Course details

# Signals and Systems

ISS Acad. year 2022/2023 Winter semester 6 credits

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.

Guarantor

Course coordinator

Language of instruction

Czech

Completion

Examination (written)

Time span

• 39 hrs lectures
• 12 hrs exercises
• 14 hrs projects

Assessment points

• 51 pts final exam (written part)
• 19 pts mid-term test (written part)
• 12 pts numeric exercises
• 18 pts projects

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

Students will learn and understand the basis of the description and analysis of discrete and continuous-time signals and systems. They will also obtain practical skills in analysis and filtering in MATLAB/Octave. Students will deepen their knowledge in mathematics and statistics and apply it to real problems of signal processing.

Learning objectives

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.

Why is the course taught

Probably anyone has already placed a call from a cell-phone. Probably everyone took a picture and stored it in JPG format. The algorithms of digital signal processing can be found behind both applications - filtering (in case of a mobile codec its for example a filter that changes its characteristics every 20 milliseconds depending on your voice) and spectral analysis (in JPG image encoding, little squares of 8x8 pixels are compared with cosine signals at different speeds). Both examples are however only a minuscule part of a vast number of signal and data processing applications, all around us - from commanding the ABS system in your car to satellite communications. Moreover, signal processing is an important component of machine learning (also called "artificial intelligence") that is nowadays influencing almost all sectors of the economy and normal life. ISS won't teach you everything, but it will give you solid mathematical bases and intuition to build upon.

Prerequisites

Prerequisite knowledge and skills

Basic maths and statistics.

Technical equipment

komerční

• Matlab

• volně dostupné
• Octave

Study literature

• http://www.fit.vutbr.cz/study/courses/ISS/public/
• Jan, J., Kozumplík, J.: Systémy, procesy a signály. Skriptum VUT v Brně, VUTIUM, 2000.
• http://www.fit.vutbr.cz/study/courses/ISS/public/
• Šebesta V.: Systémy, procesy a signály I., Skriptum VUT v Brně, VUTIUM, 1997.
• Jan J., Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4.
• Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997

Syllabus of lectures

1. Introduction to the course, mathematical basics
2. Introduction to projections and derivation of Discrete Fourier Transform (DFT)
3. Practical use and properties of DFT
4. Introduction to digital filtering, differential equation, implementation of filters, convolution
5. Frequency characteristic and stability of digital filter. Applications of filtering.
6. Random signals - introduction.
7. Random signals II - correlation, spectra, white noise.
8. Processing of 2D signals - images.
9. Analog world - continuous time signal, Fourier transform, estimation using DFT. Sampling and quantization.
10. Periodicity of signals with discrete and continuous time - definition, Fourier series, Discrete Fourier series.
11. Fundamentals of systems - properties, impulse response.
12. Continuous-time systems. - schematics, differential equation, frequency characteristic, stability.
13. Conclusion - summary of frequency transformations and filtering.

Syllabus of 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

Syllabus - others, projects and individual work of students

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

The project itself follows with an individual signal for each student, see http://www.fit.vutbr.cz/study/courses/ISS/public/#proj

Progress assessment

• 6 tests in numerical exercises, each 2 pts, total 12 pts.
• half-semester exam, written materials, computers and calculators prohibited, 19 pts.
• submission of project report - 18 pts.
• final exam - 51 pts., written materials, computers and calculators prohibited, list of basic equations will be at your disposal. The minimal number of points which can be obtained from the final exam is 17. Otherwise, no points will be assigned to the student.

