Columbia University in the City of New York · Courses
ELEN E
113 courses with the subject ELEN E, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
ELEN E1101THE DIGITAL INFORMATION AGE3.00
An introduction to information transmission and storage, including technological issues. Binary numbers; elementary computer logic; digital speech and image coding; basics of compact disks, telephones, modems, faxes, UPC bar codes, and the World Wide Web. Projects include implementing simple digital logic systems and Web pages. Intended primarily for students outside the School of Engineering and Applied Science. The only prerequisite is a working knowledge of elementary algebra
Design project planning, written and oral technical communication, the origin and role of standards, engineering ethics, and practical aspects of engineering as a profession, such as career development and societal and environmental impact. Generally taken fall of senior year just before ELEN E3390
Prerequisites: Requires approval by a faculty member who agrees to supervise the work. May be repeated for credit, but no more than 3 total points may be used for degree credit. Independent project involving laboratory work, computer programming, analytical investigation, or engineering design
Subject
ELEN E
Credits (min)
0
Credits (max)
3
Credit unit
points
Type
course
Repeatable
May be repeated for credit, but no more than 3 total points may be used for degree credit.
Prerequisites: Linear algebra, differential equations, and basic semiconductor physics. Introduction to modern display systems in an engineering context. The basis for visual perception, image representation, color space, metrics of illumination. Physics of luminescence, propagation and manipulation of light in anisotropic media, emissive displays, and spatial light modulators. Fundamentals of display addressing, the Alt-Pleshko theorem, multiple line addressing. Large area electronics, fabrication, and device integration of commercially important display types. A series of short laboratories will reinforce material from the lectures. Enrollment may be limited
Prerequisites: (ELEN E3201) and (ELEN E3801) or ELEN E3201 AND ELEN E3801; or equivalent. Approximation techniques for magnitude, phase, and delay specifications, transfer function realization sensitivity, passive LC filters, active RC filters, MOSFET-C filters, Gm-C filters, switched-capacitor filters, automatic tuning techniques for integrated filters. Filter noise. A design project is an integral part of the course
Prerequisites: (ELEN E3331) and (ELEN E3801) ELEN E3331 AND ELEN E3801 Differential and multistage amplifiers; small-signal analysis; biasing techniques; frequency response; negative feedback; stability criteria; frequency compensation techniques. Analog layout techniques. An extensive design project is an integral part of the course
Prerequisites: (ELEN E4312) ELEN E4312 Principles of electronic circuits used in the generation, transmission, and reception of signal waveforms, as used in analog and digital communication systems. Nonlinearity and distortion; power amplifiers; tuned amplifiers; oscillators; multipliers and mixers; modulators and demodulators; phase-locked loops. An extensive design project is an integral part of the course
Prerequisites: (ELEN E3331) and (ELEN E3801) ELEN E3331 AND ELEN E3801 Introduction to power electronics; power semiconductor devices: power diodes, thyristors, commutation techniques, power transistors, power MOSFETs, Triac, IGBTs, etc. and switch selection; non-sinusoidal power definitions and computations, modeling, and simulation; half-wave rectifiers; single-phase, full-wave rectifiers; three-phase rectifiers; AC voltage controllers; DC/DC buck, boost, and buck-boost converters; discontinuous conduction mode of operation; DC power supplies: Flyback, Forward converter; DC/AC inverters, PWM techniques; three-phase inverters
Prerequisites: (ELEN E3401) or ELEN E3401; or equivalent. Waves and Maxwell’s equations. Field energetics, dispersion, complex power. Waves in dielectrics and in conductors. Reflection and refraction. Oblique incidence and total internal reflection. Transmission lines and conducting waveguides. Planar and circular dielectric waveguides; integrated optics and optical fibers. Hybrid and LP modes. Graded-index fibers. Mode coupling; wave launching
