Signal Recovery Using Splines

Abstract

Practically, for all real measuring devices the result of a measurement is a convolution of an input signal with a hardware function of a unit {\phi}. We call a spline to be {\phi}-interpolating if the convolution of an input signal with a hardware function of a unit {\phi} coincides with the convolution of the spline with the hardware function. In the following article we consider conditions imposed on the hardware function {\phi} under which a second- and third-order {\phi}-interpolating spline exists and is unique. Algorithms of {\phi}-interpolating splines construction are written out.