This course introduces introduces the mathematical foundations for modeling uncertainty and analyzing stochastic phenomena in engineering systems. The course covers probability theory, random variables, common probability distributions, expectation, correlation, and limit theorems, followed by continuous-time and discrete-time random processes. Students learn key concepts such as stationarity, ergodicity, autocorrelation, and power spectral density, which are essential for signal processing and communication analysis. Practical examples from communication systems, noise modeling, and statistical inference are used to connect theory with engineering applications. By the end of the course, students develop the analytical tools needed to model and solve engineering problems involving randomness and uncertainty.
This course introduces the fundamental principles and techniques used to transmit digital information reliably over communication channels. The course covers key topics such as signal representation, modulation and demodulation, source and channel coding, detection theory, and performance analysis in noisy environments. Students learn how modern communication systems mitigate interference, distortion, and noise to achieve efficient data transmission. Practical examples from wireless, satellite, and broadband communication systems are used to connect theory with real-world applications. By the end of the course, students gain the analytical foundation needed to understand and design modern digital communication systems.
This course covers the following topics: solving systems of linear equations; matrices and linear transformations; image and kernel of a linear transformation; matrices and coordinates relative to different bases; determinants; eigenvalues and eigenvectors; least-squares approximation. Finally, we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors etc.
This course introduces the fundamental concepts used to analyze and model continuous-time and discrete-time signals and linear systems. The course covers signal representation, system properties, convolution, Fourier series, and Fourier transform. Students learn how signals are transformed and processed through linear time-invariant systems in both time and frequency domains. Emphasis is placed on developing analytical tools that serve as the foundation for signal processing, communications, and control systems. By the end of the course, students gain essential skills for understanding and designing engineering systems involving signals and dynamic responses.
This course focuses on theory, algorithms, and applications of convex optimization. Convex optimization deals with the non-linear optimization problems where the objective function and the constraints of the problem are both convex. These problems appear in a variety of applications in diverse fields of science and engineering. This course will cover how to recognize, model, and formulate the convex optimization problems. Topics include: review of least-squares, convex sets and functions, convexity with reference to inequalities, linear optimization, geometric programming, duality (Lagrange dual function), norm approximation, geometric problems, algorithm (descent, Newton, interior-point). Implementation of optimization algorithm will be carried out in CVX (MATLAB based software for convex optimization).
The course addresses the fundamentals of wireless communications and provides an overview of existing and emerging wireless communications networks. It covers radio propagation and fading models, fundamentals of cellular communications, multiple access technologies, and various wireless. Simulation of wireless systems under different channel environments will be an integral part of this course.
This course presents the fundamentals of machine learning and big data analysis along with the related mathematics background at an introductory level. It deals with advanced linear algebra, vector calculus, probability theory, and optimization tools. With the mathematical foundation, we will cover some key machine learning techniques, such as Linear Regression, Principal Component Analysis (PCA), Support Vector Machine (SVM), and Deep Neural Network (DNN) etc.
This course covers the following topics: solving systems of linear equations; matrices and linear transformations; image and kernel of a linear transformation; matrices and coordinates relative to different bases; determinants; eigenvalues and eigenvectors; least-squares approximation. Finally, we look at how to use these to do fun things with datasets - like how to rotate images of faces and how to extract eigenvectors etc.
This course provides an introduction to digital signal processing for both undergraduate students. In this course, a detailed examination of basic digital signal processing operations including sampling/reconstruction of continuous time signals, Fourier and Z-transforms will be given. The Fourier and Z-transforms will be used to analyze the stability of systems, and to find the system transfer function. The discrete Fourier transform (DFT) and fast Fourier transform (FFT) will be studied. Finally, we will examine time and frequency domain techniques for designing and applying infinite impulse response (IIR) and finite impulse response (FIR) digital filters.
The goal of this course to develop an understanding of the elements of electric circuits and the fundamental laws, general techniques such as nodal and mesh analysis, Thevenin and Norton equivalent circuits used in analyzing electric circuits, and develop phasor techniques for AC steady-state analysis of circuits. Study on energy storage elements will help students to understand the transient and the steady-state response of RLC circuits. The course also aims to introduce elementary electronic circuits such as operational amplifiers and their circuit models.
This course mainly focus on alternating current circuit analysis; phasors, sinusoidal steady-state analysis; ac power, rms values, three-phase systems and frequency response concepts. Magnetically coupled circuits, Filter design and analysis and Two-Port Networks; Introduction to system analysis in frequency domain: Laplace Transforms, Fourier Transforms and Fourier Series.
This course presents the fundamentals of analog and digital communication techniques at an introductory level. It deals with continuous wave modulation, pulse modulation, baseband data transmission, and performance analysis of analog and digital communication systems in noisy environments.
Spring 2018
This course begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinctions between discrete-time. The course proceeds to cover digital network and nonrecursive (finite impulse response) digital filters. Digital Signal Processing concludes with digital filter design and a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier transform.