Prerequisites: (ELEN E3401) or ELEN E3401; or equivalent. Planar resonators. Photons and photon streams. Photons and atoms: energy levels and band structure; interactions of photons with matter; absorption, stimulated and spontaneous emission; thermal light, luminescence light. Laser amplifiers: gain, saturation, and phase shift; rate equations; pumping. Lasers: theory of oscillation; laser output characteristics. Photons in semiconductors: generation, recombination, and injection; heterostructures; absorption and gain coefficients. Semiconductor photon sources: LEDs; semiconductor optical amplifiers; homojunction and heterojunction laser diodes. Semiconductor photon detectors: p-n, p-i-n, and heterostructure photo diodes; avalanche photodiodes
Prerequisites: (ELEN E3401) ELEN E3401; or equivalent. Introduction to optical systems based on physical design and engineering principles. Fundamental geometrical and wave optics with specific emphasis on developing analytical and numerical tools used in optical engineering design. Focus on applications that employ optical systems and networks, including examples in holographic imaging, tomography, Fourier imaging, confocal microscopy, optical signal processing, fiber optic communication systems, optical interconnects and networks
Prerequisites: (ELEN E3201) and (ELEN E3401) or ELEN E3201 AND ELEN E3401; or equivalents, or instructor's permission. Modeling of power networks, steady-state and transient behaviors, control and optimization, electricity market, and smart grid
Prerequisites: ELEN E3801; or instructor's permission. Theory of convex optimization; numerical algorithms; applications in circuits, communications, control, signal processing and power systems
Prerequisites: (ELEN E3701) or ELEN E3701; or equivalent. Digital communications for both point-to-point and switched applications is further developed. Optimum receiver structures and transmitter signal shaping for both binary and M-ary signal transmission. An introduction to block codes and convolutional codes, with application to space communications
ELEN E4720Machine Learning for Signals, Information and Data3.00
Fall 2026: ELEN E4720 Course Number Section/Call Number Times/Location Instructor Points Enrollment ELEN 4720 001/11282 W 10:10am - 12:40pm 313 Fayerweather John Paisley 3.00 78/80
Prerequisites: (ELEN E3801) ELEN E3801 Digital filtering in time and frequency domain, including properties of discrete-time signals and systems, sampling theory, transform analysis, system structures, IIR and FIR filter design techniques, the discrete Fourier transform, fast Fourier transforms
ELEN E4830Image Processing and Computer Vision3.00
Introduction to the mathematical tools and algorithmic implementation for representation, processing, and reconstruction of digital images, videos, and visual sensory data. Image representation, filtering, transform, quality enhancement, restoration, feature extraction, object segmentation, motion analysis, stitching, depth estimation, 3D reconstruction, classification, and coding for data compression. A series of programming assignments reinforces material from the lectures
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 4900 to 4909
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 4900 to 4909
Prerequisites: Instructor’s permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 4900 to 4909
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 4900 to 4909
Science and technology of conventional and advanced microfabrication techniques for electronics, integrated and discrete components. Topics include diffusion; ion implantation, thin-film growth including oxides and metals, molecular beam and liquid-phase epitaxy; optical and advanced lithography; and plasma and wet etching
Prerequisites: Requires approval by a faculty member who agrees to supervise the work. May be repeated for credit, but no more than 3 total points may be used for degree credit. Substantial independent project involving laboratory work, computer programming, analytical investigation, or engineering design
Subject
ELEN E
Credits (min)
0
Credits (max)
3
Credit unit
points
Type
course
Repeatable
May be repeated for credit, but no more than 3 total points may be used for degree credit.
