# Signals

## Subject description

Introduction: Basic definitions, short history of the signal processing theory, position of the signal processing theory in electrotechnical and other sciences.

Signals classification: Signals with finite energy and finite average power, periodical a-periodical, deterministic and random signals.

Signals representations: Use of the signals representations, types of representations and representations quality measures, examples of basic functions sequences.

Frequency analysis: Fourier series and Fourier transform.

Random signals: Approaches to the random signal processing, stationary random process, correlation and covariance functions, sampling and time averages, ergodicity.

Signals correlation and convolution: Correlation and convolution definitions and properties for different types of signals.

Applications with correlation and convolution transformations: similarity measures, random signals spectrum evaluation, convolution and linear stationary systems, detection of periodic components in combination of signals.

Sampling and quantization: Purpose of the sampling and quantization, sampling theorem, representation of sampling and reconstruction, types of quantization, quantization error signal and his properties, examples for quantization.

Digital signal processing: Discrete Fourier Transform (DFT).

## Objectives and competences

The aim of this course is to familiarize students with different types of signals and to present different approaches to signal description and processing. Students develop an understanding of the concepts used for signal representation and get acquainted with signal analysis techniques based on correlation and convolution. The course provides the theoretical basis for many practical problems in the fields of imaging technologies, speech technologies, pattern recognition, artificial intelligence and machine learning.

## Teaching and learning methods

Lectures

Interactive teaching

Practical assignements

## Expected study results

After successful completion of the course, students should be able to:
define the main types of signals and methods for their description, representation, processing and analysis,

• recognize the main characteristics of signals and their transformations,
• develop procedures for the analysis of basic signals such speech or images,
• analyse problems that may be represented as linear timeinvariant systems,
• propose the most suitable methods for the description of signals given the requirements of selected application domains,
• explain the differences between continuous and discrete signals and corresponding processing methods and the importance of continuous and discrete signals for different applications.

## Basic sources and literature

1. MIHELIČ, France, GYERGYÉK, Ludvik, EBENŠPANGER, Tomaž. Signali : priročnik z zbirko rešenih nalog. 4. popravljena in dopolnjena izd. Ljubljana: Založba FE in FRI, 2009. 132 str., ilustr. ISBN 978-961-243-116-7.

2. MIHELIČ, France. Signali. 1. izd. Ljubljana: Založba FE, 2014. ISBN 978-961-243-270-6. http://luks.fe.uni-lj.si/nluks/wp-content/uploads/2014/11/Signali.pdf

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana