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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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Application of Chebyshev Basis for Spectral Analysis
Ettl, Ondřej ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
The work is focused on finding and verifying the basic properties of Chebyshev polynomials in Hilbert space. These include their generating functions, weight functions, orthogonality and recurrent relationships. Another goal was signal processing by Chebyshev’s transform and investigation of the resulting spectrum. Lastly the focus is shifted towards demostrain of two methods for modeling of frequency spectrum with help of Chebyshev polynomials.
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Application of Chebyshev Basis for Spectral Analysis
Ettl, Ondřej ; Jirgl, Miroslav (referee) ; Mihálik, Ondrej (advisor)
The work is focused on finding and verifying the basic properties of Chebyshev polynomials in Hilbert space. These include their generating functions, weight functions, orthogonality and recurrent relationships. Another goal was signal processing by Chebyshev’s transform and investigation of the resulting spectrum. Lastly the focus is shifted towards demostrain of two methods for modeling of frequency spectrum with help of Chebyshev polynomials.
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Non-metallic resistive low temperature thermometers
Duda, Daniel ; Rotter, Miloš (advisor) ; Janů, Zdeněk (referee)
temperature calibration has been carried out on series of resistors made of RuO2 of SMD type in the bath of normal and superfluid helium in temperatures at 1.4 - 4.2 K with reference thermometer of saturated vapor pressure. Measured temperature dependence of electrical resistance of resistors was analyzed using the exponential function and Chebychev's polynomials. It was established an optimum calibration for the use of resistors as thermometers.
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Non-metallic resistive low temperature thermometers
Duda, Daniel ; Rotter, Miloš (advisor) ; Janů, Zdeněk (referee)
temperature calibration has been carried out on series of resistors made of RuO2 of SMD type in the bath of normal and superfluid helium in temperatures at 1.4 - 4.2 K with reference thermometer of saturated vapor pressure. Measured temperature dependence of electrical resistance of resistors was analyzed using the exponential function and Chebychev's polynomials. It was established an optimum calibration for the use of resistors as thermometers.
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|
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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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