MATH-200

Fundamental Concepts of Algebra

3.0 Cr.

Sets, algebraic techniques, inequalities, graphs of equations.

MATH-203

Differential and Integral Calculus I

3.0 Cr.

Prerequisite: MATH-201. Functional notation. Differentiation of polynomials. The power, product, quotient, and chain rules. Differentiation of elementary functions. Implicit differentiation. Higher derivatives. Maxima and minima. Applications: tangents to plane curves, graphing, related rates. Approximations using the differential. Antiderivatives, definite integrals, area.

MATH-251

Linear Algebra I

3.0 Cr.

Matrices and linear equations; vector spaces; bases, dimension and rank; linear mappings and algebra of linear operators; matrix representation of linear operators; determinants; eigenvalues and eigenvectors; diagonalization.

MATH-354

Numerical Analysis

3.0 Cr.

Error analysis in numerical algorithms; solution of non-linear equations; fixed point iterations, rate of convergence. Interpolations and approximations, Legendre polynomials. Numerical integration and Quadrature.

STAT-249

Probability I

3.0 Cr.

Axiomatic approach to probability; combinatorial probability; discrete and continuous distributions; expectation; conditional expectation; random sampling and sampling distributions.

ENGR-213

Applied Ordinary Differential Equations

3.0 Cr.

Prerequisite: MATH-204, MATH-205. Definition and terminology, initial-value problems, separable differential equations, linear equations, exact equations, solutions by substitution, linear models, orthogonal trajectories, complex numbers, form of complex numbers: powers and roots, theory: linear equations, homogeneous linear equations with constant coefficients, undetermined coefficients, variation of parameters, Cauchy-Euler equation, reduction of order, linear models: initial value, review of power series, power series solutions, theory, homogeneous linear systems, solution by diagonalization, non-homogeneous linear systems. Eigenvalues and eigenvectors.

ENGR-233

Applied Advanced Calculus

3.0 Cr.

Prerequisite: MATH-204, MATH-205. Functions of several variables, partial derivatives, total and exact differentials, approximations with differentials. Tangent plane and normal line to a surface, directional derivatives, gradient. Double and triple integrals. Polar, cylindrical, and spherical coordinates. Change of variables in double and triple integrals. Vector differential calculus; divergence, curl, curvature, line integrals, Green’s theorem, surface integrals, divergence theorem, applications of divergence theorem, Stokes’ theorem.

ENGR-311

Transform Calculus and Partial Differential Equations

3.0 Cr.

Prerequisite: ENGR-233. Elements of complex variables. The Laplace transform: Laplace transforms and their properties, solution of linear differential equations with constant coefficients. Further theorems and their applications. The Fourier transform: orthogonal functions, expansion of a function in orthogonal functions, the Fourier series, the Fourier integral, the Fourier transform, the convolution theorem. Partial differential equations: physical foundations of partial differential equations, introduction to boundary value problems.

ENGR-371

Probability and Statistics in Engineering

3.0 Cr.

Prerequisite: ENGR-213, ENGR-233. Axioms of probability theory. Events. Conditional probability. Bayes theorem. Random variables. Mathematical expectation. Discrete and continuous probability density functions. Transformation of variables. Probabilistic models, statistics, and elements of hypothesis testing (sampling distributions and interval estimation). Introduction to statistical quality control. Applications to engineering problems.

ENGR-391

Numerical Methods in Engineering

3.0 Cr.

Prerequisite: ENGR-213, ENGR-233, COEN-243. Roots of algebraic and transcendental equations; function approximation; numerical differentiation; numerical integration; solution of simultaneous algebraic equations; numerical integration of ordinary differential equations.

COEN-231

Introduction to Discrete Mathematics

3.0 Cr.

Prerequisite: MATH-204. Fundamental principles of counting: rules of sum and product; permutations, arrangements and combinations, the binomial theorem; combinations with repetition; distributions. Fundamentals of logic: basic connectives and truth tables; logical equivalence; the laws of logic; logical implication; rules of inference; the use of quantifiers; proofs of theorems. Sets: the laws of set theory. Boolean algebra. Relation of Boolean algebra to logical and set theoretic operations. Modulo arithmetic: representations of numbers in binary, octal and hexadecimal formats; binary arithmetic. Induction and recursion: induction on natural numbers; recursive definitions. Functions and relations: Cartesian products and relations; functions; function composition and inverse functions; computational complexity. Elements of graph theory: basic definitions of graph theory; paths, reachability and connectedness; computing paths from their matrix representation; traversing graphs represented as adjacency lists; trees and spanning trees.

