Title: Optimal order of truncation and aliasing errors for multi-dimensional Whittaker-Shannon sampling expansion
Authors: Peixin Ye; Baohuai Sheng; Xiuhua Yuan
Addresses: 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
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.
Keywords: band-limited functions; Whittaker-Shannon theorem; localised sampling; truncation errors; aliasing errors; optimal order; Sobolev class; multi-dimensional sampling; optimal error bounds.
International Journal of Wireless and Mobile Computing, 2012 Vol.5 No.4, pp.327 - 333
Received: 16 Dec 2011
Accepted: 27 Dec 2011
Published online: 20 Jan 2013 *