What question did this study set out to answer?

The aim is to determine the optimal method for deciding if an observed signal is noise or signal plus noise.

The theory of signal detectability

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This theoretical discussion derives optimal receiver methods for signal detection, indicating practical applications.

The aim is to determine the optimal method for deciding if an observed signal is noise or signal plus noise.
Derivation of likelihood ratio for various cases of signal detection.
Graphs of receiver operating characteristic (ROC) curves to evaluate detector performance.
Analysis of conditional probabilities related to error rates in detection.
The likelihood ratio receiver is optimal regardless of the method employed.
ROC curves quantify probabilities of detection and false alarms under different conditions.
Explicit formulas derived for probability detection and false alarms considering stationary white Gaussian noise.

Peterson et al. (1954) studied this question.

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