  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.
