18-752 Detection, Estimation, and Identification

(12 Units, taught everyother spring semester, next offering Spring 2005, graduate course, satisfies ECE coverage requirements) Basic graduate course in detection and estimation theory. Decision theory: Binary hypothesis testing, M-ary testing, Bayes, Neyman-Pearson, Min-Max. Performance. Probability of error, ROC. Estimation theory: linear and nonlinear estimation, parameter estimation. Bayes, MAP, maximum likelihood, Cramér-Rao bounds. Bias, efficiency, consistency. Asymptotic properties of estimators. Orthogonal decomposition of random processes and harmonic representation. Waveform detection and estimation. Wiener filtering and Kalman-Bucy filtering. Elements of identification. Recursive algorithms. Spectral estimation. Topics may vary. 4 hrs. lec. Prerequisite: 18-751.

18-751 Applied Stochastic Processes

(12 Units, taught every Fall, next offering Fall 2004, graduate course, satisfies ECE coverage requirements) We introduce random processes and their applications. Throughout the course, we emphasize the discrete-time point of view, although we also discuss the continuous-time case from time to time. Topics covered include: basic concepts of random variables, random vectors, random sequences, stochastic processes, and random fields; expectation and conditional expectation, moments, and characteristic functions; most common classes of random sequences and processes including white noise, Gaussian processes, Markov processes, Poisson processes, and Markov random fields; second order descriptions for random sequences and random processes: mean, auto and cross correlation, auto and crosscovariance; 2nd order Fourier analysis, energy and power spectral and crossspectral densities, and random processes and linear systems. We also present elements of estimation theory and optimal filtering including Wiener and Kalman-Bucy filtering. Advanced topics in modern statistical signal processing such as linear prediction, linear models and spectrum estimation are discussed. 4 hrs. lec. Prerequisites: 36-217 and 18-396 is required for undergraduates, or permission of the instructor.

18-396 Signals and Systems

(12 Units, taught every semester, undergraduate, sophomore/ junior level breadth course. Last time I taught was Spring 2006)

Basic introduction to signal transforms, linear systems, time and frequency descriptions, discrete and continuous time, emphasis on discrete time. Fourier, Laplace, Z-transforms. Sampling theorem.

18-202 Mathematical Foundations of Electrical Engineering

(12 Units, taught every semester, undergraduate, sophomore level core course. I taught Fall 07 and teach Fall 08)

Basic mathematical fundamentals of Electrical Engineering, focus on complex numbers and complex analysis, ordinary differential equations, linear algebra. Co-prerequisit for 18-220.

18-899 Adv. Topics in Signal Processing: Algebraic Signal Processing

(12 Units, 1st offering Spring 2004, not taught regularly, graduate course, satisfies ECE coverage requirements) Traditionally,


Digital Signal Processing (DSP) is taught and learned through formulas and summations. Fast algorithms, for example, the FFT, are introduced through intricate index manipulations. The underlying structure is lost with so many fast algorithms dispersed in the literature for the various linear transforms; no wonder it is more of an art of ingenious tricks to develop new fast algorithms. DSP can be understood in a different light, if only we ventured past Linear Algebra and Vector Spaces. Yes, Linear Algebra provides a beautiful geometric picture. But, going beyond illuminates much of the structure underlying many of the transforms and their fast algorithms, and provides a powerful systematization of many apparently disparate algorithms. This course will introduce basic concepts in Algebra with a focus on groups, representations, modules, algebras, and related topics. Applications covered in the course will include linear transforms, particular emphasis on the DFT and trigonometric transforms, their fast algorithms, but include others as well, possibly, in Statistics, for example, from Kendall’s Shape Theory. Students are encouraged to explore their own preferred topics or other directions. On transforms, students will experiment with their fast implementations using SPIRAL. The course will mix formal lectures with discussions of research papers. This is the first time ever this course is offered at CMU, and it is most likely also a first at most other places, so there is ample opportunity for adapting to the students particular interests. Prerequisites: good understanding of Linear Algebra.

18-799 H Adv. Topics in Signal Processing: Network Science: Modeling and inference

(12 Units, 1st offering Spring 2011, not taught regularly, graduate course, satisfies ECE coverage requirements) Do you ever wonder how seeming successfully ants forage for rich sources of food, bees move a beehive to more suitable locations, flocks of birds fly in formation? How come a tree falling in Ohio causes fifty five million people in the Northeast of the US and Canada to loose their electrical power? Why do the actions of a few in an office in the financial district in London impact so signicantly the World financial markets? Why do critical infrastructures, e.g., cellular and mobile networks, fail in times of crisis, when they are most needed? How do botnets spread and compromise millions of computers in the internet? Can companies understand the viral behavior of their three million (did you say one hundred million) (mobile) customers? These and others are background and motivational examples that guide us in this course whose goal is the study of relatively dumb agents that sense, process, and cooperate locally but whose collective, coordinated activity leads to the emergence of complex behaviors. Among others, the course will develop basic tools to understand: i) the modeling of these highly networked, large scale structures (e.g., colonies of agents, networks of physical systems, cyber physical systems;) ii) how to predict the behavior of these networked systems; and iii) how to derive and study the properties (e.g., convergence and performance) of distributed algorithms for inference and data assimilation. The course will develop graph representations and introduce tools from spectral graph theory, will cover the basics from queueing theory, Markov point processes, and stochastic networks to predict behaviors under several types of stress conditions and asymptotic regimens, and will explore consensus algorithms and several classes of distributed inference algorithms operating under infrastructure failures (intermittent random sensor and channel failures,) different resource constraints (e.g., power or bandwidth,) or random protocols (e.g., gossip.) The course is essentially self-contained. There will be a mix of homeworks, midterm exams, and projects. Students will take an active role by exploring examples of applications and applying network science concepts to fully develop the analysis of their preferred applications.