Prerequisites: Requires approval by a faculty member who agrees to supervise the work. May be repeated for up to 6 points of credit. Graduate-level projects in various areas of electrical engineering and computer science. In consultation with an instructor, each student designs his or her project depending on the students previous training and experience. Students should consult with a professor in their area for detailed arrangements no later than the last day of registration
Prerequisites: Requires approval by a faculty member who agrees to supervise the work. May be repeated for up to 6 points of credit. Graduate-level projects in various areas of electrical engineering and computer science. In consultation with an instructor, each student designs his or her project depending on the students previous training and experience. Students should consult with a professor in their area for detailed arrangements no later than the last day of registration
Prerequisites: ELEN E6001 OR ELEN E6002; A minimum of 3 points of credit in ELEN E6001 or ELEN E6002 advanced projects with the same instructor, the instructor’s permission, and completion of at least 12 points of credit in the MS program with a GPA of at least 3.5. Research in an area of Electrical Engineering culminating in a verbal presentation and a written thesis document approved by the thesis instructor. Must obtain permission from a thesis instructor to enroll. Thesis projects span at least two terms: an ELEN E6001 or E6002 Advanced Project followed by the E6003 Master’s Thesis with the same instructor. Students must use a department recommended format for thesis writing. Counts towards the amount of research credit in the MS program
Prerequisites: (ELEN E3106) ELEN E3106; or equivalent. Operation and modeling of MOS transistors. MOS two- and three-terminal structures. The MOS transistor as a four-terminal device; general charge-sheet modeling; strong, moderate, and weak inversion models; short-and-narrow-channel effects; ion-implanted devices; scaling considerations in VLSI; charge modeling; large-signal transient and small-signal modeling for quasistatic and nonquasistatic operation
Prerequisites: (ELEN E4312) ELEN E4312 Integrated circuit device characteristics and models; temperature- and supply-independent biasing; IC operational amplifier analysis and design and their applications; feedback amplifiers, stability and frequency compensation techniques; noise in circuits and low-noise design; mismatch in circuits and low-offset design. Computer-aided analysis techniques are used in homework(s) or a design project
Prerequisites: (ELEN E4312) ELEN E4312; or equivalent. Analog-to-digital and digital-to-analog conversion techniques for very large scale integrated circuits and systems. Precision sampling; quantization; A/D and D/A converter architectures and metrics; Nyquist architectures; oversampling architectures; correction techniques; system considerations. A design project is an integral part of this course
Prerequisites: (ELEN E3331) and (ELEN E3401) or ELEN E3331 AND ELEN E3401; or equivalents. Introduction to microwave engineering and microwave circuit design. Review of transmission lines. Smith chart, S-parameters, microwave impedance matching, transformation and power combining networks, active and passive microwave devices, S-parameter-based design of RF and microwave amplifiers. A microwave circuit design project (using microwave CAD) is an integral part of the course
Lect: 3. Principles behind the implementation of millimeter-wave (30GHz-300GHz) wireless circuits and systems in silicon-based technologies. Silicon-based active and passive devices for millimeter-wave operation, millimeter-wave low-noise amplifiers, power amplifiers, oscillators and VCOs, oscillator phase noise theory, mixers and frequency dividers for PLLs. A design project is an integral part of the course. Fall 2026: ELEN E6320 Course Number Section/Call Number Times/Location Instructor Points Enrollment ELEN 6320 001/11546 Th 4:10pm - 6:40pm 545 Seeley W. Mudd Building Harish Krishnaswamy 3.00 33/40 ELEN 6320 C01/20319 Harish Krishnaswamy 3.00 1/99 ELEN 6320 V01/18109 Harish Krishnaswamy 3.00 0/99
ELEN E6324Principles of RF and Microwave Measurement3.00
Principles behind, and techniques related to, RF and microwave simulation and measurements. S parameters; simulations and measurements for small-signal and large signal / nonlinear circuits in the time and frequency domains; noise
Prerequisites: (ELEN E4301) ELEN E4301 Designed for students interested in research in semiconductor materials and devices. Topics include energy bands: nearly free electron and tight-binding approximations, the k.p. method, quantitative calculation of band structures and their applications to quantum structure transistors, photodetectors, and lasers; semiconductor statistics, Boltzmann transport equation, scattering processes, quantum effect in transport phenomena, properties of heterostructures. Quantum mechanical treatment throughout
Photonic integrated circuits are important subsystem components for telecommunications, optically controlled radar, optical signal processing, and photonic local area networks. An introduction to the devices and the design of these circuits. Principle and modeling of dielectric waveguides (including silica on silicon and InP based materials), waveguide devices (simple and star couplers), and surface diffractive elements. Discussion of numerical techniques for modeling circuits, including beam propagation and finite difference codes, and design of other devices: optical isolators, demultiplexers
Prerequisites: Background in electromagnetism ELEN E3401, ELEN E4401, ELEN E4411, or Physics GR6092 and quantum mechanics APPH E3100, APPH E4100, or PHYS GU402x. An introduction to fundamental concepts of quantum optics and quantum electrodynamics with an emphasis on applications in nanophotonic devices. The quantization of the electromagnetic field; coherent and squeezed states of light; interaction between light and electrons in the language of quantum electrodynamics (QED); optical resonators and cavity QED; low-threshold lasers; and entangled states of light
Prerequisites: (IEOR E3658) IEOR E3658 Main concepts of error control codes. Linear block codes. Elements of algebra: Galois fields. BCH and Reed Solomon codes. Convolutional Codes. Modern, capacity-achieving codes: Low Density Parity Check codes, TURBO codes, and Polar codes. EXIT Charts analysis
Introduction to quantum detection and estimation theory and its applications to quantum communications, quantum radar, quantum metrology, and quantum tomography. Background on quantum mechanics, quantum detection, composite quantum systems, Gaussian states, and quantum estimation
Prerequisites: (CSEE W4119) or (ELEN E6761) CSEE W4119 or ELEN E6761 recommended, and ability to comprehend and track development of sophisticated models.
