Course detail

# Analysis of Signals and Systems

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

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Entry knowledge

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

Rules for evaluation and completion of the course

Lab exercises are mandatory for successfully passing this course and students have to obtain the required credits. For lab work and numerical exercise tests they can get 30 out of 100 points. The remaining 70 points can be obtained by successfully passing the final written examination.

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.

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.
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

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

SMÉKAL, Z.: Analýza signálů a soustav – BASS. Elektronické texty, VUT Brno, 2012. ISBN 978-80-214-4453-9 (CS)
SMÉKAL, Z.: Systémy a signály – 1D a 2D diskrétní a číslicové zpracování. Sdělovací technika, 2013. ISBN 80-86645-22-0 (CS)
SMÉKAL, Z.: Deterministické a náhodné signály pro integrovanou výuku VUT a VŠB-TUO. Elektronické texty, VUT Brno, 2013. ISBN 978-80-214-4826-1 (CS)
SMÉKAL, Z.: Signals and Systems Analysis for joint teaching programme of BUT and VSB-TUO (EN)

Not applicable.

eLearning

Classification of course in study plans

• Programme BPC-AUD Bachelor's

specialization AUDB-ZVUK , 2. year of study, winter semester, compulsory
specialization AUDB-TECH , 2. year of study, winter semester, compulsory

• Programme BPC-MET Bachelor's, 2. year of study, winter semester, compulsory
• Programme BPC-TLI Bachelor's, 2. year of study, winter semester, compulsory

#### Type of course unit

Lecture

26 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