Signals and Systems
ISS Acad. year 2019/2020 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.
Language of instruction
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.
Generic learning outcomes and competences
Students will deepen their knowledge in mathematics and statistics and apply it to real problems of signal processing.
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.
- Mathematical Analysis (IMA)
Prerequisite kwnowledge and skills
Basic maths and statistics.
- 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. (in Czech)
- Jan J., Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4. (in Czech)
- Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997
Syllabus of lectures
- Digital filters - fundamentals and practical usage
- Frequency analysis using DFT - fundamentals and practical usage
- Image processing (2D signals) - fundamentals and practical usage
- Random signals - fundamentals and practical usage
- Applications of signal processing and introduction to the theory
- Frequency analysis of continuous time signals
- Continuous time systems
- From continuous to discrete - sampling, quantization
- The discrete signal in more detail
- Spectral analysis of discrete signals in more detail.
- Digital filtering in more detail
- Random signals in more detail
- Applications and advanced topics of signal processing
Syllabus of numerical exercises
- Complex numbers, cosines and complex exponentials and operations therewith
- Basics, filtering, frequency analysis
- Continuous time signals: energy, power, Fourier series, Fourier transform
- Continuous time systems and sampling
- Operations with discrete signals, convolutions, DTFT, DFT
- 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:
- Introduction to MATLAB
- Projection onto basis, Fourier series
- Processing of sounds
- Image processing
- Random signals
- 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
- 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.
- 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.
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Course inclusion in study plans