COEN-312

Digital Systems Design I

3.5 Cr.

Prerequisite: COEN-231. Logic gates and their use in the realization of Boolean algebra statements; logic minimization, multiple output circuits. Designing with MSI and LSI chips, decoders, multiplexers, adders, multipliers, programmable logic devices. Introduction to sequential circuits; flip-flops. Completely specified sequential machines. Machine equivalence and minimization. Implementation of clock mode sequential circuits.

ELEC-264

Signal and Systems I

3.0 Cr.

Prerequisite: ELEC-273, ENGR-213. Continuous-time and discrete-time signals and systems. Linear Time Invariant [LTI] systems. Convolution-sum and convolution-integral representation of systems. Causal LTI systems. Fourier series representation of continuous-time and discrete-time periodic signals. Filters described by differential or difference equations. The continuous-time Fourier transform. Systems based on Linear Constant Coefficient Differential Equations [LCCDE-DT]. The discrete-time Fourier transform. Systems based on Linear Constant Coefficient Difference Equations [LCCDE-CT]. Computer-based simulation.

ELEC-273

Basic Circuit Analysis

3.5 Cr.

Prerequisite: ENGR-213. Units: current, voltage, power, and energy. Elementary wave-forms. Time averages. Ohm’s law. KVL and KCL. Ideal sources. Mesh and node analysis of resistive circuits. Network theorems. Inductors and capacitors and their response to the application of elementary waveforms. Transient response of simple circuits. Natural frequency and damping. Initial conditions. Steady state AC analysis: resonance, impedance, power factor. Introduction to three phase power, delta and Y connections. Ideal operational amplifiers. Ideal transformers.

ELEC-275

Principles of Electrical Engineering

3.5 Cr.

Prerequisite: ENGR-213. Fundamentals of electric circuits: Kirchhoff's laws, voltage and current sources, Ohm’s law, series and parallel circuits. Nodal and mesh analysis of DC circuits. Superposition theorem, Thevenin and Norton Equivalents. Use of operational amplifiers. Transient analysis of simple RC, RL and RLC circuits. Steady state analysis: Phasors and impedances, power and power factor. Single and three phase circuits. Magnetic circuits and transformers. Power generation and distribution.

ELEC-363

Fundamentals of Telecommunications Systems

3.5 Cr.

Prerequisite: ELEC-361, ENGR-371. Introduction to basic telecommunications concepts and systems. Analog communications: AM and FM, system level consideration of noise-bandwidth tradeoffs. Digital communications: sampling and quantization, digital modulation techniques, the matched filter. Redundancy encoding.

ELEC-364

Signal and Systems II

3.0 Cr.

Prerequisite: ELEC-264. Sampling of continuous-time and discrete-time signals. Reconstruction of a signal from its samples using interpolation. Laplace Transform. Inverse Laplace Transform. Analysis of systems using Laplace Transform. Unilateral Laplace Transform. The Z-Transform and inverse Z-Transform. Analysis of systems using Z-Transform. Unilateral Z-Transform. Time and frequency characteristics of signals and systems. Examples of continuous-time and discrete-time first and second-order systems. Amplitude modulation and demodulation. Pulse amplitude modulation. Frequency modulation. Computer-based simulation.

ELEC-365

Complex Variables and Partial Differential Equations

3.0 Cr.

Prerequisite: ENGR-213, ENGR-233. Review of complex arithmetic. Analytic functions. Taylor and Laurent series. Residue theory. Fourier series. Partial differential equations. Applications to Laplace, heat, and wave equations. Bessel and Legendre functions.

ELEC-442 / 6601

Digital Signal Processing

3.5 / 4.0 Cr.

Prerequisite: ELEC-361. Review of discrete-time signals and systems; difference equation, the Fourier transform, the z-transform, the discrete Fourier series and transform; recursive and non-recursive digital filters, common digital filter structures, common design approaches for digital filters; A/D and D/A converters, digital processing of analog signals, signal interpolation and decimation; effect of finite word lengths, description of a typical DSP chip.

ELEC-462 / 6831

Digital Communications

3.5 / 4.0 Cr.

Prerequisite: ELEC-363. Random processes and linear systems; baseband modulation/demodulation, optimal receivers in AWGN, correlation and matched-filter receivers, pulse shaping for band-limited channels; bandpass modulation techniques such as PAM, PSK, DPSK, FSK, QAM; introduction to error control coding, linear block codes, cyclic codes, convolutional codes.

ELEC-464 / 6141

Wireless Communications

3.0 / 4.0 Cr.

