Limiting forms of the discrete-time estimator- correlator detector (Corresp.)

Starting with the canonical discrete-time detection formula for random signals in Gaussian noise, we demonstrate how different noise models lead to different limiting forms Of the detector. A Brownian motion model leads to the well-known estimator-correlator formula. With a band-limited white noise model, the limiting form contains an additional term: the posterior conditional variance. This second form, which is the Radon-Nikodym derivative of two finitely additive Gaussian measures, was derived by Balakrishnan using a different formulation [10]. We thus provide an alternative development and interpretation of this second detector, and illustrate the effect of model assumptions on going from discrete-time to continuous-time problems.