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Course, academic year 2023/2024

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Fourier transform for Bc. students - B413006
Title: Fourierova transformace pro studenty bakalářského studia
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: winter
Points: winter s.:5
E-Credits: winter s.:5
Examination process: winter s.:
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Pokorný Pavel RNDr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : N413039
Annotation -
Physical motivation, definition, properties and application of Fourier Transform, Discrete FT, Fast FT, 1-dim and higher dimensional FT, Inverse FT, convolution and deconvolution, theory of distributions (generalized functions), especially Dirac Delta Distribution and Singular Value Decomposition are presented with application in (audio and image) signal processing and in infra-red spectroscopy.
Last update: Pokorný Pavel (23.02.2018)
Aim of the course -

The student will be able to use Fourier Transform for signal processing and for equation solving, to find the correct sampling frequency and

the correct measurement time according to the maximal input frequency and the correct detection of close peaks, to use convolution

and deconvolution, to use Singular Value Decomposition.

Last update: Pokorný Pavel (23.02.2018)
Literature -

R:Klíč, Volka, Dubcová: Fourierova transformace s příklady z infračervené spektroskopie. VŠCHT Praha 2002, 80-7080478-5.

A: R. Bracewell: The Fourier Transform & Its Applications, McGraw-Hill 3rd edition (1999)

Last update: Pokorný Pavel (23.02.2018)
Learning resources -

Last update: Pokorný Pavel (23.02.2018)
Teaching methods -

The teaching consists of a 2-hour lecture and a 2-hour seminar a week, of individual consultation and of self-study. The final grade is based on

the exam (test + oral).

Last update: Pokorný Pavel (23.02.2018)
Syllabus -

1. Elementary terms. Functions sin and cos.

2. Dirac delta function.

3. Definition of Fourier transform of a function.

4. Properties of Fourier transform, linearity.

5. Inverse Fourier transform.

6. Fourier image of derivative, derivative of image.

7. Translation theorem, scaling theorem.

8. Discrete Fourier transform.

9. Zero padding.

10. Fast Fourier transform.

11. Analysis of 1-dim signal.

12. Power spectrum.

13. Fourier series.

14. Relation between Fourier transform and Fourier series.

Last update: Pokorný Pavel (13.05.2019)
Registration requirements -

Mathematics A

Last update: Borská Lucie (06.05.2019)
Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0.9 24
Účast na přednáškách 1 28
Příprava na zkoušku a její absolvování 2.1 60
Účast na seminářích 1 28
5 / 5 140 / 140