# Signals and Systems

## Course description

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.

## Objectives and competences

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.

## Learning and teaching methods

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.

## Intended learning outcomes

After successful completion of the course, students should be able to:

– classify signals and systems according to criteria such as continuous/discrete, linear/non-linear, causal/non-causal, time-variant/invariant, etc.,

– compute the response of linear systems modeled by linear differential equations,

– explain the importance of superposition in the analysis of linear systems,

– use convolution to determine the response of linear systems to arbitrary inputs,

– use Laplace transform to solve differential equations, and to determine responses of linear systems to known inputs,

– use Fourier series, Fourier transform and its properties to analyze continuous-time signals and systems,

– determine response of linear systems modeled by state space representation,

– use topological methods for the analysis of electrical circuits,

– explain concepts of signal filtering,

– use methods for analysis of signals and systems in MATLAB.

## Reference nosilca

1. SEIF, Johannes Peter, DESCOEUDRES, Antoine, FILIPIČ, Miha, SMOLE, Franc, TOPIČ, Marko, HOLMAN, Zachary Charles, DE WOLF, Stefaan, BALLIF, Christophe. Amorphous silicon oxide window layers for high-efficiency silicon heterojunction solar cells. Journal of applied physics, 2014, vol. 115, no. 2, str. 1-8.

2. FILIPIČ, Miha, HOLMAN, Zachary, SMOLE, Franc, DE WOLF, Stefaan, BALLIF, Christophe, TOPIČ, Marko. Analysis of lateral transport through the inversion layer in amorphous silicon/crystalline silicon heterojunction solar cells. Journal of applied physics, 2013, vol. 114, no. 7, str. 1-7.

3. HOLMAN, Zachary, FILIPIČ, Miha, LIPOVŠEK, Benjamin, DE WOLF, Stefaan, SMOLE, Franc, TOPIČ, Marko, BALLIF, Christophe. Parasitic absorption in the rear reflector of a silicon solar cell: simulation and measurement of the sub-bandgap reflectance for common dielectric/metal reflectors. Solar energy materials and solar cells, [Print ed.], Jan. 2014, vol. 120, part A, str. 426-430.

4. FILIPIČ, Miha, BERGINC, Marko, SMOLE, Franc, TOPIČ, Marko. Analysis of electron recombination in dye-sensitized solar cell. Current applied physics, Jan. 2012, vol. 12, no. 1, str. 238-246.

5. NERAT, Marko, SMOLE, Franc, TOPIČ, Marko. A simulation study of the effect of the diverse valence-band offset and the electronic activity at the grain boundaries on the performance of polycrystalline Cu(In,Ga)Se2 solar cells. Thin Solid Films, [Print ed.], 2011, vol. 519, no. 21, str. 7497-7502.

## Study materials

1. A. V. Oppenheim, A. S. Willsky, Signals & Systems, Prentice Hall Int., 1997.

2. R. D. Sturm, D. E. Kirk, Contemporary Linear Systems Using MATLAB,

BookWare copanion series, 1999.

3. C. L. Phillips, J. M. Parr, E. A. Riskin, Signals, Systems, and Transforms, Prentice Hall, 2008.

4. Douglas K. Linder, Introduction to Signals and Systems, WCB/McGraw-Hill, 2003.

5. C. M. Close, D. K. Frederick and J. C. Newell: Modeling and Analysis of Dynamic Systems,

John Wiley & Sons, 2002.

6. K. L. Su, Analog Filters, Kluwer Academic Publishers Group, 2010.

7. Rolf Schaumann, Mac E. Van Valkenburg, Design of analog filters, Oxford University Press, 2003.

8. F. Smole, Signali in sistemi – gradivo za laboratorijske vaje, 2017.

9. F. Smole, Signali in sistemi, Založba FE, Ljubljana, 2017.

## Bodi na tekočem

Univerza v Ljubljani, Fakulteta za elektrotehniko, Tržaška cesta 25, 1000 Ljubljana