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

Live lectures, on-line lectures and recordings

Live problem solving sessions, on-line sessions and recordings

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

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

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

Live lectures, on-line lectures and recordings

Live problem solving sessions, on-line sessions and recordings

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

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