A Model for a Self-Adapting Filter

This paper deals with a system which detects unknown, randomly occurring signals which are imbedded in Gaussian noise. A model for the system is set forth and analyzed using methods derived from probability theory. The system uses a variable threshold characteristic. Approximations are given for the mean and variance of the threshold at equilibrium, as a function of the signal-to-noise ratio, the a priori probabilities of signal occurrence, and the rate of decay of the threshold.