Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions

Denote by B^sub 2σ,p^ (1 < p < ∞) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [-σ, σ]. It is shown that a function in B^sub 2σ,p^ can be reconstructed in L^sub p^() by its sampling sequences {f (κπ / σ)}^sub κ^ and {f' (κπ / σ)}^sub κ^...

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Bibliographic Details
Published in:Frontiers of mathematics in China 2006-06, Vol.1 (2), p.252-271
Main Authors: Li, Hu-an, Fang, Gen-sun
Format: Article
Language:English
Subjects:
Aliasing
Errors
Fourier transforms
Interpolation
Intervals
Mathematical analysis
Mathematical functions
Sampling
Theorems
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Summary:Denote by B^sub 2σ,p^ (1 < p < ∞) the bandlimited class p-integrable functions whose Fourier transform is supported in the interval [-σ, σ]. It is shown that a function in B^sub 2σ,p^ can be reconstructed in L^sub p^() by its sampling sequences {f (κπ / σ)}^sub κ^ and {f' (κπ / σ)}^sub κ^ using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to L^sub p^^sup r^ (), 1 < p < ∞, then the exact order of its aliasing error can be determined.[PUBLICATION ABSTRACT]
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-006-0006-x