470-4303/01 – Discrete Transforms (DT)

Gurantor departmentDepartment of Applied MathematicsCredits5
Subject guarantordoc. Ing. David Horák, Ph.D.Subject version guarantordoc. Ing. David Horák, Ph.D.
Study levelundergraduate or graduate
Study languageCzech
Year of introduction2010/2011Year of cancellation2011/2012
Intended for the facultiesFEIIntended for study typesFollow-up Master
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+1
Combined 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

Lectures
Tutorials

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: 2011/2012 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  15
        Examination Examination 70  0
Mandatory attendence parzicipation:

Show history
Combined form (validity from: 2011/2012 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30  15
        Examination Examination 70  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner