Generalized performance parameter for single-threshold detection systems

Abstract

A new generalized performance parameter for single-threshold detection systems is investigated that provides a more consistent measure of system performance than the conventional signal-to-noise ratio (SNR). It is shown explicitly that this parameter decreases monotonically as the Bayes risk and probability of error increase, and that it reduces to the SNR under appropriate conditions. An example is presented in which this parameter is monotonic with system performance, but the SNR is not. The analysis, which utilizes normalizing transformations, is also useful in the direct calculation of the Bayes risk, probability of error, and sensitivity, as is considered in detail subsequently (P. R. Prucnal, Applied Optics19, 3606 (1980)).