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

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Abstract

Denote by B 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 2σ,p can be reconstructed in L p(ℝ) by its sampling sequences {f (κπ / σ)} κ∈ℤ and {f’ (κπ / σ)} κ∈ℤ using the Hermite cardinal interpolation. Moreover, it will be shown that if f belongs to L r p (ℝ), 1 < p < ∞, then the exact order of its aliasing error can be determined.

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Authors and Affiliations

  1. College of Sciences, North China University of Technology, Beijing, 100041, China

    Li Hu-an

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Fang Gen-sun

Authors
  1. Li Hu-an
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  2. Fang Gen-sun
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Correspondence to Li Hu-an.

Additional information

Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education under grant number KM 200410009010 and by the Natural Science Foundation of China under grant number 10071006

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Li, Ha., Fang, Gs. Sampling theorem of Hermite type and aliasing error on the Sobolev class of functions. Front. Math. China 1, 252–271 (2006). https://doi.org/10.1007/s11464-006-0006-x

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  • DOI: https://doi.org/10.1007/s11464-006-0006-x

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