Course detail
Applications of Fourier Analysis
FSI-SF0Acad. year: 2024/2025
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
Department
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.
Aims
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
Prerequisites and corequisites
Basic literature
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
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus