The role of the bandwidth-duration product WT in the detectability of diotic
Judi Lapsley Miller
A thesis submitted in fulfillment of the requirements for the degree of
Doctor of Philosophy in Psychology.
Victoria University of Wellington, New Zealand.
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 is 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
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.
This thesis is available to other researchers for personal use only. If you
find it useful or interesting, please get in touch.
08 Nov 2009 04:37 PM