Course detail
Applications of Fourier Analysis
FSI-SF0 Acad. year: 2024/2025 Summer semester
Fourier series, Fourier transform, discrete Fourier transform – basic notions, properties, applications mostly in image processing and analysis.
Language of instruction
Czech
Number of ECTS credits
2
Supervisor
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.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, elective
Programme N-MET-P: Mechatronics, Master's, elective
Programme N-MAI-P: Mathematical Engineering, Master's, elective
Type of course unit
Lecture
13 hours, optionally
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
13 hours, compulsory
Syllabus
Sample applications and their implementation.