Sharpening and edge-enhancement filters are often applied to geophysical data that were collected with an uneven sample spacing and varying sample density. In this paper we propose an alternative methodology to the usual gridding/digital filtering processing pathway. We first fit a continuous global surface (CGS) to the data and then implicitly apply Fourier domain filtering to the entire surface. The CGS is constructed to optimize some property of the surface (e.g. smoothness). We find that the best approach is to optimize the properties of the filtered surface rather than the surface that fits the data. Otherwise certain filters cause the transformed surface to have singularities at the data points. We demonstrate the viability of the methodology in the computation of the second vertical derivative of a gravity survey.