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\def\classTime{{"T from 06:15 pm to 08:45 pm in Drosdick Hall 109.","T from 06:15 pm to 08:45 pm in Online SYN.",""}}
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\def\classLive{{"https://villanova.zoom.us/j/96862483018","https://villanova.zoom.us/j/96862483018",""}}
\def\classInstructor{{"Mojtaba Vaezi","Mojtaba Vaezi",""}}
\def\classInstrContact{{"http://www.ece.villanova.edu/\~mvaezi/","http://www.ece.villanova.edu/\~mvaezi/",""}}
\def\classInstrOffHrs{{"Tuesday 3 pm to 4 pm","Tuesday  3 pm to 4 pm",""}}
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\newcommand\semester{Fall 2025}
\newcommand\rsemester{202620}
\newcommand\courseNum{ECE 8072}
\newcommand\courseName{Statatistical Signal Processing}
\newcommand\courseCoordinator{Mojtaba Vaezi}
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\newcommand\meetingDesc{Two 75-minute lectures}
\newcommand\meetingMisc{Special notes on meeting info go here, if specified}
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\newcommand\textBookTitle{1. Probability, Random Variables, and Random Signal Principles, 4th ed.}
\newcommand\textBookAuth{A. Papoulis and S. U. Pillai}
\newcommand\textBookPub{McGraw Hill}
\newcommand\textBookYr{2002}
\newcommand\textBookISBN{}
\newcommand\supplMaterials{\\Lecture Notes and Handouts \\ H. Hsu, Schaum’s Outline of Probability, Random Variables, and Random Processes, McGraw Hill, 1997.}
\newcommand\refPapers{References go here, if specified}
\newcommand\textBookMisc{Special notes on textbook(s) go here, if specified}
\newcommand\catalogDesc{Discrete and continuous random variables, conditional and joint distributions, random vector and stochastic processes, correlation and spectra of stationary processes under linear transformations, smoothing and prediction in mean square estimation. Prerequisite: Background in statistics and probability.}
\newcommand\preReqs{None}
\newcommand\coReqs{None}
\newcommand\coreRequirement{Required for MS/PhD in Signal Processing and Communications (SPC)}
\newcommand\courseExpectation{At the end of the course, the students will be able to: 
\begin{itemize}  
\item Understand the basic principles of probability, probability axioms, independence, conditional probability, Bayes theorem and use these principles in solving problems.
\item  Characterize probability distributions of different functions of random variables and find their expected value, variance, and moments.
\item  Explain the difference between deterministic and stochastic signals providing examples in the context of signal processing and communications.
\item  Understand and reflect on the implications of the laws of large numbers and the central limit theorem in the context of signal acquisition and analysis.
%\item  Characterize random signals by computing first and second order statistics.
%\item  Calculate the bias and variance of an estimator, given the noise statistics.
\item  Apply the linear, maximum likelihood and Bayesian estimations methods to solve problems concerning the estimation of signal parameters.
%\item  Apply numerical solution methods to obtain the least squares and maximum likelihood estimates for problems with nonlinear signal models.
\item Understand and explain the use of Markov chains and process  in signal processing, communication and machine learning.
\end{itemize}
}
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\newcommand\covTopics{\item Introduction to probability and random variables
\item Functions of random variables, multivariate  random variables
\item Expectation, moments, correlation and covariance
\item Continuous and discrete distributions, Gaussian distribution 
\item Random vectors, random sequences, order statistics 
\item Mean square estimation, parameter estimation, and maximum likelihood  estimation
\item Convergence, laws of large numbers, and central limit theorem   
\item Stochastic processes (Poisson process, random walk, ...)
\item Stationary processes, ergodic process, white noise process
\item Markov processes and Markov chains
}
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\caption*{Tentative Schedule for \textbf{All Sections}} \vspace{0.05in}
{\renewcommand{\arraystretch}{1.5} \small
\begin{tabularx}{\linewidth}{l|l|l|l}
\toprule
\large \textbf{Week} & \large \textbf{Date} & \large \textbf{Topics and Reading} & \large \textbf{Due}\\
\midrule \midrule
1 & 8/26 & Lecture 1: Introduction to Probability Theory & \\
2 & 9/2 & Lecture 2: Random Variables & HW1\\
3 & 9/9 & Lecture 3: Functions of One Random Variable & \\
4 & 9/16 & Lecture 3: Functions of Two Random Variables & HW2\\
5 & 9/23 & Lecture 5: Vector Random Variables/Order Statistics & \\
6 & 9/30 & Lecture 6: Conditional Statistic & HW3\\
7 & 10/7 & Lecture 7: Covariance and Correlation & \\
8 & 10/14 & {\color{red} Fall break} & \\
9 & 10/21 & Lecture 8: MMSE Estimation & Paper title\\
10 & 10/28 & Lecture 9: Parameter Estimation & Midterm Exam\\
11 & 11/4 & Lecture 10: Regression vs Estimation & HW4\\
12 & 11/11 & Lecture 11: Convergence and Limit Theorems & \\
13 & 11/18 & Lecture 12: Random Processes & HW5\\
14 & 11/25 & Lecture 13: Stationary Random Processes & \\
15 & 12/1 & Course Review/Students' Presentations & Presentations\\
16 & 12/8 & {\color{red} Final Exam (tentative)} & HW6\\
 &  &  & \\
\bottomrule \end{tabularx} } \end{table}}
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\textbf{Letter grade scale:} $$A(94-100), A^{-}(90-93), B^{+}(87-89), B(83-86), B^{-}(78-82), C^{+}(74-77), 
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%\item  Assignments will be assigned on Mondays, and due a week later at 5pm.
\item Assigned on Tuesday, due the following Tuesday at 5pm.
%\item Will not be corrected! However submits with an attempt on all questions will obtain a full grade
\item Make sure that the answers are in order
and the solutions are neat and  readable (if handwritten). Please submit your work in one pdf file. 
%\item Scribes (including sample problems) should be in \LaTeX.
\end{itemize}
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Since you opted for an AI Policy, you should edit this part, choosing one of the following statements, modifying as desired:\\
\\
The use of AI-generated content is not permitted in this course.
Its use will result in an academic integrity violation and a zero on the assignment.\\
\\
OR\\
\\
The use of AI-generated content is allowed in this course.\\
\\
OR\\
\\
The use of AI-generated content is permitted as follows: (a) for generating a first draft or (b) for generating an outline or (c) for generating XXX.\\
\\
AND, if AI is allowed:\\
\\
Even if you have significantly edited AI-generated material, you must identify the AI tool used to assist in generating your work. You are required to provide the name of the tool, date used, and prompts used to generate the output.  As you may be required to submit the original AI output, you must keep a copy of the original output and provide it when requested.  If questions arise about the authorship of submitted work, you are responsible for authenticating your authorship.  You should save evidence of your authorial process, such as drafts, notes, version histories, and complete transcripts of AI assistance.
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