Course detail

Signals and Systems

FSI-VSG-KAcad. year: 2021/2022

Continuous and discrete time signals and systems. Spectral analysis in continuous time - Fourier series and Fourier transform. Systems with continuous time. Sampling and reconstruction. Discrete-time signals and their frequency analysis: Discrete Fourier series and Discrete-time Fourier transform. Discrete systems. Two-dimensional signals and systems. Random signals.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Dr. Ing. Jan Černocký

Department

Institute of Automation and Computer Science (ÚAI)

Learning outcomes of the course unit

Students will deepen their knowledge in mathematics and statistics and apply it to real problems of signal processing.

Prerequisites

Mathematical Analysis (M1, M3)

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

ASSESSMENT POINTS

51 exam, 25 half-term test, 12 labs, 12 projects

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

To learn and understand the basic theory of signals and linear systems with continuous and discrete time. To introduce to random signals. The emphasis of the course is on spectral analysis and linear filtering - two basic building blocks of modern communication and machine learning systems.

Specification of controlled education, way of implementation and compensation for absences

participation in numerical exercises is not checked, but tests are conducted in them, each worth 2 points.
Groups in numerical exercises are organized according to inscription into schedule frames.
Replacing missed exercises (and obtaining the points) is possible by (1) attending the exercise and the test with another group, (2) solving all tasks in given assignment and presenting them to the tutor, (3) examination by the tutor or course responsible after an appointment. Options (2) and (3) are valid max. 14 days after the missed exercises, not retroactively at the end of the course.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Jan J., Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4.
Jan, J., Kozumplík, J.: Systémy, procesy a signály. Skriptum VUT v Brně, VUTIUM, 2000.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N-AIŘ-K Master's 2 year of study, winter semester, compulsory

Type of course unit

 

Guided consultation

43 hod., optionally

Teacher / Lecturer

prof. Dr. Ing. Jan Černocký

Syllabus

1. Digital filters - fundamentals and practical usage
2. Frequency analysis using DFT - fundamentals and practical usage
3. Image processing (2D signals) - fundamentals and practical usage
4. Random signals - fundamentals and practical usage
5. Applications of signal processing and introduction to the theory
6. Frequency analysis of continuous time signals
7. Continuous time systems
8. From continuous to discrete - sampling, quantization
9. The discrete signal in more detail
10. Spectral analysis of discrete signals in more detail.
11. Digital filtering in more detail
12. Random signals in more detail
13. Applications and advanced topics of signal processing

Guided consultation in combined form of studies

22 hod., compulsory

Teacher / Lecturer

prof. Dr. Ing. Jan Černocký

Syllabus

NUMERICAL EXERCISES
1. Complex numbers, cosines and complex exponentials and operations therewith
2. Basics, filtering, frequency analysis
3. Continuous time signals: energy, power, Fourier series, Fourier transform
4. Continuous time systems and sampling
5. Operations with discrete signals, convolutions, DTFT, DFT
6. Digital filtering and random signals

The project aims at the practical experience with signals and systems in Matlab/Octave. Its study etap contains solved exercises on the following topics:
1. Introduction to MATLAB
2. Projection onto basis, Fourier series
3. Processing of sounds
4. Image processing
5. Random signals
6. Sampling, quantization and aliasing