Statistical Signal Processing

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Radioelectronics

Synopsis:

The course provides fundamentals in three main domains of the statistical signal processing: 1) estimation theory, 2) detection theory, 3) optimal and adaptive filtering. The statistical signal processing is a core theory with many applications ranging from digital communications, audio and video processing, radar and radio navigation, measurement and experiment evaluation, etc.

Requirements:

None

Syllabus of lectures:

1. Estimation

1a. MVU estimator, Cramer-Rao lower bound, composite hypothesis, performance criteria

1b. Sufficient statistics

1c. Maximum Likelihood estimator, EM algorithm

1d. Bayesian estimators (MMSE, MAP)

2. Detection

2a. Hypothesis testing (binary, multiple, composite)

2b. Deterministic signals

2c. Random signals

3. Optimal and adaptive filtration

3a. Signal modeling (ARMA, Padé approximation, ...)

3b. Toeplitz equation, Levinson-Durbin recursion

3c. MMSE filters, Wiener filter

3d. Kalman filter

3e. Least Squares, RLS

3f. Steepest descent and stochastic gradient algorithms

3g. Spectrum analysis and estimation

Syllabus of tutorials:

The course has only lectures

Study Objective:

The course provides theoretical foundations in the three main areas of stochatical signal processing and offers a unifying view of seemingly different approaches.

Study materials:

1. Steven Kay: Fundamentals of Statistical Signal Processing - Estimation theory

2. Steven Kay: Fundamentals of Statistical Signal Processing - Detection theory

3. Monson Hayes: Statistical digital signal processing and modeling

4. Ali Sayed: Fundamentals of Adaptive Filtering

Note:

Further information:

https://moodle.fel.cvut.cz/course/view.php?id=3821

No time-table has been prepared for this course

The course is a part of the following study plans:

• Open Electronic Systems (compulsory course of the specialization)