ECE-541: Probability Theory & Stochastic Processes

Term: Fall 2010

Instructor: Balu Santhanam

Instruction Time: TR: 3:30 - 4:45 PM

Venue : ECE-310

Pre-requisites: ECE-314, ECE-340, Working Knowledge of MATLAB

Announcements:

• Information regarding the class, exams, and assignments will be posted to the page. Please check here often.  
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Course Resources:

• Course Outline/Syllabus
• Fourier Transform Tables
• Zee Transform Tables
• Final Exam Schedule
   

Random Processes, Classification, Examples :

Preliminaries:

• Problem Set 0.0
• On the notion of statistical regularity
• Example: Sigma Algebras
• More on Independence
• On Measurable functions
• On Indicator Functions
• Solution to Exercise Problem
• Notes on the Lebesgue Measure
• Notes on Covariance Matrices
   

Definitions and Classification of Random Processes :

• Definition of a Random Processes
• Ensemble Statistics
• Stationarity
• On the Sufficiency of Second-Order Statistics
• Power Spectral Density
• More on Classification
• Random Walk Process
• Wiener Process
• Brownian Motion
• On Markov Processes
• Ergodicity
• Ergodicity in the mean
• White Noise: The All--pervasive WSS process
• Cyclostationarity
   

Calculus of Random Processes :

• On Modes of Convergence of Random Sequences
• Example: Modes of Convergence
• Mean Squared Convergence
• Hilbert Space Perspective on Random Processes
• On Mean Squared Continuity
• Example: M.S. Convergence
• Example: M.S. Continuity
• On Mean Squared Derivatives
• Mean Squared Integration

Examples of Random Processes :

• Random Oscillator Example
• Random process example:
• Cyclostationary Process Example: PAM
• Cyclostationary Process Example
• Example: Ergodicity
• Example: Ergodicity I
• Example: Classification
• Example: Independent Increments Process
• AR(1) Example: Transmission thru LTI systems
• Example: R-C Circuit Response
• Example: PSD Factorization:
• Example: Power Spectral Factorization (2)
 

Processing of Stochastic Signals :

• Random Processes and Modulation
• LTI Systems and Random Processes
• Whitening of Random Vectors
• More on Whitening
• White Noise Derived Random Sequences
• Filtering White Noise
• Notes on Rayleigh and Rician Fading
• Random Signals and Multirate Systems
• Power Spectral Factorization
• Bandlimited Sampling Theorem
• On Impulse sampling of Random Processes
• On D/A Conversion
• Uniform Quantization
• Nonuniform Quantization
• On Wold's Decomposition and Innovations
   

Optimal Filtering of Stochastic Signals :

• On MMSE Estimation
• Overview of Optimal Wiener Filtering
• Overview of FIR Wiener Filtering
• Overview of Prediction
• Overview of Optimal Causal Wiener Filtering
• Optimal Wiener Deconvolution
• Example: Optimal Smoothing
• Example: Optimal Filtering
  
• Example: Prediction
  
• Example: Schur-Cohn Stability
  
• Example: Equalization
  
• On Lattice Filters
• Overview of the Least Squares Problem
• Overview of Least Squares Inversion
• Overview of Discrete Kalman Filter
 

Review Material:

• Review of ECE-34O, ECE-314
• Electronic reserves for ECE-340
   

MATLAB Resources:

• MATLAB Online Reference Guide
• Mathworks (developer of Matlab)
• UFL MATLAB Primer
• Sample MATLAB Mfile
   

Problem Sets/Exercises:

• Problem Set # 1.0
• Solutions to PS # 1.0
• Problem Set # 2.0
• Solutions to PS # 2.0
• Problem Set # 3.0
• Solutions to PS # 3.0
• Problem Set # 4.0
• Sample: vowel /i/ wavfile
• Problem Set # 5.0
• Solutions to PS # 5.0
• Problem Set # 6.0
• Solutions to PS # 6.0
  

Exams:

• Midterm: Review Problems
• Midterm Exam
• Midterm Solutions
• Final Exam