Course detail

# Signals and Systems

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.

Learning outcomes of the course unit

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.

Prerequisites

Basic maths and statistics.

• recommended prerequisite

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

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

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

• 6 tests in numerical exercises, each 2 pts, total 12 pts.
• half-semester exam, written materials, computers and calculators prohibited, 25 pts.
• submission of project report - 12 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.

Language of instruction

Czech, English

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.

Classification of course in study plans

• Programme BIT Bachelor's, 2. year of study, winter semester, 6 credits, compulsory

• Programme IT-BC-3 Bachelor's

branch BIT , 2. year of study, winter semester, 6 credits, compulsory

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

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

Fundamentals seminar

12 hours, compulsory

Teacher / Lecturer

Syllabus

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

Project

14 hours, compulsory

Teacher / Lecturer

Syllabus

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