Error Estimate of a Gaussian Kernel Sampling Formula via Complex Analysis(Theory)

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  • Tanaka Ken'ichiro
    Graduate School of Information Science and Technology, University of Tokyo
  • Sugihara Masaaki
    Graduate School of Information Science and Technology, University of Tokyo
  • Murota Kazuo
    Graduate School of Information Science and Technology, University of Tokyo

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  • Gauss核サンプリング公式の複素関数論による誤差評価(理論)
  • Gauss核サンプリング公式の複素関数論による誤差評価
  • Gaussカク サンプリング コウシキ ノ フクソ カンスウロン ニ ヨル ゴサ ヒョウカ

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Abstract

For a sampling formula with the sinc-Gaussian kernel Qian et al. have recently given an error estimate for the class of band-limited functions with the aid of tools from Fourier analysis. By using complex analysis, we give in this paper an error estimate for a wider class of functions. Part of the result of Qian et al. can be derived from ours as an immediate corollary. Computational results show a fairly good agreement with the theoretical convergence rates.

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