457-0048/02 – Integral Transforms (INTR)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Ing. David Horák, Ph.D.Subject version guarantordoc. Ing. David Horák, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year3Semesterwinter
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.
KOZ75 prof. Ing. Tomáš Kozubek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Student should understand to basic tools and rules of integral transforms and get familiar with correct approaches for the solution of concrete problems and discuss the chosen way of their solution.

Teaching methods

Lectures
Tutorials
Project work

Summary

Subject Integral transforms belongs to basic mathematical subjects at technical universities. The students will get knowledge about the theory and usage of Laplace transform and Z transform, Fourier series, Fourier, Window Fourier and Wavelet transforms including their applications for signal processing as time-frequency analysis, compression and denoising.

Compulsory literature:

Častová, N.,Kozubek,T:Integral transforms, www.am.vsb.cz Galajda P., Schrötter Š.: Function of complex variable and operator calculus, Alfa-Bratislava, 1991. G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.

Recommended literature:

Škrášek J., Tichý Z.: The basics of applied mathematics II, SNTL, Praha, 1986.

Way of continuous check of knowledge in the course of semester

Verification of study: Test of Fourier series - max. 10 points. Test of Laplace transform - max. 10 points. Individual project of Laplace transform - max. 10 points. Individual project of Fourier series - max. 10 points. Conditions for credit: Two tests - max. 20 points. Two individual projects - max. 20 points. Maximal number of points from exercises - 40 points. Minimal number of points from exercises - 20 points.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Introduction to Fourier series. Orthogonal systems of functions. Generalized Fourier series. Applications. Introduction to integral transforms. Convolution. Laplace transform, fundamental properties. Inverse Laplace Transform. Applications. Fourier transform, fundamental properties. Inverse Fourier transform. Applications. Z-transform, fundamental properties. Inverse Z-transform. Applications. Distribution. Dirac impuls. Exercises: Examples of orthogonal systems of functions, Fourier series and applications. Practising of Laplace transform. Solution of differential equation. Practising of Fourier transform and examples. Practising of Z-transform. Solution of difference equation. Projects: Two individual works and their presentation on the theme: Fourier series. Laplace transform.

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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