SubjectsSubjects(version: 888)
Course, academic year 2020/2021
Fourier transform for Bc. students - N413039
Title: Fourierova transformace pro studenty bakalářského studia
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
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 [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Is provided by: M413001
For type: Bachelor's
Guarantor: Pokorný Pavel RNDr. Ph.D.
Is interchangeable with: B413006
Annotation -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)
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.
Aim of the course -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)

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.

Literature -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)

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)

Learning resources -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)

Teaching methods -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)

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).

Syllabus -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)

1. Basic notions about periodic functions and some useful functions. Convolution.

2. Dirac delta function, basic properties. Discretization of the continuous signal.

3. The definition of Fourier transform and its basic properties.

4. Fourier transform of delta-function and of periodic functions.

5. The signals of finite length. Instrument line shape.

6. The methods of apodization and deconvolution.

7. The influence of the discretization of the signal on the spectrum. Aliasing.

8. Discrete Fourier transform. Definition.

9. The method of zero-filling.

10. Fast Fourier transform, the main idea, usage, number of operations.

11. The theory of distribution. Regular and singular distributions. Fourier transform of distributions.

12. Two-dimentsional and higher dimensional Fourier transform.

13. Fourier series.

14. Fourier transform in infrared spectroscopy

Registration requirements -
Last update: Pokorný Pavel RNDr. Ph.D. (23.02.2018)

Prerequisite: knowledge of derivative and integral (Mathematics I).

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