Application of the Kotel'nikov Theorem in the Problem of Differentiating Functions with Finite Spectrum on a Nonuniform Interpolation Grid

Using the Kotel'nikov theorem, we obtain formulas for the $L$-fold differentiation of messages with finite spectrum that are given by their samples on a nonuniform interpolation grid. We find upper bounds on the error of differentiation caused by the truncation of an information message in the spatial domain. We show the possibility of applying the results obtained to the differentiation of messages that are approximated by functions with finite spectrum up to a definite precision. We find corresponding estimates for the systematic and random differentiation errors.