Introduction to Signals and Systems
Code  Completion  Credits  Range  Language 

F7PBBUSS  Z,ZK  4  2P+2C  Czech 
 Garant předmětu:
 Jan Kauler
 Lecturer:
 Jan Kauler
 Tutor:
 Jan Kauler
 Supervisor:
 Department of Biomedical Informatics
 Synopsis:

The aim of the course is to acquaint students with the basics of signal processing, especially with time and frequency domain operations. Emphasis is placed on a thorough understanding of Fourier analysis. The second part of the course is focused on acquainting students with systems, their properties and description. Emphasis is placed on the external and internal description of linear dynamical systems.
 Requirements:

Integral calculus, Laplace, Fourier and Z transforms
 Syllabus of lectures:

1. Systems and signals. Inspiration by practical tasks, processing of biosignals (filtration), examples of physiological models.
2. Signals. Basic terms and definitions. Continuous signals. Basic signal operations. Mathematical models of basic continuous signals. Periodic signals. Onetime signals. Decomposition of continuous periodic signals into partial harmonic components.
3. Decomposition of continuous nonperiodic signals into partial harmonic components. Fourier transform. Properties.
4. Discrete signals. Sampling. Basic operations with discrete signals. Mathematical models of basic discrete signals. Decomposition of periodic discrete periodic signals into partial harmonic components.
5. Fourier transform with discrete time. Discrete Fourier transform. Fast discrete Fourier transform. Bilinear transform and design of digital filters.
6. Convolution. Definitions and basic relations. Geometric meaning of convolution.
7. Systems. Basic attributes of systems. Technical and biological systems. Systems and their description. Continuous systems. External and status description. Linear and nonlinear system.
8. Forms of external description of a continuous linear system  differential equations, image and frequency transfer function, frequency characteristics, distribution of zeros and poles, time characteristics.
9. Discrete time systems. Forms of external description of a discrete linear system  difference equations, transfer functions, frequency characteristics, distribution of zeros and poles, time characteristics.
10. Basic phenomena in systems  examining the influence of the initial state, examining the influence of input.
11. Stability. Basic terms and definitions. Forced motion stability. Stability to initial state. Stability criteria.
12. Connecting systems. Serial connection. Parallel connection. Feedback connection. Principle of feedback regulation. Properties of feedback connection. General connection of systems  methods of gradual adjustments, Mason's rule.
13. Basic types of linear dynamic continuous systems. Proportional system. Integration system. 1st order inertia system. Derivation system. Real derivation system. 2nd order system. Delayed system.
14. Basic types of linear dynamic discrete systems. Proportional system. Accumulation system. 1st order inertia system. Differential system. 2nd order system.
 Syllabus of tutorials:

1. MATLAB programming environment  introduction, possibilities, use.
2. MATLAB programming environment  generation, loading, saving and displaying, some types of experimental signals (harmonic signal, unit pulse, unit jump). Principle of sampling.
3. Fourier transform  basic properties, signal spectra.
4. Properties of discrete Fourier transform, the phenomenon of „blur“ of the spectrum and methods of its suppression.
5. Discrete convolution, practice of manual and computer calculation, meaning of convolution. From transformation, bilinear transformation, design of digital filters.
6. Dynamic properties of continuous systems. External description (differential equations, transfer function, frequency transfer, frequency response, distribution of zeros and poles).
7. Test.
8. Dynamic properties of continuous systems. Practicing external description channeling procedures. MATLAB environment authentication.
9. Impulse and transient characteristics.
10. Ztransformation. Comparison of continuous and discrete systems.
11. Stability, quality and accuracy of systems.
12. Connection of systems (serial, parallel, feedback). Principle of feedback control.
13. Regulation of nonlinear systems.
14. Credit test.
 Study Objective:

Have the ability from the acquired knowledge to design digital filters required by LACH. Be able to analyze in the frequency domain different types of signals periodic, nonperiodic, repetitive, continuous and discrete. In the field of systems, be able to design the transmission of the controller in order to meet the required properties of the control process, such as accuracy, quality and stability for continuous and discrete control circuits.
 Study materials:

Compulsory literature:
[1] RAO, K. Deergha. and M.N.S. SWAMY. Digital Signal Processing: theory and Practice [online]. Singapore: Springer Singapore, 2018 [cit. 20190616]. Available from: <http://dx.doi.org/10.1007/9789811080814>. ISBN 9789811080814.
Recommended literature:
[1] HUSSAIN, Zahir M. Digital signal processing: an introduction with MATLAB and applications. Berlin: Springer, 2011. ISBN 9783642155918.
 Note:
 Timetable for winter semester 2022/2023:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2022/2023:
 Timetable is not available yet
 The course is a part of the following study plans:

 Biomedical Technology (compulsory course)