SubjectsSubjects(version: 855)
Course, academic year 2019/2020
  
Fourier Transform - AM413001
Title: Fourier Transform
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: English
Teaching methods: full-time
Level:  
For type: Master's (post-Bachelor)
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 : M413001, N413006
Is interchangeable with: M413001
Annotation -
Last update: Kubová Petra Ing. (22.01.2018)
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: Kubová Petra Ing. (22.01.2018)

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: Kubová Petra Ing. (22.01.2018)

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: Kubová Petra Ing. (22.01.2018)

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: Kubová Petra Ing. (22.01.2018)

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. Basic definitions, periodic function, convolution.

2. Dirac delta function, discretization of a continuous signal.

3. Definition of Fourier transform, its properties.

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

5. Fourier transform of rectangular and triangular pulse.

6. Instrument curve.

7. Nyquist condition.

8. Discrete Fourier transform.

9. Method "zero-filling".

10. Fast Fourier transform.

11. Parseval equality.

12. Fourier series.

13. Diffusion equation.

14. Relation between Fourier transform and Fourier series.

Entry requirements -
Last update: Borská Lucie RNDr. Ph.D. (13.05.2019)

Students are expected to have either completed the prerequisite course Mathematics A or possess the equivalent knowledge on differential and integral calculus prior to enrolling in the course.

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

No requirements.

 
VŠCHT Praha