SubjectsSubjects(version: 954)
Course, academic year 2023/2024
  
Fourier Transform - N413006
Title: Fourierova transformace
Guaranteed by: Department of Mathematics (413)
Faculty: Faculty of Chemical Engineering
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 [HT]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Level:  
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Pokorný Pavel RNDr. Ph.D.
Class: Předměty pro matematiku
Is interchangeable with: M413001, AM413001
Examination dates   Schedule   
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 (12.07.2013)
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 (12.07.2013)
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 (01.08.2013)
Learning resources -

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

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

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

Last update: Pokorný Pavel (12.07.2013)
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 (12.07.2013)
Syllabus -

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.

Last update: Pokorný Pavel (12.07.2013)
Registration requirements -

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

Last update: Pokorný Pavel (12.07.2013)
Teaching methods
Activity Credits Hours
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1 28
Příprava na zkoušku a její absolvování 2 56
Účast na seminářích 1 28
5 / 5 140 / 140
Coursework assessment
Form Significance
Regular attendance 10
Examination test 30
Oral examination 60

 
VŠCHT Praha