### 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

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

#### 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.

Continuous Assessment Exam
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

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

#### Study Programmes

[FER3-HR] Audio Technologies and Electroacoustics - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Communication and Space Technologies - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Computational Modelling in Engineering - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Computer Engineering - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Computer Science - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Control Systems and Robotics - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Data Science - profile
Elective Courses (1. semester) (3. semester)
Elective Courses of the Profile (1. semester) (3. semester)
[FER3-HR] Electrical Power Engineering - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Electric Machines, Drives and Automation - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Electronic and Computer Engineering - profile
(1. semester)
[FER3-HR] Electronics - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Information and Communication Engineering - profile
(1. semester)
[FER3-HR] Network Science - profile
Elective Courses (1. semester) (3. semester)
[FER3-HR] Software Engineering and Information Systems - profile
Elective Courses (1. semester) (3. semester)
[FER2-HR] Electronic and Computer Engineering - profile
Theoretical Course (1. semester)
[FER2-HR] Information Processing - profile
Theoretical Course (1. semester)
[FER2-HR] Wireless Technologies - profile
Theoretical Course (1. semester)

#### Literature

H. Stark, J. W. Woods (2002.), Probability and Random Processes with Applications to Signal Processing, 3rd Ed., Prentice Hall
Peyton Z. Peebles, Bertram Emil Shi (2015.), Probability, Random Variables, and Random Signal Principles, McGraw-Hill
S. Lončarić, D. Seršić (2021.), Slučajni signali i procesi: bilješke s predavanja, FER, FER
Tomislav Petković, Damir Seršić, Sven Lončarić (2005.), Zbirka zadataka iz slučajnih procesa, FER

#### General

ID 222782
Winter semester
5 ECTS
L1 English Level
L2 e-Learning
30 Lectures
0 Seminar
15 Exercises
8 Laboratory exercises
0 Project laboratory