SubjectsSubjects(version: 877)
Course, academic year 2020/2021
  
Fourier transform for Bc. students - B413006
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
Level:  
For type: Bachelor's
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Pokorný Pavel RNDr. Ph.D.
Interchangeability : N413039
Examination dates   Schedule   
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)

http://www.vscht.cz/mat/FT/CviceniFT.html

http://en.wikipedia.org/wiki/Fourier_transform

http://reference.wolfram.com/mathematica/ref/FourierTransform.html

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. (13.05.2019)

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.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (06.05.2019)

Mathematics A

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
 
VŠCHT Praha