Likelihood Detection of Small Signals in Stationary Noise

Abstract

An approximation to the likelihood ratio which may be used in detecting a small signal in stationary noise is derived. The result contains only low‐order moments of the signal and only stationary properties of the noise; hence it is applicable without change of form to any sufficiently long observation period. In the Gaussian case, with the signal also stationary and both signal and noise power spectra continuous, the result represents passage through a linear Eckart filter, followed by square law detection and equal‐weight smoothing.