Further study of areas such as communication protocols and architectures, flow and congestion control in data networks, performance evaluation in integrated networks. Content varies from year to year, and different topics rotate through the course numbers 6770 to 6779
Further study of areas such as communication protocols and architectures, flow and congestion control in data networks, performance evaluation in integrated networks. Content varies from year to year, and different topics rotate through the course numbers 6770 to 6779
Further study of areas such as communication protocols and architectures, flow and congestion control in data networks, performance evaluation in integrated networks. Content varies from year to year, and different topics rotate through the course numbers 6770 to 6779
Further study of areas such as communication protocols and architectures, flow and congestion control in data networks, performance evaluation in integrated networks. Content varies from year to year, and different topics rotate through the course numbers 6770 to 6779
Further study of areas such as communication protocols and architectures, flow and congestion control in data networks, performance evaluation in integrated networks. Content varies from year to year, and different topics rotate through the course numbers 6770 to 6779
Further study of areas such as communication protocols and architectures, flow and congestion control in data networks, performance evaluation in integrated networks. Content varies from year to year, and different topics rotate through the course numbers 6770 to 6779
Prerequisites: (ELEN E4810) or ELEN E4810; or instructor's permission. Fundamentals of digital speech processing and audio signals. Acoustic and perceptual basics of audio. Short-time Fourier analysis. Analysis and filterbank models. Speech and audio coding, compression, and reconstruction. Acoustic feature extraction and classification. Recognition techniques for speech and other sounds, including hidden Markov models
ELEN E6873Statistical signal processing and learning3.00
Prerequisites: ELEN E4815 Introduction to the fundamental principles of statistical signal processing related to detection and estimation. Hypothesis testing, signal detection, parameter estimation, signal estimation, and selected advanced topics. Suitable for students doing research in communications, control, signal processing, and related areas
ELEN E6876Sparse and Low-Dimensional Models for High-Dimensional Data3.00
Prerequisites: ELEN E4815; or equivalent and linear algebra. Recommended: ELEN E4810 or equivalent. Overview of theory, computation and applications for sparse and low-dimensional data modeling. Recoverability of sparse and low-rank models. Optimization methods for low-dim data modeling. Applications to imaging, neuroscience, communications, web data
Prerequisites: ELEN E4810 Advanced topics in signal processing, such as multidimensional signal processing, image feature extraction, image/video editing and indexing, advanced digital filter design, multirate signal processing, adaptive signal processing, and wave-form coding of signals. Content varies from year to year, and different topics rotate through the course numbers 6880 to 6889
Prerequisites: ELEN E4810 Advanced topics in signal processing, such as multidimensional signal processing, image feature extraction, image/video editing and indexing, advanced digital filter design, multirate signal processing, adaptive signal processing, and wave-form coding of signals. Content varies from year to year, and different topics rotate through the course numbers 6880 to 6889
Prerequisites: ELEN E4810 Advanced topics in signal processing, such as multidimensional signal processing, image feature extraction, image/video editing and indexing, advanced digital filter design, multirate signal processing, adaptive signal processing, and wave-form coding of signals. Content varies from year to year, and different topics rotate through the course numbers 6880 to 6889
Prerequisites: ELEN E4810 ELEN E4810 Advanced topics in signal processing, such as multidimensional signal processing, image feature extraction, image/video editing and indexing, advanced digital filter design, multirate signal processing, adaptive signal processing, and wave-form coding of signals. Content varies from year to year, and different topics rotate through the course numbers 6880 to 6889. Topic: Large Data Stream Processing
Advanced topics spanning electrical engineering and computer science such as speech processing and recognition, image and multimedia content analysis, and other areas drawing on signal processing, information theory, machine learning, pattern recognition, and related topics. Content varies from year to year, and different topics rotate through the course numbers 6890 to 6899
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 6900 to 6909
