Closed-Form Approximation of Hilbert Transforms of Gaussian Derivatives Based on Weighted Polynomial Fitting (CROSBI ID 662332)
Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Molnar, Goran ; Miloš, Ante ; Vučić, Mladen
engleski
Closed-Form Approximation of Hilbert Transforms of Gaussian Derivatives Based on Weighted Polynomial Fitting
Hilbert transforms of Gaussian derivatives are related to Dawson's integral. Since this integral cannot be expressed in a closed form, various methods for the approximation of the derivatives have been developed. A closed-form approximation can be obtained by using the weighted polynomial fitting in which Gaussian function is used as the weighting function. Such an approach results in explicit approximation formulas. In literature, they are available only for the derivatives of the second, third, and fourth order. Furthermore, they utilize only low-order polynomials. In this paper, we propose an approximation of the Hilbert transforms of the Gaussian derivatives of arbitrary orders, which utilize high-order polynomials. The coefficients of these polynomials are obtained by using the least- squares error criterion. Closed-form expressions are provided for their calculation.
Gaussian derivatives, Hilbert transforms, least-squares approximation, polynomial fitting
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Podaci o prilogu
123-127.
2018.
objavljeno
Podaci o matičnoj publikaciji
Proceedings of 41st International Convention on Information and Communication Technology, Electronics and Microelectronics
978-953-233-096-0
Podaci o skupu
MIPRO 2018
predavanje
21.05.2018-25.05.2018
Opatija, Hrvatska
Povezanost rada
Elektrotehnika, Računarstvo