Generalized Optimum Receivers of Gaussian Signals

Consider the problem of discriminating between two zero-mean Gaussian signals by observing the sample function x(t), 0 ^ t ^ 1. We assume that their covariances Rx(s,t) and R>(s,t) are continuous and positive-definite on [0,1] X [0,1]. According to previous results,1'2'3 if the integral equation I [ Rl(s,u)H(u,v)R-2(vtt) dudv = R.,(s,t) - /?,(«,/), 0 ^ s,t ^ 1, J O Jo 577 (1)