A Note on the Estimation of Amplitude Spectra for Stochastic Processes with Quasi-Linear Residuals

Abstract

It is shown that when a deterministic signal is observed in quasi-linear noise (herein defined), the usual estimate of the signal amplitude spectrum for a finite time interval converges uniformly and exponentially fast in probability to this spectrum as the length of the time interval becomes infinite. When the limiting amplitude spectrum exists, the estimate tends to this function exponentially fast but no longer uniformly, in general.