ECE-541: Probability Theory & Stochastic Processes
Term: Fall 2007
Instructor: Balu Santhanam
Instruction Time: TR: 4:00 - 5:15 PM
Venue : ECE-310
Pre-requisites: ECE-314, ECE-340, Working Knowledge of MATLAB
Announcements:
Course Resources:
Random Processes, Classification, Examples :
Preliminaries:
- 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
Mean-Squared Calculus of Random Processes :
- On Modes of Convergence of Random Sequences
- Mean Squared Convergence
- Hilbert Space Perspective on Random Processes
- On Mean Squared 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
- 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
- On Lattice Filters
- Overview of the Least Squares Problem
- Overview of Least Squares Inversion
- Overview of Discrete Kalman Filter
Review Material:
MATLAB Resources:
Problem Sets/Exercises:
- Problem Set 0.0
- Corrected Problem Set 1.0
- Solutions tp PS # 1.0
- Problem Set 2.0
- Solutions to Problem Set 2.0
- Problem Set 3.0
- Solutions to Problem Set 3.0
- Problem Set 4.0: complete problems 6.22, 6.27, 6.37, 6.38, 6.42 from your textbook
- Solutions to Problem Set 4.0
- Problem Session: 10/19/07
- Uniform Quantization Function
- Problem Set 5.0
- Solutions to Problem Set 5.0
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