SubjectsSubjects(version: 954)
Course, academic year 2021/2022
Advanced Methods of Signal Processing for PhD Students - P445013
Title: Pokročilé metody zpracování signálů pro doktorandy
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021 to 2023
Semester: summer
Points: summer s.:0
E-Credits: summer s.:0
Examination process: summer s.:
Hours per week, examination: summer s.:3/0, other [HT]
Capacity: unlimited / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course is intended for doctoral students only
can be fulfilled in the future
Guarantor: Mareš Jan prof. Ing. Ph.D.
Kukal Jaromír doc. Ing. Ph.D.
Is interchangeable with: AP445013
Annotation -
Specal methods of signal processing are characterized by application of functional transforms, robust statistical methods and variational approach. The techniques mentioned above enable to design of efficient procedures for signal smoothing, signal analzsis and pattern classification. The module is mainly focused on the mathematical principles and application in analytical chemistry.
Last update: Kukal Jaromír (13.06.2018)
Aim of the course -

Students will be able to:

Recognize what kind of functional transform should be useful for signal processing in given task.

Decide what technique of signal enhancement would improve its quality related to given application and signal processing aims.

Apply special statistical methods in combination with variational calculus to design novel methods of signal processing.

Last update: Kukal Jaromír (13.06.2018)
Literature -

R: Gonzales, R.C., Woods, R.E., Digital Image processing (4th edition), Pearson, New York, 2017.

R: Mitra, S.K., Sicuranza, G.L., Nonlinear Image Processing, Academic Press, New York, 2001.

R: King, W., Hilbert Transforms, Vol.1, Cambridge University Press, Cambridge, 2009.

A: Aubert, G., Kornprobst, P., Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (2nd edition), Springer, New York, 2006.

Last update: Soušková Hana (18.06.2018)
Learning resources -

internal materials

Last update: Kukal Jaromír (03.09.2018)
Teaching methods -

Lectures, preparing of project about signal analysis related to subject of doctoral study.

Last update: Kukal Jaromír (13.06.2018)
Syllabus -

The lectures and individual projects will be focused on:

1.Digital signal and its properties in frequency domain.

2.Statistical properties of sampled signal.

3.Functional transforms for signal processing (Laplace,Fourier,Hilbert,Z,DFT,FFT,DHT)

4.Signal enhancement techniques (filtering,smoothing,sharpening, deconvolution,reconstruction)

5.Signal analysis (spectrum, coherence, chaos descriptors, fractal analysis)

6.Local signal processing via robust statistical methods (M-estimates,L-estimates, special distributions)

7.Regularized methods of signal processing.

8.Variational approach in signal processing.

9.Signal as subject of pattern classification.

10.Generalization to 2D and 3D images.

Last update: Kukal Jaromír (13.06.2018)
Entry requirements -


Last update: Kukal Jaromír (13.06.2018)
Registration requirements -


Last update: Kukal Jaromír (13.06.2018)
Course completion requirements -

Preparing and defense of individual project followed by oral examination.

Last update: Kukal Jaromír (13.06.2018)