Course detail
Applications of Fourier Analysis
FSI-SF0Acad. year: 2018/2019
Fourier series, Fourier transform, discrete Fourier transform - basic notions, properties, applications.
Language of instruction
Czech
Number of ECTS credits
2
Mode of study
Not applicable.
Department
Learning outcomes of the course unit
Understanding Fourier analysis and its significance for applications in technology.
Prerequisites
Basic courses in mathematical analysis.
Co-requisites
Not applicable.
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.
Course curriculum
Not applicable.
Work placements
Not applicable.
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.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
BEZVODA, V., et al. Dvojrozměrná diskrétní Fourierova transformace a její použití - I.: Teorie a obecné užití. 1. vydání. Praha: Státní pedagogické nakladatelství, n.p., 1988. 181s. ISBN 17-135-88. (CS)
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)
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
BRACEWELL, R. N. The Fourier transform and its applications. McGraw-Hill, 1965, 2nd ed. 1978, revised 1986 (EN)
Classification of course in study plans
Type of course unit
Lecture
13 hod., 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
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 hod., compulsory
Teacher / Lecturer
Syllabus
Sample applications and their implementation.