Course detail
Applications of Fourier Analysis
FSI-SF0 Acad. year: 2023/2024 Summer semester
Fourier series, Fourier transform, discrete Fourier transform – basic notions, properties, applications mostly in image processing and analysis.
Supervisor
Department
Learning outcomes of the course unit
Understanding Fourier analysis and its significance for applications in technology.
Prerequisites
Basic courses in Mathematics – Mathematics 1, 2, 3. Basics of programming in Matlab.
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: A short semestral project (either to be done on the last seminar or individually later).
Language of instruction
Czech
Aims
Introduction to Fourier analysis and illustration of its applications in image processing and analysis.
Specification of controlled education, way of implementation and compensation for absences
Lectures are voluntary, seminars are compulsory.
The study programmes with the given course
Programme N-MET-P: Mechatronics, Master's
branch ---: no specialisation, 2 credits, elective
Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 2 credits, elective
Programme N-MAI-P: Mathematical Engineering, Master's
branch ---: no specialisation, 2 credits, elective
Type of course unit
Lecture
13 hours, optionally
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
13 hours, compulsory
Teacher / Lecturer
Syllabus
Sample applications and their implementation.