Translations:Least-squares prediction and smoothing/2/en

Often it is important to ascertain, in the least-squares sense, what the data would have been like without contamination by noise. Smoothing might be the complete problem to be addressed; alternatively, it might be combined with a prediction problem, which means that we wish to know what the uncontaminated signal will do in the future. Whereas the smoothing problem is clearly distinguishable from the prediction problem, mixed problems involving elements of both are greatly important. Indeed, good smoothing performance usually depends on introduction of a sufficient delay. If the delay is negative, filter performance suffers. On the other hand, the filter becomes a smoothing predictor, which often is a useful tool. Seismic processing must be innovative. Most geophysical data-processing methods are mathematical and physical hybrids and are based on a particular geophysical model.