Course detail
Analysis of Signals and Systems
FEKT-BPC-ASIAcad. year: 2024/2025
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
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
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
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
Prerequisites and corequisites
Basic literature
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)
SMÉKAL, Z.: Systémy a signály – 1D a 2D diskrétní a číslicové zpracování. Sdělovací technika, 2013. ISBN 80-86645-22-0 (CS)
Recommended reading
Elearning
Classification of course in study plans
- Programme BPC-AUD Bachelor's
specialization AUDB-TECH , 2 year of study, winter semester, compulsory
specialization AUDB-ZVUK , 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
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
Fourier series expansion. Examples.
Properties of the Fourier transform.
Random signals. Sampling. Quantisation noise.
Discrete Fourier transform.
Amplitude and frequency modulation, keying.
Laboratory exercise
Teacher / Lecturer
Syllabus
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