Optimal order of truncation and aliasing errors for multi-dimensional Whittaker-Shannon sampling expansion
by Peixin Ye; Baohuai Sheng; Xiuhua Yuan
International Journal of Wireless and Mobile Computing (IJWMC), Vol. 5, No. 4, 2012

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 B^p_v(ℝ^d), 1 ≤ p < ∞, be the space of all bounded band-limited functions from L_p(Rⁿ). The uniform bounds for truncated multi-dimensional Whittaker-Shannon series based on local sampling are derived for signal functions f∈ B^p_v(ℝ^d) without decay assumption. Then the optimal bounds of aliasing and truncation errors for non-band-limited signal functions from Sobolev classes U(W^r_p(ℝ^d)) 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.

Online publication date: Sun, 11-Jan-2015

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