457-0928/01 – Applets of Integral and Discrete Transforms (VSIDT)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantordoc. Ing. David Horák, Ph.D.Subject version guarantordoc. Ing. David Horák, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1999/2000Year of cancellation2010/2011
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOR33 doc. Ing. David Horák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 2+0

Subject aims expressed by acquired skills and competences

Student musí prokázat zvládnutí teorie a schopnost použít tuto teorii k řešení konkrétního praktického problému. Obhájit zvolený způsob řešení.

Teaching methods

Summary

Přednášky obsahují obecný pohled na teorii integrálních transformací na základě funkcionální analýzy s použitím zobecněných funkcí. Zahrnují spojité a diskrétní integrální transformace, jejich užití a analýzu s použitím matematického software.

Compulsory literature:

Veit, J.: Integrální transformace, SNTL, Praha 1979. Čížek, V: Diskrétní Fourierova transformace a její použití, SNTL, Praha, 1981. William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0. Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer,1999, ISBN 0-387-98639-1. Častová, N.: Syllabusy k předmětu: Vybrané statě k předmětu Integrální a diskrétní transformace, VŠB-TU Ostrava, FEI, kat. aplikované matematiky.

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Úvod do problematiky integrálních transformací. Lineární prostory, norma, metrika. Hilbertův prostor. Konvergence řad a integrálů. Ortogonální systémy funkcí. Konvoluce dvou posloupností. Konvoluce dvou funkcí. Laplaceova transformace a Fourierova transformace. Laplaceova transformace - jednostranná a dvoustranná. Zpětná Laplaceova transformace. Fourierova transformace. Zpětná Fourierova transformace. Fourierova-Laplaceova transformace. Diskrétní transformace. Diskrétní L-transformace (Dirichletovy řady). Diskrétní Fourierova transformace. Chyby diskretizace. Algoritmy FFT. Distribuce. Distribuce, Diracův impuls, L-obraz, F-obraz distribuce. Reprezentace distribuce. Konvoluce jako integrální transformace. Inverzní konvoluce (dekonvoluční soustava rovnic). Rozklad. Okenní funkce. Základy harmonické analýzy. Harmonická analýza, nerozlišitelné kmity. Shanonn-Kotelnikovova věta. Matematických filtry, užití. Gaborova transformace (úvod). Okenní Fourierova transformace. Regularizace zpětných transformací. Zobecněná Fourierová řada a wavelety (časově-frekvenční analýza). Zobecněná Fourierová řada. Waveletova báze, vlastnosti, konstrukce. Spojitá waveletová transformace. Diskrétní waveletova transformace. Multirozklad (MRA). Pyramidální algoritmus. Paketový rozklad. Komprese dat, rekonstrukce signálu a další užití. Software pro diskrétní transformace.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
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2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology K Czech Ostrava Choice-compulsory study plan
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2007/2008 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
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2005/2006 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
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2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (3907V001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2645) Electrical Engineering, Communication and Computer systems (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2612) Electrical Engineering and Computer Science (2601V013) Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
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2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
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