Scholarlink

<p>In this paper, we present new regularized Shannon sampling formulas related to the special affine Fourier transform (SAFT). These sampling formulas use localized sampling with special compactly supported, continuous window functions, namely B-spline, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10173_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sinh \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>sinh</mo> </math></EquationSource> </InlineEquation>-type, and continuous Kaiser–Bessel window functions. In contrast to the known Shannon sampling series for SAFT, the regularized Shannon sampling formulas for SAFT possesses an exponential decay of the approximation error and are numerically robust in the presence of noise, if certain oversampling condition is fulfilled.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Regularized Shannon Sampling Formulas Related to the Special Affine Fourier Transform

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年5月30日

查看全文
  • Frank Filbir,
  • Manfred Tasche

摘要

In this paper, we present new regularized Shannon sampling formulas related to the special affine Fourier transform (SAFT). These sampling formulas use localized sampling with special compactly supported, continuous window functions, namely B-spline, \(\sinh \) sinh -type, and continuous Kaiser–Bessel window functions. In contrast to the known Shannon sampling series for SAFT, the regularized Shannon sampling formulas for SAFT possesses an exponential decay of the approximation error and are numerically robust in the presence of noise, if certain oversampling condition is fulfilled.