Course detail

# Analysis of Signals

FEKT-BPA-ASIAcad. year: 2022/2023

One-dimensional (1D) and two-dimensional (2D) signals and systems with continuous time and their mathematical models. Signals sampling. One-dimensional (1D) and two-dimensional (2D) signals and discrete-time systems and their mathematical models. Examples of real signals. Representation in the time and frequency domains, Fourier representation of signals, mutual properties. FFT definition and method of calculation. Z transform, unilateral and bilateral transform, direct and inverse transform. Frequency response and transfer function. Modulations in communication technology. Definition of power spectral density. The issue is illustrated by the examples of specific signals and systems, and these examples are presented in Matlab. Numerical exercises are focused mainly on examples of signal processing and Fourier representation of signals. In the laboratory, measurements and simulations of signals and systems are done employing spectrum analyzer with FFT and using appropriate measurement products for specific measuring instruments.

Guarantor

Department

Offered to foreign students

Learning outcomes of the course unit

- define, describe and visualize continuous and discrete-time signals

- perform some operations with signals such as convolution, correlation, time shift, time scale

- define continuous and discrete-time systems and describe their properties (time invariance, linearity, causality, stability)

- work with transfer function, impulse and frequency response

- calculate a response of LTI system

- perform spectral analysis of signal using the Fourier series, Fourier transform, discrete-time Fourier transform, discrete Fourier series, discrete Fourier transform and fast Fourier transform

- understand function of simple filters

- describe A/D and D/A conversion and prevent aliasing

- apply the Z transform

- describe differences between IIR and FIR systems

- connect partial system sections

- work with basic modulations

- mathematically describe stochastic processes

- estimate power spectral density

Prerequisites

Co-requisites

Recommended optional programme components

Literature

PROAKIS, John G a Dimitris G MANOLAKIS. Digital signal processing. 4th ed. Upper Saddle River: Pearson Prentice Hall, 2007, xix, 1084 s. : il. ISBN 0-13-187374-1. (EN)

OPPENHEIM, Alan V, Alan S WILLSKY a S. Hamid NAWAB. Signals and systems. 2nd ed. Upper Saddle River: Prentice Hall, 1997, 957 s. : il. ISBN 0-13-814757-4. (EN)

MITRA, Sanjit K. Digital signal processing: a computer based approach. 3rd ed. Boston: McGraw-Hill, 2006, 972 s. ISBN 0-07-286546-6. (EN)

LITTLE, Max A. Machine learning for signal processing: data science, algorithms, and computational statistics. New York: Oxford University Press, 2019. ISBN 9780198714934. (EN)

PODLUBNY, Igor. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. San Diego: Academic Press, c1999. ISBN 9780125588409. (EN)

KILBAS, A. A., H. M. SRIVASTAVA a Juan J. TRUJILLO. Theory and applications of fractional differential equations. Amsterdam ; Boston: Elsevier, 2006. ISBN 0444518320. (EN)

Planned learning activities and teaching methods

Assesment methods and criteria linked to learning outcomes

It is possible to get 12 points for activity in lectures/exercises. The rest, i.e. 88 points, can be obtained in the final written exam.

Language of instruction

Work placements

Course curriculum

2. Systems and their mathematical models

3. Periodic signals and their spectrum

4. Fourier representation of aperiodic continuous-time signals

5. Continuous-time systems

6. Sampling of continuous-time signals

7. Discrete-time signals

8. Discrete-time Fourier transform

9. Fast Fourier Transform

10. Z transform and its properties

11. Discrete-time systems

12. Signals in base-band and shifted-band

13. Power spectral density and its calculation

Aims

Specification of controlled education, way of implementation and compensation for absences

#### Type of course unit

eLearning

**eLearning:**currently opened course