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\def\classTime{{"Tuesday  06:10 pm to 08:50 pm","Tuesday  06:10 pm to 08:50 pm",""}}
\def\classRm{{"CEER 212","CEER 212",""}}
\def\classLive{{"https://villanova.zoom.us/j/96862483018","https://villanova.zoom.us/j/96862483018",""}}
\def\classInstructor{{"Dr. Mojtaba Vaezi","Dr. Mojtaba Vaezi",""}}
\def\classInstrContact{{"http://www.ece.villanova.edu/\~mvaezi/","http://www.ece.villanova.edu/\~mvaezi/",""}}
\def\classInstrOffHrs{{"Tuesday  5 pm to 6 pm","Tuesday  5 pm to 6 pm",""}}
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\newcommand\semester{Fall 2021}
\newcommand\rsemester{202220}
\newcommand\courseNum{ECE 8072}
\newcommand\courseName{Statatistical Signal Processing}
\newcommand\courseCoordinator{Dr. Mojtaba Vaezi}
\newcommand\credits{3}
\newcommand\contactHrs{3}
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\newcommand\meetingDesc{Two 75-minute lectures}
\newcommand\meetingMisc{Special notes on meeting info go here, if specified}
\newcommand\instructorMisc{Special notes on instructor(s), TA(s) 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{This is an advanced course on probability, random variables, estimation theory, and stochastic process, and will cover
\begin{itemize}
\item \textbf{Probability and random variables:} review of the probability theory, discrete and continuous random variables,
functions and transformations of random variables, conditional and joint distributions, continuous and discrete distributions, mean, variance and higher order moments, and order statistics. 
\item \textbf{Estimation and prediction:} linear estimation, minimum mean square estimation (MMSE), parameter estimation,  Baysian estimation, and maximum-likelihood estimation.
\item \textbf{Convergence and limit theorems:} convergence in probability, convergence in mean square sense, convergence in distribution, laws of large numbers, and central limit theorem. 
\item \textbf{Random processes:} discrete-time random process,  continuous-time random process correlation,  stationary, non-stationary, and ergodic processes, independent and identically
distributed (i.i.d.) processes, Poisson process, Markov chain, random walk, Wiener process, Brownian motion, spectral analysis, Gaussian process and response of linear systems to random processes.
\end{itemize}}
\newcommand\preReqs{An undergradute course on probability}
\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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\newcommand\schedule{\begin{table}[h!] \centering 
\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 & 8/24 & Lecture 1: Introduction to Probability Theory & \\
2 & 8/31 & Lecture 2: Random Variables & HW1\\
3 & 9/7 & Lecture 3: Functions of One Random Variable & \\
4 & 9/14 & Lecture 3: Functions of Two Random Variables & HW2\\
5 & 9/21 & Lecture 5: Vector Random Variables/Order Statistics & \\
6 & 9/28 & Lecture 6: Conditional Statistic & HW3\\
7 & 10/5 & Lecture 7: Covariance and Correlation & Midterm Exam\\
8 & 10/12 & {\color{red} Fall break} & \\
9 & 10/19 & Lecture 8: MMSE Estimation & Paper title\\
10 & 10/26 & Lecture 9: Parameter Estimation & \\
11 & 11/2 & Lecture 10: Convergence and Limit Theorems & HW4\\
12 & 11/9 & Lecture 11: Random Processes & \\
13 & 11/16 & Lecture 12: Stationary Random Processes & HW5\\
14 & 11/23 & Lecture 13: Markov Processes and Chains & \\
15 & 11/30 & Course Review/Students' Presentations & Presentations\\
16 & 12/7 & {\color{red} Final Exam} & HW6/Final Exam\\
 &  &  & \\
\bottomrule \end{tabularx} } \end{table}}
\newcommand\gradingPolicy{\noindent Homework 30\%,  $\quad$  Midterm Exam 20\%,  $\quad$  Final Exam 30\%,  $\quad$  Presentation 20\%
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\textbf{Letter grade scale:} $$A(94-100), A^{-}(90-93), B^{+}(87-89), B(83-86), B^{-}(78-82), C^{+}(74-77), 
C(70-73), F(<70)$$}
\newcommand\HWandLabPolicy{\begin{itemize}
%\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.
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