# 457-0048/01 – Integral Transforms (INTR)

 Gurantor department Department of Applied Mathematics Credits 6 Subject guarantor doc. Ing. David Horák, Ph.D. Subject version guarantor doc. Ing. David Horák, Ph.D. Study level undergraduate or graduate Requirement Choice-compulsory Year 1 Semester summer Study language Czech Year of introduction 1992/1993 Year of cancellation 2009/2010 Intended for the faculties FEI Intended for study types Master
Instruction secured by
HOR33 doc. Ing. David Horák, Ph.D.
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 10+10

### 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.

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.

### 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)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 40 (40) 0
Project Project 20  0
Written exam Written test 20  0
Examination Examination 60 (60) 0
Written examination Written examination 60  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

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