The Role of the Bandwidth-Duration Product WT in the Detectability of Diotic Signals

<p>The bandwidth-duration product, WT , is a fundamental parameter in most theories of aural amplitude discrimination of Gaussian noise. These theories predict that detectability is dependent on WT , but not on the individual values of bandwidth and duration. Due to the acoustical uncertainty principle, it is impossible to completely specify an acoustic waveform with both finite duration and finite bandwidth. An observer must decide how best to trade-off information in the time domain with information in the frequency domain. As Licklider (1963) states, "The nature of [the ear's] solution to the time-frequency problem is, in fact, one of the central problems in the psychology of hearing."This problem is still unresolved, primarily due to observer inconsistency in experiments, which degrades performance making it difficult to compare models. The aim was to compare human observers' ability to trade bandwidth and duration, with simulated and theoretical observers. Human observers participated in a parametric study where the bandwidth and duration of 500 Hz noise waveforms was systematically varied for the same bandwidth-duration products (WT = 1, 2, and 4, where W varied over 2.5-160 Hz, and T varied over 400-6.25 ms, in octave steps). If observers can trade bandwidth and duration, detectability should be constant for the same WT . The observers replicated the experiments six times so that group operating characteristic (GOC) analysis could be used to reduce the effects of their inconsistent decision making. Asymptotic errorless performance was estimated by extrapolating results from the GOC analysis, as a function of replications added. Three simulated ideal observers: the energy, envelope, and full-linear (band-pass filter, full-wave rectifier, and true integrator) detectors were compared with each other, with mathematical theory and with human observers. Asymptotic detectability relative to the full-linear detector indicates that human observers best detect signals with a bandwidth of 40-80 Hz and a duration of 50-100 ms, and that other values are traded off in approximately concentric ellipses of equal detectability. Human detectability of Gaussian noise was best modelled by the full-linear detector using a non-optimal filter. Comparing psychometric functions for this detector with human data shows many striking similarities, indicating that human observers can sometimes perform as well as an ideal observer, once their inconsistency is minimised. These results indicate that the human hearing system can trade bandwidth and duration of signals, but not optimally. This accounts for many of the disparate estimates of the critical band, rectifier, and temporal integrator, found in the literature, because (a) the critical band is adjustable, but has a minimum of 40-50 Hz, (b) the rectifier is linear, rather than square-law, and (c) the temporal integrator is either true or leaky with a very long time constant.</p>

The Role of the Bandwidth-Duration Product WT in the Detectability of Diotic Signals

<p>The bandwidth-duration product, WT , is a fundamental parameter in most theories of aural amplitude discrimination of Gaussian noise. These theories predict that detectability is dependent on WT , but not on the individual values of bandwidth and duration. Due to the acoustical uncertainty principle, it is impossible to completely specify an acoustic waveform with both finite duration and finite bandwidth. An observer must decide how best to trade-off information in the time domain with information in the frequency domain. As Licklider (1963) states, "The nature of [the ear's] solution to the time-frequency problem is, in fact, one of the central problems in the psychology of hearing."This problem is still unresolved, primarily due to observer inconsistency in experiments, which degrades performance making it difficult to compare models. The aim was to compare human observers' ability to trade bandwidth and duration, with simulated and theoretical observers. Human observers participated in a parametric study where the bandwidth and duration of 500 Hz noise waveforms was systematically varied for the same bandwidth-duration products (WT = 1, 2, and 4, where W varied over 2.5-160 Hz, and T varied over 400-6.25 ms, in octave steps). If observers can trade bandwidth and duration, detectability should be constant for the same WT . The observers replicated the experiments six times so that group operating characteristic (GOC) analysis could be used to reduce the effects of their inconsistent decision making. Asymptotic errorless performance was estimated by extrapolating results from the GOC analysis, as a function of replications added. Three simulated ideal observers: the energy, envelope, and full-linear (band-pass filter, full-wave rectifier, and true integrator) detectors were compared with each other, with mathematical theory and with human observers. Asymptotic detectability relative to the full-linear detector indicates that human observers best detect signals with a bandwidth of 40-80 Hz and a duration of 50-100 ms, and that other values are traded off in approximately concentric ellipses of equal detectability. Human detectability of Gaussian noise was best modelled by the full-linear detector using a non-optimal filter. Comparing psychometric functions for this detector with human data shows many striking similarities, indicating that human observers can sometimes perform as well as an ideal observer, once their inconsistency is minimised. These results indicate that the human hearing system can trade bandwidth and duration of signals, but not optimally. This accounts for many of the disparate estimates of the critical band, rectifier, and temporal integrator, found in the literature, because (a) the critical band is adjustable, but has a minimum of 40-50 Hz, (b) the rectifier is linear, rather than square-law, and (c) the temporal integrator is either true or leaky with a very long time constant.</p>

The effect of a coding strategy that removes temporally masked pulses on speech perception by cochlear implant users

Speech recognition in noisy environments remains a challenge for cochlear implant (CI) recipients. Unwanted charge interactions between current pulses in the same and across different electrode channels are likely to impair performance. Here we investigate the effect of reducing the number of current pulses on speech perception. This was achieved by implementing a psychoacoustic temporal-masking model where current pulses in each channel were passed through a temporal integrator to identify and remove pulses that were less likely to be perceived by the recipient. The decision criterion of the temporal integrator was varied to control the percentage of pulses removed in each condition. In experiment 1, speech in quiet was processed with a standard Continuous Interleaved Sampling (CIS) strategy and with 25, 50 and 75% of pulses removed. In experiment 2, performance was measured for speech in noise with the CIS reference and with 50 and 75% of pulses removed. Speech intelligibility in quiet revealed no significant difference between reference and test conditions. For speech in noise, results showed a significant improvement of 2.4 dB when removing 50% of pulses. Performance both in quiet and in noise was not significantly different between the reference and when 75% of pulses were removed. Further, by reducing the overall amount of current pulses by 25, 50, and 75% but accounting for the increase in charge necessary to compensate for the decrease in loudness, estimated average power savings of 21.15, 40.95, and 63.45%, respectively, could be possible for this set of listeners. In conclusion, removing temporally masked pulses may improve speech perception in noise and result in substantial power savings.

Extrapolating for attaining high precision solutions for fractional partial differential equations

This paper aims at obtaining a high precision numerical approximation for fractional partial differential equations. This is achieved through appropriate discretizations: firstly we consider the application of shifted Legendre or Chebyshev polynomials to get a spatial discretization, followed by a temporal discretization where we use the Implicit Euler method (although any other temporal integrator could be used). Finally, the use of an extrapolation technique is considered for improving the numerical results. In this way a very accurate solution is obtained. An algorithm is presented, and numerical results are shown to demonstrate the validity of the present technique.