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A8B37SSP	Statistical Signal Processing
Roles:	PO	Extent of teaching:	4P+0C
Department:	13137	Language of teaching:	CS
Guarantors:	Sýkora J.	Completion:	Z,ZK
Lecturers:	Sovka P., Sýkora J.	Credits:	6
Tutors:	Sýkora J.	Semester:	L

Anotation:

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.

Content:

Parameter estimates, MVU estimator, Cramer-Rao bound, composite hypotheses, estimator properties. Sufficient statistics. Maximum plausible estimate, EM algorithm. Bayesian estimators (MMSE, MAP). Detection. Hypothesis testing Parametric methods, types and relations. Using the least squares method to design filters. Optimal filtration - Wiener and Kalman filter. Spectral analysis and adptive filtration.

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 outline:

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

Subject is included into these academic programs:

Program	Branch	Role	Recommended semester
BPOES_2020	Common courses	PO	6
BPOES	Common courses	PO	6

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Page updated 17.3.2025 17:51:06, semester: Z,L/2024-5, Z,L/2025-6, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)