Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

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Statistical Signal Processing

Course Code	: EEE541
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 6

Objectives of the Course

The course objectives are to provide the understanding of: 1. Stochastic signal models and their use in signal processing applications 2. Optimal linear-time invariant (LTI) filtering of stochastic processes 3. Estimation theory using classical and Bayesian approaches.

Course Content

Random processes. Power spectral density. Auto-regressive processes. Moving-average processes. Periodic processes. Spectral decomposition. Whitening filter. Innovations. Stochastic signal models. Yule-Walker equations. Linear-time invariant filtering of random processes. Estimation. Linear Estimators. Linear minimum mean square error estimator. Wiener filter. Optimal FIR filters. Optimal IIR filters. Filtering, prediction, smoothing applications. Reduced dimension stochastic signal representation. Karhunen-Loeve transform.

Name of Lecturer(s)

Learning Outcomes

1.	To analyze WSS stochastic processes using first and second moments
2.	To analyze WSS stochastic processes that are processed by LTI systems
3.	To analyze estimators
4.	To derive optimal linear filters
5.	To use linear models to analyze WSS stochastic signals

Recommended or Required Reading

1.	M. H. Hayes, Statistical Signal Processing and Modeling, Wiley, New York, NY, 1996
2.	Therrien, Charles W., Discrete random signals and statistical signal processing, Prentice Hall, c1992.
3.	Louis L. Scharf, Statistical Signal Processing, Addison-Wesley Publishing Company, Inc., Reading, MA, 1991.

Weekly Detailed Course Contents

Week 1 - Theoretical

Review of Some Linear Algebra Concepts: Matrices as Transformations, Matrices as Linear Combiners, Matrices as Equation Systems

Week 2 - Theoretical

Review of Some DSP Concepts: Discrete time processing of continuous time signals, Discrete Time Operations,

Week 3 - Theoretical

Random Processes.

Week 4 - Theoretical

Random Processes.

Week 5 - Theoretical

Signal Modeling : LS methods, Pade, Prony (Deterministic methods), AR, MA, ARMA Processes (Stochastic approach), Yule-Walker Equations,

Week 6 - Theoretical

Signal Modeling : Non-linear set of equations for MA system fit, All-pole modeling, Covariance Method, Auto-correlation Method, Harmonic Processes, Wold decomposition, Decorrelating transforms such as Fourier Transforms for Harmonic Processes and KL transform in general

Week 7 - Theoretical

Signal Modeling : Applications: Signal Compression, Signal Prediction, System Identification, Spectrum Estimation.

Week 8 - Theoretical

Estimation Theory: Cost Functions: Mean Square, Mean absolute, max error, - Midterm Exam

Week 9 - Theoretical

Estimation Theory: MSE, ML, absolute error estimators, Min MSE estimators, Regression line, orthogonality

Week 10 - Theoretical

Estimation Theory: Linear min MSE estimators, Linear unbiased min MSE estimators.

Week 11 - Theoretical

Estimation Theory: Bias, consistency, efficiency, bias-error variance trade-off. Discussion of LS estimator for Ax=b + n systems.

Week 12 - Theoretical

Estimation Theory: Wiener Filters as optimal estimators, Linear predictors defined from Wiener filters, Levinson-Durbin recursion for efficient solution of Wiener-Hopf equations.

Week 13 - Theoretical

Estimation Theory: Lattice Structures for efficient implementation of Wiener filters.

Week 14 - Theoretical

Estimation Theory: IIR Wiener Filters, Non-causal, Causal

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Attending Lectures	1	%2
Assignment	5	%8
Midterm Examination	1	%20
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	1	3	56
Assignment	5	2	2	20
Individual Work	6	1	1	12
Midterm Examination	1	10	5	15
Final Examination	1	20	30	50
TOTAL WORKLOAD (hours)				153

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7
OÇ-1	4	4	4	4	4	4	4
OÇ-2	4	4	4	4	4	4	4
OÇ-3	4	4	4	4	4	4	4
OÇ-4	4	4	4	4	4	4	4
OÇ-5	4	4	4	4	4	4	4

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