Prerequisites: Instructor's permission. Analysis, modeling and design of transceiver architectures for wireless communication and sensing. Fundamentals of RF system analysis and design. Introduction to discrete-time behavioral modeling of transceiver analog blocks and digital methods for compensating analog impairments. Topics include transceiver architectures for ultra-low power communication, high-throughput sub-THz communication and compressed-sampling architectures for energy-efficient wideband spectrum sensing and rapid direction-of-arrival finding
Prerequisites: Instructor’s permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 6900 to 6909
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 6900 to 6909
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 6900 to 6909
ELEN E6908TOPICS IN ELECTRICAL AND COMPUTER ENGINE3.00
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 6900 to 6909
Prerequisites: Instructor's permission. Selected topics in electrical and computer engineering. Content varies from year to year, and different topics rotate through the course numbers 6900 to 6909
Prerequisites: (EECS E4321) ELEN E4321 A comprehensive introduction to modern power management integrated circuits (PMIC) design. Advanced topics in power management will be introduced including: linear regulators; digital linear regulator; switch-mode power converter; control schemes for DC-DC converters; power losses in DC-DC converter; switched capacitor converters; wireless power conversion; power converter modeling and simulation; design examples. Topics may change from year to year
Prerequisites: (ELEN E3106) and (ELEN E3401) or ELEN E3106 AND ELEN E3401; or equivalents. Recommended: ELEN E4944. This course provides an understanding of the methods used for structuring matter on the nanometer length: thin-film technology; lithographic patterning and technologies including photon, electron, ion and atom, scanning probe, soft lithography, and nanoimprinting; pattern transfer; self-assembly; process integration; and applications
Prerequisites: Obtained internship and approval from a faculty advisor. May be repeated for credit, but no more than 3 total points may be used for degree credit. Only for electrical engineering and computer engineering graduate students who include relevant off-campus work experience as part of their approved program of study. Final report required. May not be taken for pass/fail credit or audited
Subject
ELEN E
Credits (min)
1
Credits (max)
1.5
Credit unit
points
Type
course
Repeatable
May be repeated for credit, but no more than 3 total points may be used for degree credit.
Prerequisites: Requires approval by a faculty member who agrees to supervise the work. Points of credit to be approved by the department. Requires submission of an outline of the proposed research for approval by the faculty member who is to supervise the work of the student. The research facilities of the department are available to qualified students interested in advanced study
Prerequisites: Requires approval by a faculty member who agrees to supervise the work. Points of credit to be approved by the department. Requires submission of an outline of the proposed research for approval by the faculty member who is to supervise the work of the student. The research facilities of the department are available to qualified students interested in advanced study
Prerequisites: Open to doctoral candidates, and to qualified M.S. candidates with instructor’s permission. Theoretical and experimental studies of semiconductor physics, devices, and technology
Lect: 2. Open to doctoral candidates, and to qualified M.S. candidates with the instructor's permission. Study of recent developments in electronic circuits. Fall 2026: ELEN E9303 Course Number Section/Call Number Times/Location Instructor Points Enrollment ELEN 9303 002/20507 Th 9:00am - 11:00am 1306 Seeley W. Mudd Building Matthias Preindl 3 9/15
Prerequisites: (ELEN E4411) ELEN E4411 Open to doctoral candidates and to qualified M.S. candidates with instructor's permission. Recent experimental and theoretical developments in various areas of photonics research. Examples of topics that may be treated include squeezed-light generation, quantum optics, photon detection, nonlinear optical effects, and ultrafast optics
ELEN E9701Seminar in information and communication theories3
Lect: 2. Open to doctoral candidates, and to qualified M.S. candidates with the instructor's permission. Recent developments in telecommunication networks, information and communication theories, and related topics. Spring 2026: ELEN E9701 Course Number Section/Call Number Times/Location Instructor Points Enrollment ELEN 9701 001/18223 F 1:10pm - 3:40pm 306 Uris Hall Gil Zussman 3 8/20
A candidate for the Eng.Sc.D. degree in electrical engineering must register for 12 points of doctoral research instruction. Registration in ELEN E9800 may not be used to satisfy the minimum residence requirement for the degree
