# Continuous Signals and Systems

## Course description

Continuous time linear casual time invariant systems (LTI, system equation).

Basic continuous time electric signals: selected types and operations. Representation and analysis of continuous signals using Fourier series, Fourier transform (frequency and power spectrum) and Laplace transform.

Definition, properties and limitations of a linear circuit. Topological circuit description, describing a circuit using matrix equations. Using different methods to analyse the circuit (branch current method, window current method and intersection potential method). Power source transformation theorem.

Classical analysis of circuits using differential equations, interpretation, convolution. Steady state analysis (pointers, system function, power). Single input circuits (Thevenin equivalent, maximum power transmission theorem, resonance). Dual-input circuits: reciprocity theorem, modelling circuit as a quadripole and determining different quadripole parameters, Bode diagram.

Spectral analysis (using spectrum to analyse circuits), using Laplace to analyse circuits.

## Objectives and competences

The objective of the course is to familiarize students with basics of time continuous linear circuits and systems including the relationship of signal representation domain and type of system analysis.

Basic understanding of linear circuits and systems. Understanding of the relationship between continuous time signal representations and linear system analysis. Recognition of a system type according to types of their components. Recognition and understanding of selected phenomena in linear systems in terms of communications.

## Learning and teaching methods

Lectures provide theoretical backgrounds and basic reasoning supported by illustrative examples. Tutorials adds more examples and focus on improvement of analytical skills of students. Both methods are supported by a web based linear system simulator allowing hands-on learning and voluntary student’s work at home. It covers analyzable examples of linear systems in terms of system response. Signal representations on different domains are supported by web based Jupyter Python system.

## Intended learning outcomes

After completing this course the student will be able to:

• Classify system according to linearity, time invariance and causality;
• Perfrom basic operations on signals;
• Analyse system response in terms of transients and stationary states, and in terms of zero-input response;
• Select the analysis method based on the input signal type;
• Perform complex signal analysis, including amplitude and phase spectrum calculation;
• Perform harmonic analysis of the system including one-port and two port circuits;
• Replace complex two-port circuits with simplified two-port circuits with correctly calculated parameters.

## Reference nosilca

1. KOVAČ, Uroš, KOŠIR, Andrej. Fast estimation of the non-stationary amplitude of a harmonically distorted signal using a Kalman filter. Metrol. Syst. Pomiarowe, 2013, str. 27-42.

2. PERKON, Igor, KOŠIR, Andrej, ITSKOV, Pavel M., TASIČ, Jurij F., DIAMOND, Mathew. Unsupervised quantification of whisking and head movement in freely moving rodents. Journal of neurophysiology, 2011, str. 1950-1962.

3. PESKO, Marko, JAVORNIK, Tomaž, VIDMAR, Luka, KOŠIR, Andrej, ŠTULAR, Mitja, MOHORČIČ, Mihael. The indirect self-tuning method for constructing radio environment map using omnidirectional or directional transmitter antenna. EURASIP Journal on wireless communications and networking, 2015, str. 1 – 12.

4. KOŠIR, Andrej, MUJČIĆ, Aljo, SULJANOVIĆ, Nermin, TASIČ, Jurij F. Noise variance estimation based on measured maximums of sampled subsets. Math. comput. Simul, 2004, str. 629-639.

5. VODLAN, Tomaž, KOŠIR, Andrej. Using social signal of hesitation in multimedia content retrieval: Graphical analysis of selection traces in the matrix-factorization space of multimedia items. International journal of advanced computer science & applications, 2014, str. 1-26.

## Study materials

1. B. P. Lahti: Linear Systems and Signals, Oxford University Press, 2005.

2. A. V. Oppenheim, A. S. Willsky: Signals and Systems, Pearson Education Lim., 2014.

3. J. Mlakar: Linearna vezja in signali, Založba FE in FRI, 2007.

4. A. Košir: Linearna vezja in signali, zbirka rešenih vaj, Založba FE in FRI, 2005.

## Bodi na tekočem

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