Signals and Systems

Definitions and classification of signals and systems. Signal expressions. Fourier and Laplace representation of signals. Analysis of continuous signals. Correlation and convolution. Mathematical models and system analysis methods. Unit impulse, unit step and sine response. Using transformations in solving systems. Input, output and transfer functions. Frequency characteristics. Bode diagrams, polar diagrams.

Basic connections between systems. Feedback systems. Absolute and relative stability. Routh and Nyquist stability criterion.

Gain and phase margins. Frequency compensation. Sensitivity analysis of feedback systems.

State space, state space variables. Equations in state space and solving them. Trajectories in state space. Equilibrium points. Controllability and observability. State of equilibrium and stability conditions of equilibrium.

Topology of electrical circuits. Topological analysis of electric circuits. Systematically solving electrical circuits in the state space.

Basics of filtering. Transmission of signals without distortion. An approximation of the ideal frequency characteristics. Frequency mapping. Synthesis of transfer functions of passive filters. Realization of active filters. SC filters. Computer aided design of analog filters.

To recognize various signal forms and methods for their description and processing. To acquire basic knowledge about systems theory, which enables systematic analysis and design of the systems. To learn about the use of modern computer tools for systems analysis and simulation. To present the implementation of basic system theory into systematic solutions for analysis and design of electric circuits and filters.

The lectures provide a theoretical background on particular subjects, practical examples are presented at auditory practise. Practical work is being performed in the laboratory environment.