Course detail
Analysis of Signals
FEKT-BPA-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
Offered to foreign students
Entry knowledge
Rules for evaluation and completion of the course
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.
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
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)
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)
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)
Recommended reading
Elearning
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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. Z transform and its properties
10. Discrete-time systems
11. Signals in base-band and shifted-band
12. Stochastic variables, stochastic processes and their properties
13. Power spectral density and its calculation
Exercise in computer lab
Teacher / Lecturer
Syllabus
1. Signals and their mathematical models
2. Complex numbers
3. Periodic signals and their spectra
4. Continuous-time impulse signals
5. Signals and systems with discrete time
6. Operations with discrete signals
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