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

Abstract

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 freedomhalf the number available in Rayleigh noise.When asked to discriminate small differences in the am-. plitude of two sounds, human observers do not perform at the same level as an ideal observer that makes the best possible use of the information available in the waveforms. There is nothing remarkable in this, but the exact nature of the information not used by human observers is an open question. One possibility is that the discrepancy between ideal and human observers depends upon the waveform's bandwidth. For wide-band noise, Green (1960) and Irwin (1989) reported a discrepancy of 5-7 dB between ideal and human observers, but for an approximation to narrow-band noise, Ronken (1969) reported a discrepancy of only 0.7 dB. Ronken's (1969) results are important because he studied a special case of narrow-band noise known as Rayleigh noise. A band-limited noise waveform can be represented by a finite number of equally spaced discrete samples and, according to Shannon's sampling theorem, the number of samples required is equal to 2 WT, where W is the bandwidth of the noise in hertz and T is its duration in seconds. For Rayleigh noise, the duration is the reciprocal of the bandwidth and, therefore, 2WT = 2. This is a limiting case because every additional cycle of the noise's bandwidth requires two additional samples to represent it (Green & McGill, 1970). Furthermore, the energy in such a waveform is distributed as chi square with 2WT = 2 df. The amplitude of the waveform is dis-

Two Models for Estimating the Discriminability of Foods and Beverages

“…An important consideration in research of this kind is how many observers are required to obtain useful data. For detection-theoretic research into the senses other than taste it is customary to study only a few observers, each making many judgments (e.g., Hautus and Irwin 1992). The precision of estimated parameters is therefore derived from the number of judgments made, not from the number of observers.…”

Investigation of Test Performance Over Repeated Sessions Using Signal Detection Theory: Comparison of Three Nonattribute‐specified Difference Tests 2‐afcr, A‐not a and 2‐afc

“…To compare the performance of the three protocols over repeated sessions, d′ estimates, which indicate the perceptual difference between the two margarine products, “A” and “B” (Not A), were calculated for each protocol by fitting receiver operating characteristic (ROC) curves. ROC analysis software for the A‐Not A task was used, based on maximum likelihood estimation (software written by Hautus [1994], based on an algorithm by Dorfman and Alf [1969]). First, data from all subjects were pooled into a single response matrix for each session, and then the data for adjacent sessions (1st and 2nd, 3rd and 4th, 5th and 6th, and 7th and 8th) were combined to counterbalance order effects and to increase the response frequencies (Table 2).…”

Handbook of Research Methods in Human Operant Behavior

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