Optimal order of truncation and aliasing errors for multi-dimensional Whittaker-Shannon sampling expansion

  • Authors:

  • Peixin Ye;Baohuai Sheng;Xiuhua Yuan

  • Affiliations:

  • School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, China;Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China;School of Mathematical Science, Nankai University, Tianjin 300071, China

  • Venue:
  • International Journal of Wireless and Mobile Computing
  • Year:
  • 2012

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Abstract

Optimal error bounds for multi-dimensional Shannon sampling expansion approximation are derived for both band-limited signals and some regular band-limited signals. Let Bpv(ℝd), 1 ≤ p < ∞, be the space of all bounded band-limited functions from Lp(Rn). The uniform bounds for truncated multi-dimensional Whittaker-Shannon series based on local sampling are derived for signal functions f∈ Bpv(ℝd) without decay assumption. Then the optimal bounds of aliasing and truncation errors for non-band-limited signal functions from Sobolev classes U(Wrp(ℝd)) with r ≥ d are obtained up to a logarithmic factor in their original OpenMP form and in the code form resulting from our translation is encouraging.