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.