GENERALIZED HERMITE INTERPOLATION AND SAMPLING THEOREM INVOLVING DERIVATIVES

• Published : 2002.10.01

Abstract

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

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2. Generalized sinc-Gaussian sampling involving derivatives vol.73, pp.4, 2016, https://doi.org/10.1007/s11075-016-0129-4
3. Truncation error estimates for generalized Hermite sampling vol.74, pp.2, 2017, https://doi.org/10.1007/s11075-016-0159-y