Signal Recovery Using Splines

TL;DR

This paper investigates conditions for the existence and uniqueness of second- and third-order {}-interpolating splines for signal recovery, providing algorithms for their construction based on hardware convolution functions.

Contribution

It establishes conditions on hardware functions for the existence and uniqueness of certain interpolating splines and presents algorithms for their construction.

Findings

Conditions for existence of second- and third-order {}-interpolating splines.

Algorithms for constructing {}-interpolating splines.

Theoretical framework for 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.