Naslov
Closed-Form Approximation of Hilbert Transforms of Gaussian Derivatives Based on Weighted Polynomial Fitting

Autori
Molnar, Goran ; Miloš, Ante ; Vučić, Mladen

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of 41st International Convention on Information and Communication Technology, Electronics and Microelectronics / - , 2018, 123-127

ISBN
978-953-233-096-0

Skup
41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO 2018)

Mjesto i datum
Opatija, Hrvatska, 21.05.2018. - 25.05.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Gaussian derivatives, Hilbert transforms, least-squares approximation, polynomial fitting

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Elektrotehnika, Računarstvo

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