From: malcolm@interval.com (Malcolm Slaney)
Date: Sat, 28 Oct 1995 12:22:19 -0700
Subject: Cochlear Modelling and Gammatones at CCRMA
Message-Id: <v02120d05acb82d249cab@[199.170.108.19]>

As described at last week's CCRMA Hearing Seminar, the Gammatone function
is a useful model of auditory responses.  This week at the Hearing Seminar,
Dick Lyon will be exploring variations of the Gammatone and their
behaviour.  A simplified version of the Gammatone filter bank is a more
useful starting point for adaptive models of the cochlea.

        Who:    Richard F. Lyon (Apple)
        What:   Gammatone Filters for Auditory Modeling
        When:   Thursday November 2 at 11AM
        Where:  CCRMA Library (Top Floor of the Knoll at Stanford)

We have a schedule for the rest of the year.  Mark these dates in your
calendar and plan on attending the CCRMA Hearing Seminar.  I am especially
happy that we have a series of three talks related to auditory attention!

11/2    Richard Lyon (Apple) Gammatone Cochlear Models
11/9    Pierre Divenyi (VA) Pitch or Cocktail Party
11/16   Erv Hafter (UCB) Attention and Auditory Filters
11/23   No Seminar (Thanksgiving)
11/30   Diane Schiano (Interval) Cocktail Party Overview
12/7    Dick Duda (SJSU)  To Be Determined - Something related to binaural
12/14   Bev Wright (UCSF) To Be Determinded - Detection of Unexpected Sounds?

See you at CCRMA.

-- Malcolm
P.S.  This is a great chance for all of you to ask questions.... especially
for those of you that have given talks and had to answer Dick's questions
of your work :-)!


The All-Pole Gammatone Filter and Auditory Models

Richard F. Lyon
Apple Computer, Inc. m/s 301-3M
One Infinite Loop
Cupertino, CA 95014 USA
phone: (408) 974-4245, fax: (408) 974-8414

The All-Pole Gammatone Filter (APGF) is defined by discarding the zeros
from a pole-zero decomposition of the Gamma-Tone Filter (GTF) that was
popularized in auditory modeling by Johannesma, de Boer, Patterson, and
others. Equivalently, the order-N APGF is the Nth power of a filter with a
complex-conjugate pair of poles; the GTF has this same set of poles, but in
addition has "spurious" zeros on the real axis that complicate its
description and behavior. The One-Zero Gammatone Filter (OZGF) is also
introduced, by differentiating, or adding one zero at DC to, the APGF.
Order-3 GTF and OZGF were originally used by Flanagan in 1960 to model
Basilar Membrane motion. The APGF was recently named by Slaney as a useful
approximation to the GTF--the OZGF is now proposed as an even better
approximation.

The APGF does not have the simple time-domain description of the GTF (a
gamma distribution times a tone), but is simpler and more well-behaved in
other ways, and provides a more robust foundation for modeling and
analyzing a
variety of auditory data that involve filter asymmetry, frequencies well
below CF, level dependence, etc. The GTF magnitude frequency response is
approximately symmetric, while the APGF frequency response is inherently
asymmetric, being exactly symmetric in frequency-squared space. The
low-frequency tail of the APGF is unafffected by the bandwidth parameter,
unnlike the awkward behavior of the GTF, making the APGF (and OZGF)
suitable for a range of nonlinear and parametric applications not well
addressed by the GTF. Fixing the low-frequency tail gain, rather than the
peak gain, as parameters are varied with level, allows
better answers to questions about how the auditory system behaves across
levels, emphasizing approximate linearity at very low frequencies; varying
the damping parameter of the APGF poles can then be interpreted in terms of
automatic gain control (AGC) near CF. The APGF has a simple efficient
implementation, a cascade of N identical two-pole filter stages, and is
very closely related to the system of nonlinear differential equations of
Kim, Molnar, and Pfeiffer and to the even more efficient caascade
filterbank auditory models of Lyon and Mead.

Fitting the APGF parameters to cochlear mechanics data over a wide range of
intensity levels, using new simple gain-bandwidth-delay-order relations,
leads to an order estimate of 8 to 10, in contrast to the often-used GTF
orders of 3 and 4. The APGF provides an improved time-domain match to
Basilar Membrane mechanical impulse response measurements, with initial
zero-crossing intervals being stretched out, even at low orders. The APGF
concept is offered as a hub around which various other auditory modeling
approaches can be related, opening up an opportunity for better
understanding and cross fertilization.