EE 140: Stochastic Processes, Detection and Estimation
The goal of this class is the development of basic analytical tools for the modeling and analysis of random phenomena and the application of these tools to a range of problems arising in engineering, manufacturing, and operations research. The first portion of this class will cover introductory probability theory including sample spaces and probability, discrete and continuous random variables, conditional probability, expectations and conditional expectations, and derived distributions. The balance of the class will be concerned with statistical analysis methods including hypothesis testing, confidence intervals and nonparametric methods.
- Tuesdays and Thursdays, 10:30 - 11:45 AM, Lecture Zoom, Halligan Hall Room 111A,
- Office Hours
- Probability and Statistics: EE-24/104 or equivalent
- Linear Systems: EE-23 or equivalent
- Linear Algebra/Vector Spaces: Math 70 or equivalent
Tentative Grading Scheme
- Homeworks: 30%
- In-class mid-term exam: 30%
- Final or final project: 40%
Tufts holds its students strictly accountable for adherence to academic integrity. The consequences for violations can be severe. It is critical that you understand the requirements of ethical behavior and academic work as described in Tufts’ Academic Integrity handbook. If you ever have a question about the expectations concerning a particular assignment or project in this course, be sure to ask me for clarification. The Faculty of the School of Arts and Sciences and the School of Engineering are required to report suspected cases of academic integrity violations to the Dean of Student Affairs Office. If I suspect that you have cheated or plagiarized in this class, I must report the situation to the dean.
- Shynk, John J. Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications. Wiley, 2013.
- Yates, Roy D., and David J. Goodman. Probability and Random Processes: A Friendly Introduction for Electrical and Computer Engineers. Third Edition. Wiley, 2014.
- Levy, Bernard C., Principles of Signal Detection and Parameter Estimation, Springer, 2008. Tufts students should be able to access this text online here.
- Notes and additional chapters from the two texts on the Canvas Site under Files/ClassNotes
- Leon-Garcia, Alberto. Probability, Statistics and Random Processes for Electrical Engineering. Third Edition, Prentice Hall, 2008
- Kobayashi, Hisashi, Brian L. Mark, and William Turin. Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queuing Theory and Mathematical Finance. Cambridge University Press, 2011.
- Gubner, John A., Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006.
- Stark, Henry, and John William Woods. Probability, Statistics and Random Processes for Engineers. Prentice-Hall, 2011.
|Jan. 16||Overview, Introduction to Random Vectors, First and Second Moments|
|Jan. 21||First and Second Moments of Random Vectors, Gaussian Models|
|Jan. 23||Gaussian Models, Introduction to Estimation, Minimum Mean Square Optimal Estimation|
|Jan. 28||MMSE and Maximum a Posteriori Estimation|
|Jan. 30||Maximum a Posteriori Estimation, Maximum Likelihood Estimation|
|Feb. 4||Cramer-Rao Bound, Vector Estimation, Bayes Linear Least Squares Estimation|
|Feb. 6||Binary and M-Ary Hypothesis Testing|
|Feb. 11||Binary and M-Ary Hypothesis Testing|
|Feb. 13||Binary and M-Ary Hypothesis Testing|
|Feb 18.||Binary and M-Ary Hypothesis Testing|
No class: Monday schedule
|Feb. 25||Asymptotic Analysis of Likelihood Ratio Tests|
|Feb. 27||Composite Hypothesis Testing|
|Mar. 3||Introduction to Random Processes|
|Mar. 5||Stationarity, First and Second Moment Analysis of Random Processes|
|Mar. 11||Independent and Identically Distributed Processes|
|Mar. 12||Mid-term Exam|
|Mar. 17||No class: spring break|
|Mar. 19||No class: spring break|
|Mar. 24||Markov Processes, Discrete Time Markov Chains|
|Mar. 26||Bernoulli Processes, Poisson Processes|
|Mar. 31||Wiener Process|
|Apr. 2||Linear Shift Invariant Systems and Wide Sense Stationary Processes, Power Spectral Density|
|Apr. 7||Cross-spectral Density and Optimal Estimation|
|Apr. 9||Optimal Estimation, Non-Causal Wiener Filter, Causal Wiener Filter|
|Apr. 14||Discrete Wiener Filters|
|Apr. 16||Discrete Wiener Filters|
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
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