SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Fourier Transform - P413008
Title: Fourierova transformace
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type: doctoral
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Pokorný Pavel RNDr. Ph.D.
Interchangeability : D413026
Is interchangeable with: AP413008
Annotation -
Last update: Pátková Vlasta (28.05.2018)
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: Pátková Vlasta (28.05.2018)

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. (24.10.2018)

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)

A: Eric W Hansen: Fourier Transforms. Wiley 2014. ISBN-13: 978-1118479148f

Learning resources -
Last update: Pátková Vlasta (28.05.2018)

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: Pátková Vlasta (28.05.2018)

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).

Requirements to the exam -
Last update: Pokorný Pavel RNDr. Ph.D. (25.09.2018)

The student is expected to take an active part in seminars and in lectures during the semester.

Syllabus -
Last update: Pátková Vlasta (28.05.2018)

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.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

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

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

none

Course completion requirements -
Last update: Pokorný Pavel RNDr. Ph.D. (25.09.2018)

The final examination consists of the written and of the oral part.

 
VŠCHT Praha