EE 503

Signal Analysis and Processing

Course Description:

The course goal is to establish the fundamentals required for the study of advanced signal processing methods. The course emphasizes processing of random signals which is the topic of statistical signal processing; but an overview of deterministic signals and their processing techniques is also given. The students are expected to have familiarity of basic linear algebra, basic random processes and undergraduate level signal processing techniques.  The course is a pre-requiste for EE504.

Course Outline:

1. Deterministic Signals and Processing Methods
1. Review of linear algebra (Matrices, basis expansions, linear space, sub-space, special matrices, eigenvalue-eigenvector)
2. Review of DSP topics, (Fourier Transform, Z-transform, Linear time invariant systems, impulse response, convolution, connections of DSP operators with matrices, convolution matrix, downsampling matrix, projection  matrix etc.)
3. Review of discrete time processing of continuous signals (Fundamental idea of DSP)
2. Random Signals
1. Probability and random processes
2. Expectations, mean and moment calculations, characteristic functions
3. Ergodicity (mean ergodic, auto-correlation ergodic)
4. Power spectrum density
5. Random vectors, auto-correlation matrices, covariance
6. Gaussian processes
3. Parameter estimation
1. Bias, consistency
2. MS estimation
3. Linear MS estimation
4. Cramer – Rao bound and efficient estimates
5. LS estimates
6. Applications to signal modelling
4. Optimal Filtering
1. AR, MA, ARMA models
2. Wiener Filtering, Linear Prediction
3. Lattice implementations
5. Signal Modeling
1. LS, Pade, Prony
2. Lattice filters, Levinson Recursion

Grading: HW’s with Matlab assignments plus two midterms and a final

Textbooks:

1. Charles. W. Therrien, “Discrete Random Signals And Statistical Processing,” Prentice Hall, 1992. (will be followed closely)
2. M.H. Hayes, “Statistical Digital Signal Processing and Modelling”, Wiley, 1996. (textbook of EE504, highly recommended, slightly more advanced)
3. A. Papoulis, “Probability, Random Variables and Stochastic Processes,” Mc-Graw Hill, 1984. (very valuable reference book, contains topics of EE503, EE504, EE531 and more)

Instructor: Çağatay Candan, C-105, 210-2355, ccandan .at. metu