Course detail
Digital Signals and Systems
FEKT-MPA-CSIAcad. year: 2025/2026
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
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 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
Prerequisites and corequisites
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)
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
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