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Fractional order LTI SISO systems modelling using generalized Laguerre functions
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.
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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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Comparison Of Methods For Impulse Response Computation
Karsky, Vilem
This paper deals with obtaining impulse responses from integer order and fractional ordertransfer functions. There are shown three method how to compute inverse Laplace transform. The firstmethod is based on Mittag-Leffler functions, the second method is formed on generalized Laguerrefunctions and the third method lays on Fourier transform. These methods are also compared on twoexamples.
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Comparison Of Discretization Methods
Kárský, Vilém
This paper deals with discretization of the continuous systems. There will be presented two common methods how to do this job and one uncommon. The uncommon method is to look at the system as filter. So the system could be implemented as a FIR filter. In the end of this paper these methods will be compared.
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Optimal Parameters Of Generalized Laguerre Functions
Kárský, Vilém
This article concentrates on the Laguerre functions and on choosing optimal values of their free parameters. On an example there are compared errors in approximation using the Laguerre functions with different values of their free parameters. These free parameters were at first firmly selected, then they were calculated using mathematical moments, and in the end, their values were further corrected using the Newton’s method.
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Fractional order LTI SISO systems modelling using generalized Laguerre functions
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.
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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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