Signals and Systems
ISS Acad. year 2010/2011 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
Grézl František, Ing., Ph.D. (DCGM FIT BUT)
Hannemann Mirko, Dipl.-Ing. (DCGM FIT BUT)
Hubeika Valiantsina, Ing. (DCGM FIT BUT)
Jančík Zdeněk, Ing. (DCGM FIT BUT)
Janda Miloš, Ing. (DCGM FIT BUT)
Kombrink Stefan, Dipl.-Inf -Ling (DCGM FIT BUT)
Mikolov Tomáš, Ing. (DCGM FIT BUT)
Plchot Oldřich, Ing., Ph.D. (DCGM FIT BUT)
Subject specific learning outcomes and competences
Students will learn and understand basis of description and analysis of discrete and continuous-time signals and systems. They will also obtain practical skills in analysis and filtering in MATLAB.
Generic learning outcomes and competences
Students will deepen their knowledge in mathematics and statistics and apply it on real problems of signal processing. During the course, they will get acquainted with math- and visualization-SW Matlab.
To learn and understand 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 - 2 basic building blocks of modern communication systems.
- 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.
- 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
Syllabus of lectures
- Introduction, motivation, organization of the course. Examples of signal processing systems. Basic classification of signals - continuous/discrete time, periodic/non-periodic. Transformation of time.
- Continuous and discrete time periodic signals: sinusoids and complex exponentials. Overview of basic notions in complex numbers. Discrete and continuous time systems. Linear, time invariant systms (LTI). Representation of signals as series of pulses, convolution. Describing systems using differential and difference equations.
- Continuous time signals and their frequency analysis: periodic - Fourier series, coefficients. Non-periodic - Fourier transform, spectral function. Spectra of typical signals. Signal energy - Parseval's theorem.
- Continuous-time systems - Laplace transform, transfer function, frequency response, stability. Example of a simple analog circuit.
- Sampling and reconstruction - ideal sampling, aliasing, sampling theorem. Spectrum of sampled signal, ideal reconstruction. Normalized time and frequency. Quantization.
- Discrete-time signals and their frequency analysis - Discrete Fourier series, Discrete-time Fourier transform. Circular convolution, fast convolution.
- Discrete Fourier transform (DFT) and what it really computes. Fast Fourier transform.
- Discrete systems - z-transform, finite and infinite impulse response systems (FIR and IIR), transfer function, frequency response, stability. Example of a digital filter: MATLAB and C.
- Discrete systems cont'd: design of simple digital filters, sampling of frequency response, windowing. Links between continuous-time and discrete-time systems.
- Two-dimensional (2D) signals and systems: space frequency, spectral analysis (2D-Fourier transform), filtering using a mask. Example - JPEG.
- Random signals - random variable, realization, distribution function, probability density function (PDF). Stationarity and ergodicity. Parameters of a random signal: mean, etc. Estimation - ensemble and temporal.
- Random signals cont'd: correlation function, power spectral density (PSD). Processing of random signals by LTI systems.
- Summary of basic notions, systematic organization of signal processing knowledge. Examples.
Syllabus of computer exercises
- Introduction to MATLAB
- Projection onto basis, Fourier series
- Processing of sounds
- Image processing
- Random signals
- Sampling, quantization and aliasing
Syllabus - others, projects and individual work of students
The individual project aims at image processing, see http://www.fit.vutbr.cz/study/courses/ISS/public/#proj
- active participation in computer labs, presentation of results to the tutor - 2 pts. each, total 12 pts.
- half-semester exam, written materials, computers and calculators prohibited, 25 pts.
- submission of project report - 12b.
- 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 computer labs is not checked but active participation and presentation of results to the tutor is evaluated by 2 pts.
- Groups in computer labs are organized according to inscription into schedule frames.
Course inclusion in study plans