**
Singularities of interpolation of
2π
-periodic functions with a finite spectrum Fourier **

**
on the basis of the sampling theorem**

I. S.
Dmitriev, M. P. Slichenko

JSC «Sozvezdie
«Concern», Voronezh

The paper is received
on December 23, 2013

**Abstract.** The exact closed
expression is received, allowing to calculate values of 2π-periodic function with a finite
spectrum Fourier, and also its derivative of a random order in an arbitrary
point in the form of the final weighed sum of references of function on its
phase. The kernel of the received expansion is analysed.

**Keywords:** periodic function, finite
spectrum, interpolation, the sampling theorem.