Course detail

Applications of Fourier Analysis

FSI-SF0Acad. year: 2018/2019

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.


Basic courses in mathematical analysis.


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

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


Work placements

Not applicable.


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.

Classification of course in study plans

  • Programme B3A-P Bachelor's

    branch B-MAI , 3. year of study, summer semester, 2 credits, elective (voluntary)

  • Programme M2A-P Master's

    branch M-MAI , 1. year of study, summer semester, 0 credits, elective (voluntary)

Type of course unit



13 hours, optionally

Teacher / Lecturer


Fourier series
Hilbert space
Fourier transform
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 hours, compulsory

Teacher / Lecturer


Sample applications and their implementation.