Energy-Detection Model for Monaural Auditory Detection

Abstract

In the auditory detection of a sinusoidal signal in the presence of random noise, it has previously been demonstrated that the presence of a “pedestal” or background sinusoid of the same frequency and phase as the signal increases detectability. This increase was confirmed in a two-interval forced choice experiment in which a 1000-cps sinusoid was present in one of two 0.1-sec intervals, and the noise plus pedestal were present in both intervals. Pedestals of moderate intensity in phase with the signal increased detectability. Pedestals in quadrature (90° out of phase) with the signal did not improve detectability. Very large pedestals decreased detectability irrespective of phase. A simple energy-detection model was developed and its performance compared with the experimental results. The model consists of a bandpass filter, a square-law element, and an integrator. The probability of correct detection varies with signal level in a manner similar to the auditory results. Detectability is improved by an in-phase pedestal and approaches that of a correlation detector in the limit of infinite pedestal. Detectability is not improved by quadrate pedestals. The model can be modified to predict the decreasing detectability with large pedestals.

Masking functions and fixed-signal functions for low-level 1000-Hz tones

“…In a negative masking paradigm an investigator examines the behavior of DX DL for levels of X close to absolute threshold. The pedestal effect is best demonstrated in plots relating proportion correct to pedestal level (Pfafflin and Mathews, 1962); a plot we call the fixed-signal function. If the level of a signal, DX, is held constant while X varies, and a performance index such as proportion correct is measured, then it has been found that the addition of a pedestal around threshold enables an observer to distinguish the fixed level DX with greater ease than if no pedestal had been present (Green, 1960(Green, , 1966Laming, 1986;Pfafflin and Mathews, 1962).…”

“…The pedestal effect is best demonstrated in plots relating proportion correct to pedestal level (Pfafflin and Mathews, 1962); a plot we call the fixed-signal function. If the level of a signal, DX, is held constant while X varies, and a performance index such as proportion correct is measured, then it has been found that the addition of a pedestal around threshold enables an observer to distinguish the fixed level DX with greater ease than if no pedestal had been present (Green, 1960(Green, , 1966Laming, 1986;Pfafflin and Mathews, 1962). The nonmonotonic form of the fixed-signal function is not accommodated by Weber's law, which stipulates that as X increases the difference between X and XþDX must increase proportionally to maintain a fixed level of performance.…”

Auditory Intensity Discrimination

“…One is the detectability index for an energy detector. In this case, the detector is simply monitoring the energy in a band, W, with noise density, No, and trying to detect a potential signal of energy, E s ' and duration, T Pfaffiin and Mathews (1962) and Green and Swets (1966) have analyzed this case. To a good first approximation…”

The effect of a Poisson "internal noise" process on theoretical acoustic signal detectability

“…Historically, however, theoretical predictions of perception have often overestimated the capabilities of the human auditory system. The discrepancies between theorctical and experimcntal results were commonly corrected by adding a Gaussian noise source to the system (e.g., [2]). Howevcr, as this procedure was not physiologically-based, the parameters of the noise sourcc had to be adjusted for each detection problem, reducing the generality of the approach.…”

“…+ t t > 0 (2). Since the functional mapping is strictly monotonic, the probability density function can he derived using the formula, where ti = t ; ( y ) and .q'(t;) # 0[ I 11.…”