Course detail

# Analysis of Signals

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.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

On completion of the course, students are able to:
- 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

Knowledge of the high school level math and physics is required. Emphasis is placed on the knowledge of complex numbers and their application.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The subject includes both lectures, and computer and laboratory exercises. The teaching methods are chosen according to type of education. The lectures combine modern audiovisual presentation with more detailed derivation of fundamental methods and algorithms on the board. Applets are also used to increase the clarity of instruction. All lectures and examples are given in e-learning. In computer exercises, the students learn the basic mathematical methods for the analysis of signals and systems. In laboratory exercises the students will try signals and systems analysis using specially designed hardware.

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.

Course curriculum

1. Signals and their mathematical models
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

Work placements

Not applicable.

Aims

The aim of the course is to acquaint students with one-dimensional (1D) and two-dimensional (2D) signals and systems with continuous-time, signals and systems with discrete-time, and with impulse and digital signals and systems. It is also necessary to introduce the concept of 1D and 2D signal spectrum and emphasize its difference from the frequency response of 1D and 2D system. Consequently, the aim is to provide students with basic information about random signals and their impact on systems, introduce modulations and define description of the characteristics of communication systems.

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

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

SMÉKAL, Z.: From Analog to Digital Signal Processing: Theory, Algorithms and Implementation. Prague, Sdelovaci technika, 2018, 504 pages. ISBN 978-80-86645-24-4 (EN)
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)

Not applicable.

eLearning

Classification of course in study plans

• Programme BPA-ELE Bachelor's

specialization BPA-ECT , 2. year of study, summer semester, compulsory

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

Signals. Examples, definition. Harmonic signal.
Periodic signals. Fourier series expansion. Properties.
Fourier Transform. Properties of the Fourier transform.
Linear time-invariant systems and their description. Filtering.
Continuous-time random signals.
Sampling and signal recovery. Digital signals.
Discrete-time signals. Discrete Fourier series.
Discrete Fourier transform. FFT.
Random sequences. Pseudorandom sequences. PSD.
Discrete-time systems. Z transform. Examples.
Communication systems. Baseband signals.
Amplitude modulation. Frequency modulation. ASK, FSK, PSK.
I-Q modulations. Multiplexing and multiple-access techniques.

Exercise in computer lab

14 hours, compulsory

Teacher / Lecturer

Syllabus

Description of signals.
Fourier series expansion. Examples.
Properties of the Fourier transform.
Random signals. Sampling. Quantisation noise.
Discrete Fourier transform.
Amplitude and frequency modulation, keying.

Laboratory exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

Introduction.
Spectral analysis of the periodic signals.
Amplitude and frequency modulation. Analysis of the random signal.
Sampling, aliasing.
Digital signal processing of the own speech.
The frequency response of the discrete-time system.

eLearning