In Chapter , subroutine invint1() solved the problem of inverse linear interpolation, which is, given scattered data points, to find a function on a uniform mesh from which linear interpolation gives the scattered data points. To cope with regions having no data points, the subroutine requires an input roughening filter. This is a bit like specifying a differential equation to be satisfied between the data points. The question is, how should we choose a roughening filter? The importance of the roughening filter grows as the data gets sparser or as the mesh is refined.
Figures - suggest that the choice
of the roughening filter need not be subjective,
nor a priori,
but that the prediction-error filter (PEF) is the ideal roughening filter.
Spectrally, the PEF tends to the inverse of its input
hence its output tends to be ``level''.
Missing data that is interpolated with this ``leveler''
tends to have the spectrum of given data.