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A modification of the periodic nonuniform sampling involving derivatives with a Gaussian multiplier.

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Title: A modification of the periodic nonuniform sampling involving derivatives with a Gaussian multiplier.
Authors: Asharabi, Rashad M.1 (AUTHOR) rashad1974@hotmail.com, Khirallah, Mustafa Q.1 (AUTHOR)
Source: Calcolo. Nov2024, Vol. 61 Issue 4, p1-33. 33p.
Subjects: Irregular sampling (Signal processing), Approximation theory, Integral functions, Exponential functions, Sampling errors, Analytic functions
Abstract: The periodic nonuniform sampling series, involving periodic samples of both the function and its first r derivatives, was initially introduced by Nathan (Inform Control 22: 172–182, 1973). Since then, various authors have extended this sampling series in different contexts over the past decades. However, the application of the periodic nonuniform derivative sampling series in approximation theory has been limited due to its slow convergence. In this article, we introduce a modification to the periodic nonuniform sampling involving derivatives by incorporating a Gaussian multiplier. This modification results in a significantly improved convergence rate, which now follows an exponential order. This is a significant improvement compared to the original series, which had a convergence rate of O (N - 1 / p) where p > 1 . The introduced modification relies on a complex-analytic technique and is applicable to a wide range of functions. Specifically, it is suitable for the class of entire functions of exponential type that satisfy a decay condition, as well as for the class of analytic functions defined on a horizontal strip. To validate the presented theoretical analysis, the paper includes rigorous numerical experiments. [ABSTRACT FROM AUTHOR]
Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Calcolo%22">Calcolo</searchLink>. Nov2024, Vol. 61 Issue 4, p1-33. 33p.
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  Data: <searchLink fieldCode="DE" term="%22Irregular+sampling+%28Signal+processing%29%22">Irregular sampling (Signal processing)</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+functions%22">Integral functions</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink><br /><searchLink fieldCode="DE" term="%22Sampling+errors%22">Sampling errors</searchLink><br /><searchLink fieldCode="DE" term="%22Analytic+functions%22">Analytic functions</searchLink>
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  Data: The periodic nonuniform sampling series, involving periodic samples of both the function and its first r derivatives, was initially introduced by Nathan (Inform Control 22: 172–182, 1973). Since then, various authors have extended this sampling series in different contexts over the past decades. However, the application of the periodic nonuniform derivative sampling series in approximation theory has been limited due to its slow convergence. In this article, we introduce a modification to the periodic nonuniform sampling involving derivatives by incorporating a Gaussian multiplier. This modification results in a significantly improved convergence rate, which now follows an exponential order. This is a significant improvement compared to the original series, which had a convergence rate of O (N - 1 / p) where p > 1 . The introduced modification relies on a complex-analytic technique and is applicable to a wide range of functions. Specifically, it is suitable for the class of entire functions of exponential type that satisfy a decay condition, as well as for the class of analytic functions defined on a horizontal strip. To validate the presented theoretical analysis, the paper includes rigorous numerical experiments. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Approximation theory
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      – SubjectFull: Integral functions
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      – SubjectFull: Sampling errors
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              Text: Nov2024
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