Prerequisite: ELEC-462. Review of modulation and error control coding. Modulation vs. coding trade-off, communications link analysis. Introduction to cellular systems: frequency reuse, trunking and grade of services, sectoring and cell splitting, coverage and capacity. Modulation techniques for mobile communications. Mobile radio channels. Spread-spectrum techniques. Multiplexing and multiple access techniques.

ENCS-6021

Engineering Analysis II

4.0 Cr.

Sturm-Liouville problem; orthogonal functions; integral transforms; partial differential equations; boundary value problems; applications of above; topics in engineering problems.

ENCS-6141

Probabilistic Methods in Design

4.0 Cr.

Elements of probability theory, decision models, expected costs and benefits, models from random occurrences, extreme value statistics, Monte Carlo simulation, reliability analysis, general applications to engineering design problems.

ENCS-6161

Probability and Stochastic Processes

4.0 Cr.

Axioms and rules of probabilities, Bayes’ Theorem, binary communication systems, Bernoulli trials and Poisson Theorem, random variables, distributions and density functions, moments, correlation, Chebyshev and Markov’s inequalities, characteristic functions, Chernoff inequality, transformation of random variable, random processes, stationarity, Bernoulli, Random Walk, Poisson, shot noise, random telegraph, and Wiener processes, stopping time; Wald’s equation, elements of Renewal Theory, Mean-Ergodic Theorem, auto and cross-correlation functions, correlation time, auto-correlation receiver, Wiener-Khinchin Theorem, power spectral density, linear system with stochastic inputs, matched filtering.

ELEC-6161

Stochastic Processes for Com. and Signal Processing 

4.0 Cr.

Bayesian, maximum likelihood and mean-square estimation, mean square sense ergodicity, differentiation and integration, Wiener and Kalman filters, nonlinear systems with stochastic input, direct and Rice methods for calculation of an autocorrelation function, linearization methods, discrete-time Markov chains, state occupancy time, global balance, limiting probabilities, Markov process, Gauss-Markov (Ornstein-Ulenbeck) process.

ELEC-6111

Detection and Estimation Theory

4.0 Cr.

Prerequisite: ENCS-6161. Basic hypothesis testing, cost functions, Bayes and Neyman Pearson tests, the power of a test, sequential tests; estimation, Bayes estimates, maximum a posteriori estimates. the Cramer-Rao inequality, maximum likelihood estimates; composite hypothesis testing, application of estimation theory to phase locked loops, vector representation of signals in noise, application of the Kharhunen-Loeve expansion, complex analytic representation of signals; detection and estimation of signals in white and non-white noise, the matched filter, composite hypothesis testing, random amplitude and phase, multi-path channels, waveform estimation, Wiener filters, Kalman filters.

ELEC-6121

Spread Spectrum Communications

4.0 Cr.

Prerequisite: ELEC-6831. Direct sequence, frequency hopping, time hopping, chirp and hybrids, maximal Gold and nonlinear codes, probability or error analysis, under tone, partial band jamming for different systems, serial and parallel, initial acquisition, delay lock loops and tau dither loops, fading effects and potential coding techniques, new acquisition and tracking techniques, interception and repeated jammers.

ELEC-6131

Error Detecting and Correcting Codes

4.0 Cr.

Prerequisite: ENCS-6161. Communication channels and the coding problem; important linear block codes (cyclic, Hamming and BCH codes); encoding and decoding with shift registers; threshold decoding; introduction to convolutional codes; coding in system design considerations, bit error rates and coding gain, trade-offs in power, bandwidth, data rate and system reliability; codulation.

ELEC-6151

Information Theory and Source Coding

4.0 Cr.

Prerequisite: ENCS-6161. Entropy of a source, rate distortion functions, source coding, analog to digital conversion, effects of sampling and quantization, vector quantization, discrete memoryless channels and their capacity, cost functions, channel coding theorem, channel capacity, fundamental concepts of information theory with applications to digital communications, theory of data compression, broadcast channels, application to encryption, DES, public key encryption, computational complexity.

ELEC-6841

Digital Communications II

4.0 Cr.

Prerequisites: ENCS-6161, ELEC-6831. Digital signaling over band-limited channels: signal design for band-limited channels, maximum likelihood sequence detection, equalization techniques, e.g., zero-forcing, minimum mean squared error, adaptive equalization. Advanced coding and modulation: concatenated coding with iterative decoding, coded modulation techniques. Diversity techniques for fading channels. Synchronization techniques: carrier and timing recovery, frequency estimation techniques, frame and network synchronization, maximum-likelihood estimation and Cramer-Rao bounds.

