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.
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. Ststem 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.
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.
continuous and discrete signals, Fourier series and Fourier transformations, static and dynamic system, control of dynamic systems