A Pole-Zero Filter Cascade Provides Good Fits to Human Masking Data and to Basilar Membrane and Neural Data
Abstract
A cascade of two-pole–two-zero filters with level-dependent pole and zero dampings,
with few parameters, can provide a good match to human psychophysical and
physiological data. The model has been fitted to data on detection threshold for
tones in notched-noise masking, including bandwidth and filter shape changes over a
wide range of levels, and has been shown to provide better fits with fewer
parameters compared to other auditory filter models such as gammachirps. Originally
motivated as an efficient machine implementation of auditory filtering related to
the WKB analysis method of cochlear wave propagation, such filter cascades also
provide good fits to mechanical basilar membrane data, and to auditory nerve data,
including linear low-frequency tail response, level-dependent peak gain, sharp
tuning curves, nonlinear compression curves, level-independent zero-crossing times
in the impulse response, realistic instantaneous frequency glides, and appropriate
level-dependent group delay even with minimum-phase response. As part of exploring
different level-dependent parameterizations of such filter cascades, we have
identified a simple sufficient condition for stable zero-crossing times, based on
the shifting property of the Laplace transform: simply move all the $s$-domain
poles and zeros by equal amounts in the real-$s$ direction. Such pole-zero filter
cascades are efficient front ends for machine hearing applications, such as music
information retrieval, content identification, speech recognition, and sound
indexing.
