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
ExercisesLive problem solving sessions, on-line sessions and recordings
LaboratoryExercises 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
Study Programmes
University graduate
[FER3-HR] Audio Technologies and Electroacoustics - profile
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(1. semester)
(3. semester)
[FER3-HR] Communication and Space Technologies - profile
Elective Courses
(1. semester)
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[FER3-HR] Computational Modelling in Engineering - profile
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[FER3-HR] Computer Engineering - profile
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[FER3-HR] Computer Science - profile
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[FER3-HR] Control Systems and Robotics - profile
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[FER3-HR] Data Science - profile
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Elective Courses of the Profile
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[FER3-HR] Electrical Power Engineering - profile
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(1. semester)
(3. semester)
[FER3-HR] Electric Machines, Drives and Automation - profile
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(1. semester)
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[FER3-HR] Electronic and Computer Engineering - profile
(1. semester)
[FER3-HR] Electronics - profile
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(1. semester)
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[FER3-HR] Information and Communication Engineering - profile
(1. semester)
[FER3-HR] Network Science - profile
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(1. semester)
(3. semester)
[FER3-HR] Software Engineering and Information Systems - profile
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(1. semester)
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[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
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
Lecturers
Associate Lecturers
For students
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
Grading System
88 Excellent
75 Very Good
62 Good
51 Sufficient