Course detail

# Digital Signals and Systems

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

Czech

Number of ECTS credits

7

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.

Aims

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. Systémy a signály – 1D a 2D diskrétní a číslicové zpracování. Praha: Sdělovací technika, 2013. ISBN 80-86645-22-0 (CS)
SMÉKAL, Z.: Analog and Digital Signal Processing in Examples and Programs, VUTIUM Press, 2021, Brno, ISBN 978-80-214-5883-3 (EN)

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)

eLearning

Classification of course in study plans

• Programme MPC-KAM Master's, any year of study, summer semester, elective
• Programme MPC-MEL Master's, any year of study, summer semester, elective

• Programme MPC-AUD Master's

specialization AUDM-TECH , 1. year of study, summer semester, compulsory
specialization AUDM-ZVUK , 1. year of study, summer semester, compulsory

• Programme MPC-TIT Master's, 1. year of study, summer semester, compulsory
• Programme MPC-IBE Master's, 2. year of study, summer semester, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Fundamentals seminar

13 hours, compulsory

Teacher / Lecturer

Exercise in computer lab

39 hours, compulsory

Teacher / Lecturer

eLearning