Course detail

Applications of Fourier Analysis

FSI-SF0Optional (voluntary)Bachelor's (1st cycle)Acad. year: 2016/2017Summer semester1, 3. year of study2  credits

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

Learning outcomes of the course unit

Understanding Fourier analysis and its significance for applications in technology.

Mode of delivery

90 % face-to-face, 10 % distance learning

Prerequisites

Basic courses in mathematical analysis.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

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.
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.
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.
BRACEWELL, R. N. The Fourier transform and its applications. McGraw-Hill, 1965, 2nd ed. 1978, revised 1986
KÖRNER, T. W., Fourier Analysis, Cambridge University Press, 1995

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.

Language of instruction

Czech

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.

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

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

seminars in computer labs

13 hours, compulsory

Teacher / Lecturer

Syllabus

Sample applications and their implementation.