Course details

# Signals and Systems

ISS Acad. year 2023/2024 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

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.
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.

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.

Recommended prerequisites

Prerequisite knowledge and skills

Basic maths and statistics.

Study literature

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.

• 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 2024-02-19 L116 10:0012:00 3. op specialni
Mon exam 2024-01-15 A112 A113 C228 D0206 D0207 D105 E104 E105 E112 G108 G202 L314 M104 M105 S206 15:0017:50 řádná
Mon exercise 3., 5., 7., 9., 11., 13. of lectures N204 18:0019:5020 2BIA 2BIB 3BIT xx Brukner
Mon exercise odd week N204 18:0019:5020 2BIA 2BIB 3BIT xx Brukner
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N203 12:0013:5020 2BIA 2BIB 3BIT xx Grézl
Tue exercise odd week N203 12:0013:5020 2BIA 2BIB 3BIT xx Grézl
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N203 14:0015:5020 2BIA 2BIB 3BIT xx Grézl
Tue exercise odd week N203 14:0015:5020 2BIA 2BIB 3BIT xx Grézl
Tue exercise 3., 5., 7., 9., 11., 13. of lectures N204 18:0019:5020 2BIA 2BIB 3BIT xx Brukner
Tue exercise odd week N204 18:0019:5020 2BIA 2BIB 3BIT xx Brukner
Wed lecture lectures D0206 D105 08:0010:50900 2BIB 3BIT xx 20 - 29 Černocký
Wed exam 2024-01-31 D0206 D0207 D105 15:0017:50 2. op termín
Wed exercise 3., 5., 7., 9., 11., 13. of lectures N204 16:0017:5020 2BIA 2BIB 3BIT xx Polok
Wed exercise odd week N204 16:0017:5020 2BIA 2BIB 3BIT xx Polok
Wed exercise 3., 5., 7., 9., 11., 13. of lectures N204 18:0019:5020 2BIA 2BIB 3BIT xx Polok
Wed exercise odd week N204 18:0019:5020 2BIA 2BIB 3BIT xx Polok
Thu exam 2024-01-25 D0206 D0207 D105 E104 E105 E112 13:0015:50 1. opravny termín
Thu exercise 3., 5., 7., 9., 11., 13. of lectures N204 14:0015:5020 2BIA 2BIB 3BIT xx Han In English
Thu exercise 4., 6., 8., 10., 12. of lectures N204 14:0015:5020 2BIA 2BIB 3BIT xx Han In English
Thu exercise 3., 5., 7., 9., 11., 13. of lectures M104 16:0017:5020 2BIA 2BIB 3BIT xx Pavlus
Thu exercise 3., 5., 7., 9., 11., 13. of lectures N204 16:0017:5020 2BIA 2BIB 3BIT xx Han In English
Thu exercise 4., 6., 8., 10., 12. of lectures N204 16:0017:5021 2BIA 2BIB 3BIT xx Han In English
Thu exercise odd week M104 16:0017:5020 2BIA 2BIB 3BIT xx Pavlus
Thu exercise 3., 5., 7., 9., 11., 13. of lectures M104 18:0019:5020 2BIA 2BIB 3BIT xx Pavlus
Thu exercise 3., 5., 7., 9., 11., 13. of lectures N203 18:0019:5020 2BIA 2BIB 3BIT xx Rohdin In English
Thu exercise 4., 6., 8., 10., 12. of lectures M104 18:0019:5020 2BIA 2BIB 3BIT xx Pavlus
Thu exercise odd week N203 18:0019:5020 2BIA 2BIB 3BIT xx Rohdin In English
Thu exam 2023-11-02 D0206 D105 20:0021:30 pulsemestralka ISS termin 1
Fri lecture 2023-10-06 E112 07:0008:50154 1BIA 1BIB 3BIT xx Černocký nahrada prednasky 29.9.
Fri lecture 1., 3., 5., 6., 7., 8., 10., 11., 12., 13. of lectures E112 09:0011:50900 2BIA 3BIT xx 10 - 19 Černocký
Fri exercise 3., 5., 7., 11., 13. of lectures N204 10:0011:5020 2BIA 2BIB 3BIT xx Grézl
Fri exercise odd week N204 10:0011:5020 2BIA 2BIB 3BIT xx Grézl
Fri exercise 3., 5., 7., 11., 13. of lectures N204 12:0013:5020 2BIA 2BIB 3BIT xx Grézl
Fri exercise odd week N204 12:0013:5020 2BIA 2BIB 3BIT xx Grézl
Fri exercise 3., 5., 7., 11., 13. of lectures D0206 16:0017:5020 2BIA 2BIB 3BIT xx Peng in English
Fri exercise 3., 5., 7., 11., 13. of lectures N103 16:0017:5020 2BIA 2BIB 3BIT xx Mošner
Fri exercise odd week D0206 16:0017:5020 2BIA 2BIB 3BIT xx Peng in English
Fri exercise odd week N103 16:0017:5020 2BIA 2BIB 3BIT xx Mošner
Fri exam 2023-11-03 D105 18:0019:30 pulsemestralka ISS 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