Course detail

Applications of Fourier Analysis

FSI-SF0Acad. year: 2019/2020

Fourier series, Fourier transform, discrete Fourier transform - basic notions, properties, applications.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

prof. RNDr. Miloslav Druckmüller, CSc.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Understanding Fourier analysis and its significance for applications in technology.

Prerequisites

Basic courses in mathematical analysis.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Accreditation: attendance.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Introduction to Fourier analysis and illustration of its applications - solving differential equations, signal and image processing and analysis. Harmonic analysis.

Specification of controlled education, way of implementation and compensation for absences

Will be specified.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BEZVODA, V., et al. Dvojrozměrná diskrétní Fourierova transformace a její použití - I.: Teorie a obecné užití. 1. vydání. Praha: Státní pedagogické nakladatelství, n.p., 1988. 181s. ISBN 17-135-88. (CS)
ČÍŽEK, V. Diskrétní Fourierova transformace a její použití. 1st edition. Praha: SNTL - Nakladatelství technické literatury, n.p., 1981. 160s. Matematický seminář SNTL. ISBN 04-019-81. (CS)
FOLLAND, G. B. Fourier Analysis and Its Applications. Second Edition. Providence (Rhode Island, U.S.A.): The American Mathematical Society, 2009. 433s. The Sally series, Pure and Applied Mathematics, Undergraduate Texts. ISBN 978-0-8218-4790-9. (EN)
KÖRNER, T. W., Fourier Analysis, Cambridge University Press, 1995 (EN)

Recommended reading

BRACEWELL, R. N. The Fourier transform and its applications. McGraw-Hill, 1965, 2nd ed. 1978, revised 1986 (EN)

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-MAI , 1 year of study, summer semester, elective (voluntary)

  • Programme B3A-P Bachelor's

    branch B-MAI , 3 year of study, summer semester, elective (voluntary)

Type of course unit

 

Lecture

13 hod., optionally

Teacher / Lecturer

Ing. Jindřich Dospiva

Syllabus

Fourier series
Hilbert space
Fourier transform
Convolution
Discrete Fourier transform
Image registration - phase correlation
Image processing - filtration, compression, computer tomography (CT)
Signal processing - compression of music
Solving ODE, PDE
Harmonic analysis

Computer-assisted exercise

13 hod., compulsory

Teacher / Lecturer

Ing. Jindřich Dospiva

Syllabus

Sample applications and their implementation.