Controlled instruction

• 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.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exam 2023-01-09 A112 A113 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 L314 M104 M105 S206 09:0011:50řádná
Mon exam 2023-02-27 L220 12:0014:003. mimoradna oprava
Mon exercise 3., 5., 7., 9., 11., 13. of lectures N203 14:0015:5020 2BIA 2BIB 3BIT xx Nguyen Nguyen Son Hai
Mon exercise odd week N203 14:0015:5020 2BIA 2BIB 3BIT xx Nguyen Nguyen Son Hai
Mon exam 2023-01-16 D0206 D0207 D105 E104 E105 E112 15:0017:501. oprava
Mon exercise 3., 5., 7., 9., 11., 13. of lectures N203 16:0017:5020 2BIA 2BIB 3BIT xx Brukner Jan Brukner
Mon exercise odd week N203 16:0017:5020 2BIA 2BIB 3BIT xx Brukner Jan Brukner
Mon exercise 3., 5., 7., 9., 11., 13. of lectures A112 18:0019:5020 2BIA 2BIB 3BIT xx Brukner Jan Brukner
Mon exercise odd week A112 18:0019:5020 2BIA 2BIB 3BIT xx Brukner Jan Brukner
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N203 10:0011:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Tue exercise odd week N203 10:0011:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Tue exercise odd week N203 12:0013:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N203 16:0017:5020 2BIA 2BIB 3BIT xx Pavlus Jan Pavlus
Tue exercise odd week N203 16:0017:5020 2BIA 2BIB 3BIT xx Pavlus Jan Pavlus
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N203 18:0019:5020 2BIA 2BIB 3BIT xx Pavlus Jan Pavlus
Tue exercise odd week N203 18:0019:5020 2BIA 2BIB 3BIT xx Pavlus Jan Pavlus
Wed lecture 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures D0206 D105 08:0010:50999 2BIB 3BIT xx 20 - 29 Černocký česky
Wed exercise 3., 5., 7., 9., 11., 13. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Wed exercise 4., 6., 8., 10., 12. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Wed exercise 3., 5., 7., 9., 11., 13. of lectures N203 14:0015:5020 2BIA 2BIB 3BIT xx Hanák Jiri Hanák
Wed exercise 4., 6., 8., 10., 12. of lectures N203 14:0015:5020 2BIA 2BIB 3BIT xx Hanák Jiri Hanák
Wed exercise 3., 5., 7., 9., 11., 13. of lectures N203 16:0017:5020 2BIA 2BIB 3BIT xx Silnova Anna Silnova - EN
Wed exercise 4., 6., 8., 10., 12. of lectures N203 16:0017:5020 2BIA 2BIB 3BIT xx Silnova Anna Silnova - EN
Wed exercise 3., 5., 7., 9., 11., 13. of lectures N203 18:0019:5020 2BIA 2BIB 3BIT xx Mošner Ladislav Mosner
Wed exercise 4., 6., 8., 10., 12. of lectures N203 18:0019:5020 2BIA 2BIB 3BIT xx Mošner Ladislav Mosner
Wed exam 2022-11-23 D105 20:0022:00půlsemestrálka ISS - termín 1
Thu exercise 3., 5., 7., 11., 13. of lectures N203 10:0011:5020 2BIA 2BIB 3BIT xx Peng Junyi Peng - EN
Thu exercise odd week N203 10:0011:5020 2BIA 2BIB 3BIT xx Peng Junyi Peng - EN
Thu exercise 3., 5., 7., 11., 13. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Peng Junyi Peng - EN
Thu exercise odd week N203 12:0013:5020 2BIA 2BIB 3BIT xx Peng Junyi Peng - EN
Thu exercise 3., 5., 7., 11., 13. of lectures N204 14:0015:5020 2BIA 2BIB 3BIT xx Nguyen Nguyen Son Hai
Thu exercise odd week N204 14:0015:5020 2BIA 2BIB 3BIT xx Nguyen Nguyen Son Hai
Fri lecture 1., 2., 3., 4., 7., 8., 9., 10., 11., 12., 13. of lectures E112 09:0011:50999 2BIA 3BIT xx 10 - 19 Černocký English
Fri exercise 2., 4., 8., 10., 12. of lectures N205 12:0013:5020 2BIA 2BIB 3BIT xx Novák Jiri Novak
Fri exercise 3., 5., 7., 9., 11., 13. of lectures N205 12:0013:5020 2BIA 2BIB 3BIT xx Novák Jiri Novak
Fri exam 2023-01-27 D0206 D105 13:0015:502. oprava
Fri exercise 2., 4., 8., 10., 12. of lectures N205 14:0015:5020 2BIA 2BIB 3BIT xx Grézl Frantisek Grezl
Fri lecture 2022-10-21 E105 14:0016:5070 2BIA 3BIT xx 10 - 19 Černocký English
Fri exam 2022-11-25 D105 16:0018:00ISS pulsemestralka - termin 2,

Course inclusion in study plans

• Programme BIT, 2nd year of study, Compulsory
• Programme BIT (in English), 2nd year of study, Compulsory
• Programme IT-BC-3, field BIT, 2nd year of study, Compulsory