Applications of Fourier Analysis (FSI-SF0)

Academic year 2018/2019
Supervisor: prof. RNDr. Miloslav Druckmüller, CSc.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
Introduction to Fourier analysis and illustration of its applications - solving differential equations, signal and image processing and analysis. Harmonic analysis.
Learning outcomes and competences:
Understanding Fourier analysis and its significance for applications in technology.
Prerequisites:
Basic courses in mathematical analysis.
Course contents:
Fourier series, Fourier transform, discrete Fourier transform - basic notions, properties, applications.
Teaching methods and criteria:
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.
Controlled participation in lessons:
Will be specified.
Type of course unit:
    Lecture  13 × 1 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture 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 Sample applications and their implementation.
Literature - fundamental:
1. 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.
2. 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.
3. 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.
5. KÖRNER, T. W., Fourier Analysis, Cambridge University Press, 1995
Literature - recommended:
4. BRACEWELL, R. N. The Fourier transform and its applications. McGraw-Hill, 1965, 2nd ed. 1978, revised 1986
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3A-P full-time study B-MAI Mathematical Engineering -- Cr 2 Elective (voluntary) 1 3 S
M2A-P full-time study M-MAI Mathematical Engineering -- Cr 0 Elective (voluntary) 2 1 S