Statistical Signal Processing

B242 - Summer 2024/2025

A8B37SSP

Statistical Signal Processing - A8B37SSP

Credits	6
Semesters	Summer
Completion	Assessment + Examination
Language of teaching	Czech
Extent of teaching	4P+0C

Annotation

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.

Study targets

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

Course outlines

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

Exercises outlines

The course has only lectures

Literature

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

Requirements

None