Random Signals and Processes

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Random Signals and Processes

Course Description

The course gives knowledge of the theory of random signals and processes, as well as its applications in systems for signal processing and analysis. Continuous and discrete random signals. Random processes. Stationarity and independence. Correlation functions and power spectral density. Wiener-Kinchin relations. Random process in linear systems. Signal parameters estimation. Detection. System identification using cross correlation. Noise modeling and characterization. Noise factor. Optimum linear systems. Wiener filter. Matched filter. Kalman filter. Realization of the optimum systems. Signal extraction from the noise by correlation and using matched filter. Signal quantization. Applications in communication, automation and measurements.

Learning Outcomes

Apply knowledge of mathematics, physics, natural sciences, electrical engineering and computing, and similar and multidisciplinary research areas
Define and describe concepts of stochastic processes in systems
Define and explain use of theory of stochastic processes
Use best practise and develop standards for using appropriate procedures, skills and contemporaary tools in practical applications
Combine acquired knowledge and propose a solution to the given problem
Evaluate a practical solution obtained using stochastic processes

Forms of Teaching

Lectures

Live lectures, on-line lectures and recordings

Exercises

Live problem solving sessions, on-line sessions and recordings

Laboratory

Exercises are based on individual preparation work, group work in the laboratory, writing and handing in the reports.

Grading Method

	Continuous Assessment		Exam
Type	Threshold	Percent of Grade	Threshold	Percent of Grade
Laboratory Exercises	50 %	20 %	50 %	20 %
Seminar/Project	20 %	20 %	20 %	20 %
Mid Term Exam: Written	20 %	30 %	0 %
Final Exam: Written	20 %	30 %
Exam: Written			50 %	60 %

Comment:

The threshold on the sum of the midterm and the final exam is 50%.

Week by Week Schedule

Finite-dimensional distributions of processes, Moments; correlation and covariation functions
Classes of processes: Markov, homogenous Markov, weak/strong stationary, independent increment processes, Transition and density matrix and Chapman-Kolmogorov equation for Markov processes.
Correlation and covariance functions of random processes, Fourier transform of stochastic process; Power spectrum density (PSD); Wiener-Kinchin relations
Fourier transform of stochastic process; Power spectrum density (PSD); Wiener-Kinchin relations
Minimal mean-squared error estimation; Linear estimation of random processes; Prediction
Behavior of RP in LTI systems, Second order transfer function
System identification
Midterm exam
Scalar and vector quantization, Quantization noise, Uniform quantization
Optimum quantization
Wiener filter, Description of Wiener filtering
Matched filter
Kalman filter
Applications in signal and image restoration, Applications in radar and sonar
Final exam