SubjectsSubjects(version: 953)
Course, academic year 2021/2022
  
Fourier Transform - AP413008
Title: Fourier Transform
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0, other [HT]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Level:  
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 : P413008
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: Pátková Vlasta (16.11.2018)
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: Pátková Vlasta (16.11.2018)
Literature -

R. Bracewell: The Fourier Transform & Its Applications, McGraw-Hill 3rd edition (1999)

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

Last update: Jahoda Milan (29.11.2018)
Learning resources -

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

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

Last update: Jahoda Milan (29.11.2018)
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: Pátková Vlasta (16.11.2018)
Requirements to the exam -

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

Last update: Pátková Vlasta (16.11.2018)
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.

12. Fourier transform of distributions.

13. Fourier series.

14. Application of Fourier transform in the area of the student.

Last update: Pokorný Pavel (04.06.2020)
Entry requirements -

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

Last update: Borská Lucie (16.09.2019)
Registration requirements -

none

Last update: Borská Lucie (16.09.2019)
Course completion requirements -

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

Last update: Pátková Vlasta (16.11.2018)
 
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