Signals and Systems (FSI-VSG-K)

Academic year 2021/2022
Supervisor: prof. Dr. Ing. Jan Černocký  
Supervising institute: ÚAI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
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.
Learning outcomes and competences:
Students will deepen their knowledge in mathematics and statistics and apply it to real problems of signal processing.
Prerequisites:
Mathematical Analysis (M1, M3)
Course contents:
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.
Teaching methods and criteria:
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
Controlled participation in lessons:
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.
Type of course unit:
    Guided consultation in combined form of studies  1 × 22 hrs. compulsory                  
    Guided consultation  1 × 43 hrs. optionally                  
Course curriculum:
    Guided consultation in combined form of studies 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
    Guided consultation 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
Literature - fundamental:
1. Jan, J., Kozumplík, J.: Systémy, procesy a signály. Skriptum VUT v Brně, VUTIUM, 2000.
2. Jan J., Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-AIŘ-K combined study --- no specialisation -- Cr,Ex 5 Compulsory 2 2 W