457-0037/01 – Discrete Transforms (DITR)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. Ing. Nina Častová, CSc.Subject version guarantordoc. Ing. Nina Častová, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year4Semestersummer
Study languageCzech
Year of introduction1992/1993Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
C1A55 doc. Ing. Nina Častová, CSc.
HOR11 Ing. David Horák
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

To give students knowledge of concepts and numerical algorithms of integral and discrete transformations.

Teaching methods

Summary

Discrete transformations are the tools of effective numerical solution of technical problems. The subject contains classical and modern theory and algorithms.

Compulsory literature:

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994. Bachman G., Narici L., Becktenstein E.: Fourier and wavelet analysis, Springer, 2000.

Recommended literature:

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994. Bachman G., Narici L., Becktenstein E.: Fourier and wavelet analysis, Springer, 2000. W.L.Briggs, V.E. Henson: The DFT, SIAM, 1995.

Way of continuous check of knowledge in the course of semester

Verification of study: Test of discrete Fourier transform and distribution - max. 10 points. Computer test of using of implemented algorithms - max. 10 points. Five computer examples from numerical exercises - max. 10 points. Individual project - max. 20 points. Conditions for credit: Two tests - max. 20 points. One individual project and presentation - max. 20 points. Five computer examples from numerical exercises - max. 10 points. Maximal number of points from exercises - 50 points. Minimal number of points from exercises - 25 points.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Orthogonal discrete systems. Distributions and Delta-operator. Systems of convolution equations. Deconvolution. Discrete Laplace transform and two-side Laplace transform. Discrete Fourier transform, FFT. Inverse transforms and problems of the discrete inverse transforms. Regularization. Applications. Windowed Fourier transforms. Applications. Wavelet transforms. Discrete wavelet transform. Multiresolution. Analysis. Applications. Exercises: Preparing to computer exercises. Projects: Project and its presentation on the realization of a particular problem. Computer labs: Introduction to MATLAB. Orthogonal discrete systems (Haar, Walsh, Rademacher etc.). Numerical analysis of signals using discrete Fourier transform. FFT algorithm and implementation. Windowed Fourier transforms. Algorithm and implementation. Discrete wavelet transform. Algorithm and implementation. Applications of mentioned algorithms in technical problems.

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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2005/2006 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
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2004/2005 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
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2003/2004 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
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2002/2003 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
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2002/2003 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
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