Method of local peak functions for reconstructing the original profile in the Fourier transformation

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Method of local peak functions for reconstructing the original profile in the Fourier transformation. / Dosch, H.; Slavyanov, S. Yu.

в: Theoretical and Mathematical Physics, Том 131, № 1, 01.12.2002, стр. 459-467.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{e22476a718d44425a2ca306267d6548f,

title = "Method of local peak functions for reconstructing the original profile in the Fourier transformation",

abstract = "We propose a method for reconstructing the original profile function in the one-dimensional Fourier transformation from the module of the Fourier transform function analytically. The major concept of the method consists in representing the modeling profile function as a sum of local peak functions. The latter are chosen as eigenfunctions generated by linear differential equations with polynomial coefficients. This allows directly inverting the Fourier transformation without numerical integration. The solution of the inverse problem thus reduces to a nonlinear regression with a small number of optimizing parameters and to a numerical or asymptotic study of the corresponding modeling peak functions taken as the eigenfunctions of the differential equations and their Fourier transforms.",

author = "H. Dosch and Slavyanov, {S. Yu}",

year = "2002",

month = dec,

day = "1",

doi = "10.1023/A:1015145517620",

language = "English",

volume = "131",

pages = "459--467",

journal = "Theoretical and Mathematical Physics (Russian Federation)",

issn = "0040-5779",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Method of local peak functions for reconstructing the original profile in the Fourier transformation

AU - Dosch, H.

AU - Slavyanov, S. Yu

PY - 2002/12/1

Y1 - 2002/12/1

N2 - We propose a method for reconstructing the original profile function in the one-dimensional Fourier transformation from the module of the Fourier transform function analytically. The major concept of the method consists in representing the modeling profile function as a sum of local peak functions. The latter are chosen as eigenfunctions generated by linear differential equations with polynomial coefficients. This allows directly inverting the Fourier transformation without numerical integration. The solution of the inverse problem thus reduces to a nonlinear regression with a small number of optimizing parameters and to a numerical or asymptotic study of the corresponding modeling peak functions taken as the eigenfunctions of the differential equations and their Fourier transforms.

AB - We propose a method for reconstructing the original profile function in the one-dimensional Fourier transformation from the module of the Fourier transform function analytically. The major concept of the method consists in representing the modeling profile function as a sum of local peak functions. The latter are chosen as eigenfunctions generated by linear differential equations with polynomial coefficients. This allows directly inverting the Fourier transformation without numerical integration. The solution of the inverse problem thus reduces to a nonlinear regression with a small number of optimizing parameters and to a numerical or asymptotic study of the corresponding modeling peak functions taken as the eigenfunctions of the differential equations and their Fourier transforms.

UR - http://www.scopus.com/inward/record.url?scp=0036253560&partnerID=8YFLogxK

U2 - 10.1023/A:1015145517620

DO - 10.1023/A:1015145517620

M3 - Article

AN - SCOPUS:0036253560

VL - 131

SP - 459

EP - 467

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -

ID: 36182448