Course detail

Applications of Fourier Analysis

FSI-SF0Acad. year: 2023/2024

Fourier series, Fourier transform, discrete Fourier transform - basic notions, properties, applications mostly in image processing and analysis.

Language of instruction


Number of ECTS credits


Mode of study

Not applicable.

Entry knowledge

Basic courses in Mathematics – Mathematics 1, 2, 3. Basics of programming in Matlab.

Rules for evaluation and completion of the course

Accreditation: A short semestral project (either to be done on the last seminar or individually later).

Lectures are voluntary, seminars are compulsory.


Introduction to Fourier analysis and illustration of its applications in image processing and analysis.

Understanding Fourier analysis and its significance for applications in technology.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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)
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 B-MAI-P Bachelor's, 3. year of study, summer semester, elective
  • Programme N-MAI-P Master's, 1. year of study, summer semester, elective
  • Programme N-MET-P Master's, 1. year of study, summer semester, elective

Type of course unit



13 hours, optionally

Teacher / Lecturer


1. Vector space, basis, vector spaces of infinite dimension
2. Unitary space, Hilbert spae
3. Fourier series
4. One-dimensional Fourier transform and its properties, convolution
5. Two-dimensional Fourier transform and its properties
6. Discrete Fourier transform
7. Spectrum visualization, spectum modification
8. Image filtration
9. Analysis of directions in image
10. Image registration - phase correlation
11. Image compression (JPG)
12. Computer tomography (CT)

Computer-assisted exercise

13 hours, compulsory

Teacher / Lecturer


Sample applications and their implementation.