The paper deals with the problem, frequently encountered in radar, of extracting simple numerical information from a noisy waveform. It is suggested that the only ideal way of doing this is to use the principle of inverse probability and convert the wave-form into a probability distribution for the quantity sought. The method is applied to the problem of determining the time delay of a periodically modulated rf waveform in the presence of white Gaussian noise when the undelayed waveform without noise is exactly known. As a result, the matched predetection filter of Van Vleck and Middleton is automatically specified, and the theory of ideal detection is briefly indicated.