SubjectsSubjects(version: 916)
Course, academic year 2022/2023
Advanced Methods of Signal Processing for PhD Students - AP445013
Title: Advanced Methods of Signal Processing for PhD Students
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021
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: unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
For type: doctoral
Note: can be fulfilled in the future
Guarantor: Mareš Jan doc. Ing. Ph.D.
Kukal Jaromír doc. Ing. Ph.D.
Interchangeability : P445013
Annotation -
Last update: Pátková Vlasta (19.11.2018)
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.
Aim of the course -
Last update: Pátková Vlasta (19.11.2018)

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.

Literature -
Last update: Pátková Vlasta (19.11.2018)

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.

Learning resources -
Last update: Pátková Vlasta (19.11.2018)

internal materials

Teaching methods -
Last update: Pátková Vlasta (19.11.2018)

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

Syllabus -
Last update: Pátková Vlasta (19.11.2018)

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.

Entry requirements -
Last update: Pátková Vlasta (19.11.2018)


Registration requirements -
Last update: Pátková Vlasta (19.11.2018)


Course completion requirements -
Last update: Pátková Vlasta (19.11.2018)

Preparing and defense of individual project followed by oral examination.