Course detail
Applications of Fourier Analysis
FSI-SF0 Acad. year: 2019/2020 Summer semester
Fourier series, Fourier transform, discrete Fourier transform – basic notions, properties, applications.
Language of instruction
Czech
Number of ECTS credits
2
Supervisor
Department
Learning outcomes of the course unit
Understanding Fourier analysis and its significance for applications in technology.
Prerequisites
Basic courses in mathematical analysis.
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.
Aims
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.
The study programmes with the given course
Programme B3A-P: Applied Sciences in Engineering, Bachelor's
branch B-MAI: Mathematical Engineering, elective (voluntary)
Programme M2A-P: Applied Sciences in Engineering, Master's
branch M-MAI: Mathematical Engineering, elective (voluntary)
Type of course unit
Lecture
13 hours, optionally
Teacher / Lecturer
Syllabus
Fourier series
Hilbert space
Fourier transform
Convolution
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
Syllabus
Sample applications and their implementation.