Course detail

Digital Signals and Systems

FEKT-MPA-CSIAcad. year: 2023/2024

Definition and classification of 1D and 2D discrete signals and systems. Signal and system examples. Spectral analysis using FFT. Spectrograms and moving spectra. The Hilbert transform. Representation of bandpass signals. Decimation and interpolation. Transversal and polyphase filters. Filter banks with perfect reconstruction. Quadrature mirror filters (QMF). The wavelet transform. Signal analysis with multiple resolution. Stochastic variables and processes, mathematical statistics. Power spectral density (PSD) and its estimation. Non-parametric methods for PSD calculation. Linear predictive analysis. Parametric methods for PSD calculation. Complex and real cepstra. In computer exercises students verify digital signal processing method in the Matlab environment. Numerical exercises are focused on examples of signals and systems analysis.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Entry knowledge

The subject knowledge on the Bachelor´s degree level with emphasis on digital signal processing is required. Furthermore, the basic ability to program in the Matlab environment is necessary.

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. They can get 15 points in computer labs and 15 points in numerical exercises. The remaining of 70 points (out of 100) can be obtained by successfully passing the final 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.


The aim of the course is to present modern methods of 1D and 2D digital signal processing and discrete system analysis. Furthermore, the students will learn about parametric and non-parametric spectral analysis of stochastic signals and about mathematical statistics. They will know how to use linear prediction and how to process signals using digital filter banks with different sampling frequencies in real practise.
On completion of the course, students are able to:
- define, describe and visualize 1D and 2D signals
- calculate Fourier, cosine, Hilbert, wavelet and Z transform of discrete signal
- define discrete systems and analyse their properties using different methods
- change signal sampling frequency
- use analytical and complex signal
- use a bank of digital filters
- perform a short-time spectral analysis using Gabor or short-time Fourier transform
- mathematically describe stochastic processes and test statistical hypotheses
- use linear predictive analysis
- estimate power spectral density using parametric and non-parametric methods
- use cepstral analysis and homomorphic filtering
- perform discrete-time signal and system analysis in Matlab

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

SMÉKAL, Z.: From Analog to Digital Signal Processing: Theory, Algorithns, and Implementation. Prague, Sdelovaci technika, 2018, 518 pp., ISBN 973-80-86645-25-4 (EN)
SMÉKAL, Z.: Analog and Digital Signal Processing in Examples and Programs, VUTIUM Press 2021, ISBN 978-80-214-5883-3 (EN)

Recommended reading

PROAKIS, J.G., INGLE, V.K.: A Self-Study Guide for Digital Signal Processing. Prentice Hall, New Jersey, 2004. ISBN 0-13-143239-7 (EN)

Classification of course in study plans

  • Programme MPA-CAN Master's, 1. year of study, winter semester, compulsory
  • Programme MPAD-CAN Master's, 1. year of study, winter semester, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Characteristics and classification of 1D and 2D discrete signals
2. Characteristics and classification of discrete systems
3. One-dimensional LTI discrete systems analysis
4. Discrete cosine transform. Digital processing of signals with changing sampling frequency
5. Band-limited signals representation
6. Bank of digital filters
7. Short-time spectral analysis
8. Wavelet transform and its relation to bank of filters
9. Stochastic processes and their properties
10. Linear predictive analysis
11. Non-parametric power spectral density calculation methods
12. Parametric power spectral density calculation methods
13. Cepstral analysis 

Exercise in computer lab

39 hours, compulsory

Teacher / Lecturer


1. Introduction to Matlab programming, generation of basic deterministic signals, visualization techniques
2. Discrete Fourier Transform (DFT), fast DFT, circular convolution, block analysis, overlap add method, short-time Fourier analysis
3. Characteristics of linear time-invariant systems (1), linear discrete convolution, impulse response
4. Characteristics of linear time-invariant systems (2), transfer function, frequency response, zeros and poles
5. Design of digital filters with infinite impulse response (IIR)
6. Test num. 1
7. Design of digital filters with finite impulse response (FIR)
8. Upsampling and downsampling of digital signals in Matlab, resampling of digital signals by a rational number ratio
9. Stochastic discrete signals generation in Matlab, statistics, correlation, covariation, testing stacionarity and ergodicity of a system
10. Wavelet transform in Matlab, Wavelet toolbox
11. Test num. 2
12. Replacement exercises