Signals and Systems

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

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

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. 

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.

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.

• Discrete Mathematics (IDM)
• Mathematical Analysis 1 (IMA1)
• Mathematical Analysis 2 (IMA2)

Basic maths and statistics.

• 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

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.

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

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, 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.