I. Introduction
The subject of signal detection and estimation deals with the processing of information-bearing signals in order to make inferences about the information that they contain. Series representations of stochastic processes is one of the most used techniques to solve such problems (for the estimation problem see, e.g., [1]–[4]; and for the signal detection problem [2], [5]–[7]). It is well known that the Karhunen–Loève (KL) expansion is the optimal representation in the sense that the mean-square error resulting from a finite representation of the process is minimized [8]. However, this expansion has two drawbacks in order to solve these problems.
From a theoretical point of view, the condition of continuity that has to be imposed on the covariance kernel is stronger than those required to solve the linear estimation problem [3], [4] or to ensure that the Gaussian signal detection problem is nonsingular [6]. Moreover, such an expansion is only valid on closed intervals of the real line.
From a practical standpoint, computation of the eigenfunctions and eigenvalues may be extremely involved.