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Course detail

Applications of Fourier Analysis

Course unit code: FSI-SF0
Academic year: 2016/2017
Type of course unit: optional (voluntary)
Level of course unit: Bachelor's (1st cycle)
Year of study: 1, 3
Semester: summer
Number of ECTS credits:
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.
Course contents (annotation):
Fourier series, Fourier transform, discrete Fourier transform - basic notions, properties, applications.
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.
Course curriculum:
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: prof. RNDr. Miloslav Druckmüller, CSc.
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: Ing. Hana Druckmüllerová, Ph.D.
Ing. Petra Rozehnalová, Ph.D.
Syllabus: Sample applications and their implementation.

The study programmes with the given course