Aim of this thesis is provide basic information about characteristic function used in statistic and compare its properties with the Fourier transform used in engineering applications. First part of this thesis is theoretical, there are discussed basic concepts, their properties and mutual relations. The second part is devoted to some possible applications, for example normality testing of data or utilization of the characteristic function in independent component analysis. The first chapter describes the introduction to probability theory for the unification of terminology and mentioned concepts will be used to demonstrate the interesting properties of characteristic function. The second chapter describes the Fourier transform, definition of characteristic function and their comparison. The second part of this text is devoted to applications the empirical characteristic function is analyzed as an estimate of the characteristic function of examined data. As an example of application is describe a simple test of normality. The last part deals with more advanced applications of characteristic function for methods such as independent component analysis.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:220664 |
| Date | January 2014 |
| Creators | Mžourek, Zdeněk |
| Contributors | Mekyska, Jiří, Smékal, Zdeněk |
| Publisher | Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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