ELEC-6881

Fundamentals and Applications of MIMO Comm.

4.0 Cr.

Prerequisite: ELEC-6141. Multiple Input Multiple Output (MIMO) communication systems and wireless channel models; Diversity techniques and array processing; MIMO channel capacity; Space-time black and trellis codes; Spatial multiplexing and layered space-time architectures, diversity-versus-multiplexing tradeoff; Differential and unitary space-time coding; MIMO OFDM and space-frequency coding; Concatenated coding and iterative decoding for MIMO systems; Applications of MIMO in wireless systems.

ELEC-6611

Digital Filters

4.0 Cr.

Prerequisite: ELEC-6601. Approximation and design of recursive and non-recursive digital filters. Transformations. Stability. Digital filter structures including wave and lattice structures. Effect of quantization, noise and limit cycles. Hardware implementation. Digital filter applications.

ELEC-6621

Digital Waveform Compression

4.0 Cr.

Prerequisites: ELEC-6601, ENCS-6161. Numerical representation of waveform information; common waveform communication systems; statistical models used for waveforms; visual psychophysics. Differential PCM, motion estimation/compensation for video compressions. Transform coding: run length coding, Huffman and arithmetic coding, control of Q factor and Q table, segmentation/contour/edge based coding; pre-processing and post-processing strategies. Vector quantization. Sub-band coding and Wavelet Transform. Zero trees. Channel concerns: robustness, error

recovery, masking video/image bit rate source models. Coding of two-level graphics. Review of standards: JPEG, MPEG, H.261.

ELEC-6631

Digital Video Processing

4.0 Cr.

Prerequisites: ELEC-6601, ENCS-6161. Video processing fundamentals; video signals and systems. Fourier analysis of

video signals, video scanning and transmission, spatio-temporal sampling, selected material on the Human Visual System, modelling of video components, motion estimation and representation. Video filtering and enhancement: noise reduction, noise estimation, de-interlacing, frame-rate conversion, signal processing for improved TV-systems. An introduction to video compression, Lowlevel video analysis: local operators, linear and non-linear operators, rankorder filters, morphological filters, edge detection, segmentation.

ELEC-7601

Adaptive Signal Processing

4.0 Cr.

Prerequisites: ELEC-6601, ENCS-6161. Optimal filtering; filter structures for adaptive filtering; the LMS stochastic gradient algorithm; block least-squares methods; lattice structures. Convergence properties of transversal and lattice stochastic gradient algorithms. Stability and sensitivity analysis of adaptive filters.

ELEC-7631

Multi-dimensional Signal and Image Processing

4.0 Cr.

Prerequisite: ELEC-6601. Multidimensional signals and systems. Two-dimensional discrete Fourier analysis: discrete Fourier transform, computation of DFT and computational considerations. Two-dimensional FIR filters: convolutional and DFT implementations, design using windows, least-squares design. Recursive systems. Two-dimensional IIR filters: implementations, space-domain design methods, frequency domain design, design for specialized structures. One of more specialized topics: finite-word-length effects, symmetry in two-dimensional filters, signal reconstruction and real-time image processing.

ENCS-8511

Doctoral Research Proposal

6.0 Cr.

The goal of the doctoral research proposal is to focus the student’s Ph.D. research. Students will be assessed on the basis of written and oral presentations. The proposal must include: (i) a critical review of previous work relevant to the subject of the thesis, and (ii) a detailed research plan of action and expected milestones. Students are required to defend their doctoral research proposal before a committee that will normally be comprised of the same members as the Comprehensive Examination Committee. Students must demonstrate the viability of their project and their capacity to undertake doctoral thesis research. The proposal may be accepted, returned for modifications, or rejected. The rejection of a proposal will result in the student’s withdrawal from the program. A student whose proposal is accepted will be admitted to candidacy for the Ph.D.

ENCS-8011

Ph.D. Seminar 

2.0 Cr.

Grading on a Pass/Fail basis only. No credit value!! 

ENGR-8911

Doctoral Research and Thesis

70.0 Cr.

Students are required to plan and carry out a suitable research, development, or design project, which leads to an advance in knowledge. The student must submit a thesis based upon this work and defend it in an oral examination. For purposes of registration, this work will be designated ENGR-8911: Doctoral Research and Thesis (70 credits). Theses will be examined by a committee consisting of the student’s supervisory committee, an external examiner, and other examiners as approved by the Faculty Graduate Studies Committee and the Dean of Graduate Studies.