Title:  Signals and Systems 

Code:  ISSe 

Ac.Year:  2016/2017 

Term:  Winter 

Curriculums:  

Language:  English 

Credits:  6 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Sem. Exercises  Lab. exercises  Comp. exercises  Other 

Hours:  39  0  0  12  14 

 Examination  Tests  Exercises  Laboratories  Other 

Points:  55  25  0  0  20 



Guarantee:  Černocký Jan, doc. Dr. Ing., DCGM 

Lecturer:  Černocký Jan, doc. Dr. Ing., DCGM Grézl František, Ing., Ph.D., DCGM 
Faculty:  Faculty of Information Technology BUT 

Department:  Department of Computer Graphics and Multimedia FIT BUT 

 Learning objectives: 

  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.  Description: 

  Continuous and discrete time signals and systems. Spectral analysis in continuous time  Fourier series and Fourier transform. Systems with continuous time. Sampling and reconstruction. Discretetime signals and their frequency analysis: Discrete Fourier series and Discretetime Fourier transform. Discrete systems. Twodimensional signals and systems. Random signals.  Knowledge and skills required for the course: 

  basic maths and statistics  Subject specific learning outcomes and competences: 

  Students will learn and understand basis of description and analysis of discrete and continuoustime 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 visualizationSW Matlab.  Syllabus of lectures: 


 Introduction, motivation, organization of the course. Examples of signal processing systems. Basic classification of signals  continuous/discrete time, periodic/nonperiodic. 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. Nonperiodic  Fourier transform, spectral function. Spectra of typical signals. Signal energy  Parseval's theorem.
 Continuoustime 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.
 Discretetime signals and their frequency analysis  Discrete Fourier series, Discretetime Fourier transform. Circular convolution, fast convolution.
 Discrete Fourier transform (DFT) and what it really computes. Fast Fourier transform.
 Discrete systems  ztransform, 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 continuoustime and discretetime systems.
 Twodimensional (2D) signals and systems: space frequency, spectral analysis (2DFourier 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 discretetime signals in MATLAB.
 Sinusoids and complex exponentials. Convolution.
 Fourier analysis of continuoustime signal: 1) by hand, 2) semiautomatic (manual generation of e^(j2pift) functions, 3) using MATLAB functions (+their limitations).
 Simple LTI system, sdescription, processing of signals. Comparison with theoretical frequency response.
 Discrete Fourier series and DTFT  by hand and using MATLABfunctions. Computing of spectrum of a continuoustime signal using DFT.
 Discretetime 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 undersampling   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.
The project will then consist in work with supplied and own signal, the results will be submitted using WIS.  Fundamental literature: 


 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 8021415584.
 Study literature: 

  Controlled instruction: 

 
 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.
 Progress assessment: 

 
 active participation in computer labs, presentation of results to the tutor  2 pts. each, total 12 pts.
 halfsemester exam, all written material authorized, 25 pts.
 submission of project report  13b.
 final exam  50 pts., written materials prohibited, list of basic equations will be at your disposal.
 Passing bounary for ECTS assessment  50 points
 
