Inversion of finite filters

TL;DR

This paper introduces a method to decompose finitely supported filters into invertible and non-invertible parts, enabling direct inversion of the invertible component and analyzing how the non-invertible part affects signal resolution.

Contribution

It provides a novel decomposition approach for finite filters, distinguishing invertible and non-invertible components to facilitate signal processing tasks.

Findings

Invertible component can be directly inverted.

Non-invertible component reduces signal resolution.

Decomposition aids in understanding filter effects on signals.

Abstract

We present a decomposition of finitely supported filters ( aka instrument function PSF) as a composition of invertible and non-invertible filters. The invertible component can be inverted directly and the non-invertible component is shown to decrease the resolution of the acquired signal.