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

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.