INTRODUCTION

Knowledge of signal spectrum and noise spectrum allows us to find filters for optimally separating data $\bold d$ into two components, signal $\bold s$and noise $\bold n$ Claerbout (1999). Actually, it is the inverses of these spectra which are required. In Claerbout's textbook example 1999 he estimates these inverse spectra by estimating prediction-error filters (PEFs) from the data. He estimates both a signal PEF and a noise PEF from the same data $\bold d$.A PEF based on data $\bold d$ might be expected to be named the data PEF D, but Claerbout estimates two different PEFS from $\bold d$and calls them the signal PEF S and the noise PEF N. They differ by being estimated with different number of adjustable coefficients, one matching a signal model (two plane waves) having three positions on the space axis, the other matching a noise model having one position on the space axis.

Meanwhile, using a different approach, Spitz (1999) concludes that the signal, noise, and data inverse spectra should be related by D=SN. The conclusion we reach in this paper is that Claerbout's estimate of S is more appropriately an estimate of the data PEF D. To find the most appropriate S and N we should use both the ``variable templates'' idea of Claerbout and the $D\approx SN$ idea of Spitz. Here we first provide a straightforward derivation of the Spitz insight and then we show some experimental results.