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.
Sound and human speech systems, phonetics and phonology, speech signal representations, role of pitch and formants, pitch-scale and time-scale modifications, basics of speech coding and VoIP systems, fundamentals of pattern and speech recognition, search algorithms for speech recognition.
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.
Review of multi-dimensional sampling theory, aliasing, and quantization, fundamentals of color, human visual system, 2-D Block transforms, DFT, DCT and wavelets. Image filtering, edge detection, enhancement, and restoration. Basic video file formats, resolutions, and bit rates for various digital video applications. Motion analysis and estimation using 2D and 3D models. Motion-compensated filtering methods for noise removal, de-interlacing, and resolution enhancement. Digital image and video compression methods and standards, including JPEG/JPEG2000 and MPEG-1/2 and 4. Content-based image and video indexing and MPEG-7.
Study of computational models of visual perception and their implementation in computer systems. Topics include: image formation; edge, corner and boundary extraction, segmentation, matching, pattern recognition and classification techniques; 3-D Vision: projection geometry, camera calibration, shape from stereo/silhouette/shading, model-based 3D object recognition; color texture, radiometry and BDRF; motion analysis.
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.
Adaptive Filtering, LMS, RLS and Fast Algorithms, Array Signal Processing, Blind Algorithms & Subspace Methods for Channel Identification and Equalization, Convex Optimization and Its Applications, Multirate Signal Processing and Filter Banks.
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.
Issues in digital integrated circuit design. The devices. CMOS Inverter. Combinational logic gates in CMOS. Designing sequential logic circuits. Designing arithmetic building blocks. Timing issues in digital circuits. Memories and array structures. Design verification and testing. Design projects using computer aided design tools: SPICE, MAGIC, IRSIUM, OCTTOOLS. Project design requirements include architectural design, logic and timing verification, layout design, and test pattern generation. The resulting chips may be fabricated.
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.
Review of 2-D linear system theory and 2-D Fourier transforms. Integral transforms used in optical signal processing; Fundamentals of physical optics and diffraction theory; Fourier and imaging properties of optical systems; Coherent and Incoherent optical image processing; Fundamental architectures for correlation and spectrum analysis; Interferometry; Discrete analog optical processors; Holography; Review of 3D Display technologies.
Introduction to optical fiber communication systems. Transmission properties of optical fibers. Optical amplifiers. Lasers and photo-detectors. Analog and digital modulation schemes. Modulator, transmitter and receiver design. Dense and ultra-dense wavelength division multiplexing. Transmission impairments, noise, nonlinearities, dispersion compensation and management, modeling and simulation. Optical fiber communication networks, optical interconnect for high-speed VLSI.
Survey of the properties and applications of photonic materials and devices; semiconductors; photon detectors, light emitting diodes, noise in light detection systems; light propagation in anisotropic media, Pockels and Kerr effects, light modulators, electromagnetic wave propagation in dielectric waveguides, waveguide dispersion; nonlinear optical materials, second harmonic generation, Raman converters.
Applications of Maxwells equations. Electrostatic versus electrodynamic phenomena, and concept of electromagnetic radiation; radiation from a moving point charge; definitions of some radiation parameters like the input impedance, gain and radiation patterns of antennas; radiation from Thin-Wire Antennas and their electrical characteristics; concept of arrays and their applications; microstrip antennas and their roles in emerging telecommunication systems; Propagation for wireless communications systems; cellular network design based on propagation studies.
Wireless network applications, wireless channel and communication fundamentals, medium access control protocol, routing protocol, topology control, time synchronization, data-centric networking, wireless communication standards.
Fundamentals of optics and applications of the optical technology: photon and wave nature of light, geometrical optics, optical instruments, electro-magnetic waves, interference and interferometers, fiber optics, diffraction, diffraction gratings, polarization and its applications, multi-layer films, Fresnel equations, and rainbows. Real world applications of course topics.
Hypothesis Testing, Signal Detection, Parameter Estimation, Cramer-Rao Lower Bound, Maximum Likelihood/ Maximum a Posteriori Estimation, Stochastic Least Squares Estimation and Kalman Filtering.
Review of multimedia (image, video and audio) source coding/compression techniques and standards (JPEG, MPEG, H26x), Review of communication and networking architectures and IP networks, QoS, delay, jitter, rate control, scheduling, and traffic engineering for real-time multimedia delivery, Reliability, error control, error concealment and resilience techniques, Streaming media and real-time communication techniques and protocols, RTP/RTCP, IntServ, DiffServ, MPLS, Transmission of multimedia over Internet, wireless channels, mobile cellular networks, GSM, 3G, 4G wireless systems, and satellite networks, Current and future applications of multimedia communications, e.g., voice-over-IP (VoIP), Internet Video conferencing, SIP, IMS, video-on-demand, digital video broadcasting systems, real-time delivery of 3DTV, Current state-of-the-art and future visions in multimedia communications research.
Quantum description of light-matter interactions and advanced photonic devices; review of Quantum mechanics, Schrödinger and Heisenberg representations, harmonic oscillator, operator formalism, Fermi?s golden rule, semiclassical theory of stimulated emission, quantization of the electromagnetic field, blackbody radiation, quantum theory of spontaneous emission, Rabi oscillations; Selected topics in semiconductor lasers, photonic waveguides, noise, and light modulators.
Fabrication and characterization techniques for micro and nano electro mechanical systems, MEMS & NEMS (including: microlithography; wet & dry etching techniques; physical & chemical vapor deposition processes; electroplating; bonding; focused ion beams; top-down approaches - electron-beam lithography, SPM, soft lithography - ; bottom-up techniques based on self-assembly). Semiconductor nanotechnology. Nanotubes & nanowires. Biological systems. Molecular electronics.