  Various physics observables can be determined from the localisation of
distinct edge-like features in distributions of measurement values. In this
paper, we address the observation that neither differentiating nor fitting the
measured distributions is robust against significant fluctuations in the
experimental data. We propose the application of Finite Impulse Response (FIR)
filters instead. To demonstrate the method, we consider the typical case in
particle physics in which the precise localisation of kinematic edges, often
blurred by e.g.\ background contributions and detector effects, is crucial for
determining particle masses. We show that even for binned data, typical for
high energy physics, the optimal FIR filter kernel can be approximated by the
{\em first derivative of a Gaussian} (FDOG). We study two highly complementary
supersymmetric scenarios that, if realised in nature, could be observed at a
future high-energy $e^+e^-$ collider such as the International Linear Collider
(ILC) or the Compact Linear Collider (CLIC). The first scenario considers the
production of $\tilde{e}^{\pm}-$pairs while the second focuses on the
$\tilde{\chi}^{\pm}_{1}$ and $\tilde{\chi}^{0}_{2}$-pair production. We
demonstrate that the FIR filter method for edge extraction is superior to
previously employed methods in terms of robustness and precision.
