Introduction to Systems and Signals
- Garant předmětu:
- Department of Biomedical Informatics
To introduce students to basics of theory of signals and systems. To explain main principles on applications from biology and medicine. To become acquainted with basic mutual relations in computer laboratories by means of MATLAB.
Credit inclusion: Taking two tests with at least 50 % sucess each. First test is dedicated to signals and second to systems. Knowledge of practical use of Matlab.
Exam: Written and oral.
- Syllabus of lectures:
1. Systems and signals. Practical tasks and motivation. Biosignal processing (filtration). Examples of physiological models.
2. Signals. Basic terms and definitions. Continuous signals. Basic operations with signals. Mathematic models of basic continuous signals. Periodic signals. Unrepeated signals.
3. Decomposition of continuous periodical signals to single harmonic components. Fourier transformation. Features.
4. Discrete signals. Sampling. Basic operations with discrete signals. Mathematic models of basic discrete signals. Decomposition of discrete periodical signals to single harmonic components.
5. Fourier transformation with discrete time. Discrete Fourier transformation. Fast Fourier Transform.
6. Convolution. Definitiona and basic equations. Geometric im,portance of convolution.
7. Systems. Basic attributes of systems. Technical and biological systems. Systems and their description. Continuous systems. Inner and outer description. Linear and nonlinear system.
8. Forms of outer description of continuous linear system - differential equation, frequnce transfer characteristics, pole and null location, time characteristics
9. Systems with discrete time. Forms of outer description of linear system - difference equation, transfer functions, frequence characteristics, pole and null location, time characteristics
10. Basic phenomenons in systems - investigation of initial state influence and exploration of output influence
11. Stability. Basic terms and definitions. Stability of forced movement. Stabiluity with respect to initial state. Criteria of stability.
12. System connecting. Serial and parallel ordering. Feedback (closed-loop system). Feedback control. Features of feedback. General connection of systems - method of consecutive modifications. Mason's rule.
13. Basic types of linear dynamic systems. Continuous systems. Proportional systems. Integration systems. Systems with 1st order momentum. (Real) Derivation system. System of 2nd order. System with time delay.
14. Discrete systems. Proportional systems. Cummulative system. Systems with 1st order momentum. Difference system. System, of 2nd order.
- Syllabus of tutorials:
The practical laboratories reflect theoretical knowledge of lectures. The outline is similar to the outline of lectures.
- Study Objective:
The goal of the subject is to introduce students to basics of signals, their processing and manipulation in time and frequency domain the subjects focuses on Fourier analysis. The second part of the subject is dedicated to basics of systems, their description and features.
- Study materials:
Oppenheim, A.V. Willsky A.S. Nawab S.H. Signals & Systems. New Jersey, Prentice Hall 1997, Lathi, B.
Linear Systems and Signals, Oxford, Oxford University Press 2
Kamen, E.W. Heck B.S. Fundamentals of signals and Systems using the Web and Matlab.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Biomedical Informatics - full-time study (compulsory course)