Amplitude discrimination of sinusoids and narrow-band noise with Rayleigh properties

The ability of human observers to discriminate differences in the amplitude of sinusoids and narrow-band noises was measured by the rating method of detection theory. Although each sinusoid (always 1000 Hz) was presented at a fixed amplitude, its amplitude on any trial was drawn from one of two Rayleigh probability distributions that differed in mean amplitude: a signal distribution and a noise distribution. Similarly, the amplitudes of the narrow-band noises were distributed as the Rayleigh distribution by virtue of the reciprocal relation between their bandwidth (100 Hz centered on 1000 Hz) and duration (10 msec). The obtained psychometric functions showing the area under the ROC as a function of signal-to-noise ratio were similar for both kinds of signals and were displaced, on average, about 4 dB from an ideal observer's function. The slopes of the obtained functions were similar to those of an ideal observer using 1 degree of freedom--half the number available in Rayleigh noise.