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

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_p ^r (ℝ), 1 < p < ∞, then the exact order of its aliasing error can be determined.

Keywords

Marcinkiewicz type inequality / bandlimited function / derivative sampling / Sobolev classes of functions / aliasing error / 41A05 / 41A25

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