Yiyuan Lin | 林翊源

Yiyuan Lin | 林翊源

he/him

PhD Student in Electrical and Computer Engineering

ECE 4110/5110 - Random Signals in Communications and Signal Processing

Undergrad & grad course, Cornell University, School of Electrical and Computer Engineering, 2024

General Information

  • Instructor: Qing Zhao, 325 Rhodes Hall. Email: qz16@cornell.edu
  • Lecture: MW 1:25pm - 2:40pm, Hollister Hall 320
  • Discussion: F 10:10pm - 11:00pm, Hollister Hall 206
  • Office Hour: W: 4:30-6:00 via Zoom
  • Credits: 4

Prerequisites

ECE 3100 Probability and ECE 3250 Signals and Systems (or equivalent courses).

References and Reading Materials

  • Class notes posted on Canvas.
  • Probability, Statistics, and Random Processes for Electrical Engineering, Third Edition, by A. Alberto Leon-Garcia, Prentice Hall, 2008.
  • Introduction to Probability, Second Edition, by Dmitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2008.
  • Introduction to Probability for Computing, by Mor Harchol-Balter, Cambridge University Press, 2024, available online https://www.cs.cmu.edu/ harchol/Probability/book.html.

Course Description

Introduction to models for random signals in discrete and continuous time; Poisson processes, Gaussian processes, Markov chains, renewal processes, queuing theory, power spectral densities, response of linear systems to random signals.

  1. Review of probability
    1. Probabilistic models
    2. Conditional probability, total probability theorem and Bayes rule, independence and conditional independence
    3. Discrete and continuous random variables, PMF, PDF, and CDF
    4. Expectation and moments of a random variable
    5. Jointly distributed random variables: conditional distribution, conditional mean, correlation and covariance
    6. Bayesian statistical inference: MAP and MMSE
    7. Random vectors, jointly Gaussian random variables
  2. Basic concepts of random processes
  3. Definition and description of a random process
  4. Important properties of a random process: 1. Stationarity and wide-sense stationarity 2. Independent increments
  5. Examples of widely used random processes: 1. Discrete-time processes: i.i.d. sequence, sum process, random walk, and Binomial counting process 2. Continuous-time processes: Poisson process, Gaussian process, Wiener process and Brownian motion
  6. Markov chains, renewal processes, and queueing theory
  7. Discrete-time Markov chains: transition matrix, Chapman-Kolmogorov equations, stationary distribution, classification of states, recurrence and transience, ergodicity and limit theorem
  8. Continuous-time Markov processes: transition rate matrix, stationary distribution, global balance equations
  9. Renewal processes
  10. Queueing systems, M/M/1 queue, Little’s formula
  11. Analysis and processing of random signals
  12. Correlation functions and power spectral densities
  13. Response of linear systems to random signals
  14. Wiener filtering