A New Method for Finding Optimal Signal Detectors and Estimators in the Presence of Noise

摘要

A new method for finding solutions to the problems of (1) detecting a known signal in Gaussian noise, (2) detecting a Guassian signal in Gaussian noise, and (3) the problem of finding the best linear estimate of signals in noise. It is shown that all three problems can be reduced to the problem of solving a generalized integral equation. The main result is a new method for solving such equations. The method is general in that it is applicable to any ordinary integral equation with a positive definite kernel. (Author)