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 [-?, ?]. It is shown that a function in B_2σ,p can be reconstructed in L_p(R) by its sampling sequences {f(k?/?)}_k∈Z and{f 2(k?/?)}_k∈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.