinear problems & linearization. Numerical solution of linear algebraic equations. Gaussian elimination, computations with sparse & structured matrices. Floating point number representation & arithmetic. Numerical conditioning, ill-conditioned problems. Numerical solution of nonlinear algebraic equations. Fixed point iteration & Newton’s method in one dimension. Newton’s method for system of coupled nonlinear algebraic equations. Improving convergence of Newton’s method. Numerical solution of ordinary differential equations. Forward & backward Euler, trapezoidal rule. Multistep methods, accuracy & stability. Implicit vs explicit techniques, region of stability, stiff problems.

Review of electromagnetism; electromagnetic nature of light, radiation, geometrical optics, Gaussian beams, transformation of Gaussian beams; electromagnetic modes of an optical resonator, interaction of light with matter, classical theory of absorption and dispersion, broadening processes, Rayleigh scattering, quantum theory of spontaneous and stimulated emission, optical amplification, theory of laser oscillation, examples of laser systems, Q switching and mode locking of lasers.

Introduction to Microsystems, MEMS and its integration with optics; Microfabrication and process integration; MEMS Modeling and design; Actuator and sensor design; Mechanical structure design; Optical system design basics; Packaging; Optical MEMS application case studies; Scanning systems (Retinal Scanning Displays, Barcode scanners); Projection display systems (DMD and GLV); Infrared imaging cameras; Optical switching for telecommunications.

Supervised Adaptive Filtering (Least Mean Square, Recursive Least Squares, Fast Algorithms), Unsupervised Adaptive Filtering (Higher Order Statistics Methods, Blind Deconvolution, Blind Source Separation, Independent Component Analysis), Model Based Signal Processing (Sparsity, Boundedness, Subspace Algorithms), Multirate Signal Processing, Filter-banks and Wavelets.

The optoelectronic devices such as light-emitting diodes, lasers, photodetectors, etc. are widely used in modern lighting, information and telecommunication technologies. We will discuss the following topics with mathematical derivations and exciting practical examples: wave nature of light, dielectric waveguides and optical fibers, semiconductor science and light-emitting diodes, stimulated emission devices: optical amplifiers and lasers, photodetectors and image sensors, and polarization and modulation of light.

Design, simulation, and optimization of integrated photonics structures, the notion of fabless silicon photonics, metal and dielectric waveguides, planar waveguide modes, coupled mode theory, integrated passive couplers and splitters, Mach-Zehnder Interferometers, ring and disk resonators, adiabatic couplers, Bragg gratings, grating and edge couplers, photonic crystal waveguides and structures, principles of integrated modulator and detector operation, fabrication-dependent design considerations, use of transfer matrix, eigenmode expansion, and finite difference time-domain simulation techniques throughout the semester, design oriented and simulation based assignments and term project.

Topics will be announced when offered.

A capstone design course where students apply engineering and science knowledge in an electrical-electronics engineering design project. Development, design, implementation and management of a project in teams under realistic constraints and conditions. Emphasis on communication, teamwork and presentation skills..

A capstone design project on an industrially relevant problem. Students work on teams in consultation with various faculty and industrial members.

Discrete and continuous random variables and processes, functions of random variables, independence of random variables. Central Limit Theorem. Discrete-time random processes, continuous-time random processes, stationary random processes, ergodicity, auto and cross correlation functions, power spectral density; spectral estimation, white noise processes, Markov chains.

Linear Algebra Review, Normal Matrices, Quadratic Forms and Semidefinite Matrices, Inner Product and Norm Spaces, State Space Descriptions for Continuous and Discrete Time Systems, Controllability, Observability, Stability, Realization Theory.

Entropy, Relative Entropy and Mutual Information; Asymptotic Equipartition Theory; Entropy Rates of a Stochastic Process; Data Compression; Kolmogorov Complexity; Channel Capacity; Differential Entropy; The Gaussian Channel; Maximum Entropy and Spectral Estimation; Rate Distortion Theory, Network Information Theory.

Characterization of communication signals & systems, digital modulation schemes, optimum reception for the additive white Gaussian noise (AWGN) channel, signal design for band-limited channels, Nyquist criterion, intersymbol interference (ISI), optimum reception for channels with ISI and AWGN, linear equalization, decision feedback equalization, adaptive equalization, channel capacity & coding, linear block codes, convolutional codes, multichannel and multicarrier systems, spread spectrum signals for digital communications, multiuser communications. Design oriented exercises using computer aids.

The cellular concept, channel assignment strategies, frequency reuse, handoff strategies, interference sources, mobile radio propagation, large-scale path loss, small-scale fading and multipath, modulation techniques for mobile radio, diversity combining, transmit and receive antennas for wireless communication systems, multiple access techniques in wireless, wireless system design for delay intolerant services, wireless system design for delay tolerant services, error correction coding and ARQ schemes, wireless networking, wireless systems & standards: GSM, IS-95, cdma2000, W-CDMA, 3GPP2 1xEV-DO, 3GPP2 1xEV-DV, fourth generation wireless system proposals. Design oriented exercises using computer aids.

Introduction to mathematical formulations and computational techniques for the modeling and simulation of engineering and other kinds of systems, including electronic, mechanical, biological, biochemical, virtual, abstract and multi-domain dynamical systems. Applications from various engineering disciplines and the sciences. Matrix formulation of equations for linear problems. Formulation of equations for nonlinear problems & linearization. Numerical solution of linear algebraic equations. Gaussian elimination, computations with sparse & structured matrices. Floating point number representation & arithmetic. Numerical conditioning, ill-conditioned problems. Numerical solution of nonlinear algebraic equations. Fixed point iteration & Newton’s method in one dimension. Newton’s method for system of coupled nonlinear algebraic equations. Improving convergence of Newton’s method. Numerical solution of ordinary differential equations. Forward & backward Euler, trapezoidal rule. Multistep methods, accuracy & stability. Implicit vs explicit techniques, region of stability, stiff problems.

Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.

Introduction to Microsystems, MEMS and its integration with optics; Microfabrication and process integration; MEMS Modeling and design; Actuator and sensor design; Mechanical structure design; Optical system design basics; Packaging; Optical MEMS application case studies; Scanning systems (Retinal Scanning Displays, Barcode scanners); Projection display systems (DMD and GLV); Infrared imaging cameras; Optical switching for telecommunications.