Title:  Signals and Systems 

Code:  ISS 

Ac.Year:  2005/2006 

Term:  Winter 

Curriculums:  

Language:  Czech 

Public info:  http://www.fit.vutbr.cz/study/courses/ISS/public/ 

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:  0  0  0  0  0 



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

Lecturer:  Černocký Jan, doc. Dr. Ing., DCGM 
Faculty:  Faculty of Information Technology BUT 

Department:  Department of Computer Graphics and Multimedia FIT BUT 

Prerequisites:  

 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 knowldge 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: 


 Organization.
 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: 


 Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997.
 Study literature: 


 http://www.fit.vutbr.cz/~cernocky/sig
 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.
 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, the study groups are considered only
as auxiliary information.
 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
 
