Signals and Systems (in English)
ISSe Acad. year 2019/2020 Winter semester 6 credits
Language of instruction
* This course is prepared for incoming Erasmus+ students only, and it is instructed in English.
* This course will be open if a certain/sure minimum of enrolled students is at least five students.
Subject specific learning outcomes and competences
Generic learning outcomes and competences
Prerequisite kwnowledge and skills
- Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997
- 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.
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
- Generating and plotting of continuous and discrete-time signals in MATLAB.
- Sinusoids and complex exponentials. Convolution.
- Fourier analysis of continuous-time signal: 1) by hand, 2) semi-automatic (manual generation of e^(j2pift) functions, 3) using MATLAB functions (+their limitations).
- Simple LTI system, s-description, processing of signals. Comparison with theoretical frequency response.
- Discrete Fourier series and DTFT - by hand and using MATLAB-functions. Computing of spectrum of a continuous-time signal using DFT.
- Discrete-time systems - filtering. Design of a simple filter, frequency response, zeros and poles, stability. Influence of quantization of coefficients.
Syllabus - others, projects and individual work of students
- Individual project - preparation:
- Sampling - aliasing. Generating of discrete signal with given frequency. Over- and under-sampling - - demonstration of aliasing.
- Random signals - generating, ensemble and temporal estimation of parameters, estimation of F(x) a p(x) using histogram.
- Random signals - correlation, power spectral density, processing by a filter.
- Mid-semester exam, all written material authorized, 20 pts.
- Submission of project report - 20b.
- Final exam - 60 pts., written materials prohibited, list of basic equations will be at your disposal.
- Passing bounary for ECTS assessment - 50 points
- 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.