Spectral estimation

In Figure 10 we did not care about spectral resolution, since we knew theoretically that the spectrum was white. But in practice we do not have such foreknowledge. Indeed, the random factors we deal with in nature rarely are white. A widely used model for naturally occurring random functions, such as microseism, or sometimes reflection seismograms, is white noise put into a filter. The spectra for an example of this type are shown in Figure 7. We can see that smoothing the envelope of the power spectrum of the output gives an estimate of the spectrum of the filter. But we also see that the estimate may need even more smoothing.