Scholarlink

<p>In the last two decades, sampling theorem expansions related to the linear canonical transform (LCT) domain have garnered considerable attention in both mathematics and engineering, despite their slow convergence rate. In this paper, we accelerate the recurrent nonuniform sampling expansion within the LCT domains by incorporating two different regularization kernels. The first kernel is a bandlimited function in the Fourier transform domain, while the second is a Gaussian kernel, which is not a bandlimited function in that domain. The first modification applies to functions within the Paley-Wiener space in the LCT domain, while the second modification is suitable for a broader range of functions within the Paley-Wiener space in the LCT domain, including entire functions that meet a decay condition and analytic functions defined on a horizontal strip. The convergence rate in the first modification improves, primarily due to the decay of the convergence factor. The second modification leads to a significantly improved convergence rate, now following an exponential order. To validate our theoretical analysis, we conduct rigorous numerical experiments.</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 recurrent nonuniform sampling formulations in the linear canonical transform domain

  • 期刊论文

  • 发表日期：

    2025年11月5日

查看全文
  • Rashad M. Asharabi,
  • Hamoud Al-Haddad

摘要

In the last two decades, sampling theorem expansions related to the linear canonical transform (LCT) domain have garnered considerable attention in both mathematics and engineering, despite their slow convergence rate. In this paper, we accelerate the recurrent nonuniform sampling expansion within the LCT domains by incorporating two different regularization kernels. The first kernel is a bandlimited function in the Fourier transform domain, while the second is a Gaussian kernel, which is not a bandlimited function in that domain. The first modification applies to functions within the Paley-Wiener space in the LCT domain, while the second modification is suitable for a broader range of functions within the Paley-Wiener space in the LCT domain, including entire functions that meet a decay condition and analytic functions defined on a horizontal strip. The convergence rate in the first modification improves, primarily due to the decay of the convergence factor. The second modification leads to a significantly improved convergence rate, now following an exponential order. To validate our theoretical analysis, we conduct rigorous numerical experiments.