# Re: Roots of the term "gammatone"

And while we're on coincident roots ...


I looked a long time for uses of gammatone-like filters earlier and outside the hearing field. It seemed like such a simple structure (cascade of N resonators) and simple parameterization was sure to have been investigated before, and the connection to gamma distributions or gamma functions would likely have been noticed.


I eventually found some. Back in the day, before the use of impulse response was standard, people used to analyze filters by their step response (like when Karl Kupfmuller first described the ideal lowpass filter by its step response, the "integralsinus", as opposed to its modern description by its sinc function impulse response).


In 1945, Eaglesfield observed that the envelope step response of the cascade of N identical resonators is the "incomplete gamma function", which is the integral of the gamma distribution. So he shows the gamma distribution t^(N-1) exp(-t/tau) as an integrand; this envelope step response is implicitly multiplying a tone. So he had a gammatone filter, just not the name.


Tamas, I'll send you a copy. Also a paper by Tucker who investigated such filters, 1946, and quoted Eaglesfield on the "incomplete gamma function"; he also showed a fascinating alternative way to describe the envelope step response in an N-term closed form without the integral.

Dick

the refs:

@article{eaglesfield1945,
author = {C. C. Eaglesfield},

title = {Carrier Frequency Amplifiers: The Unit Step Response of Amplifiers with Single and Double Circuits},
  year = {1945},
journal = {Wireless Engineer},
volume = {22},
pages = {523--532}
}

@article{tucker1946,
author = {D. G. Tucker},
title = {Transient Response of Tuned-Circuit Cascades},
year = {1946},
journal = {Wireless Engineer},
volume = {23},
pages = {250--258}
}

At 8:36 AM -0700 3/28/12, Richard F. Lyon wrote:

Tamas,


I recounted some of those mis-attributions in http://dicklyon.com/tech/Hearing/APGF_Lyon_1996.pdf
and concluded:

Aertsen and Johannesma [AJ80] appear to have coined the catchy name;
referring to the envelope, they said:

The form m(t) appears both as the integrand in the definition
of the Gamma function $\Gamma(g)$ and as the density function
of the Gamma distribution, therefore we propose to use ... the
term "Gamma-tone" or "$\gamma$-tone."

... The non-hyphenated "gammatone," as an adjective modifying
"filter," appears to be due to Patterson et al. [P88].

Dick

At 10:05 AM +0200 3/28/12, Tamas Harczos wrote:

Dear List,

I am looking for the first time use of the term "gammatone". Flanagan
('65), Johannesma and de Boer ('72,'75) did not use that term. Patterson
et al. write in their '88 APU report "An efficient auditory filterbank
based on the gammatone function" that "Johannesma (1972) used this
function to summarize revcor data, although he did not refer to it as
the gammatone function, and the function was not fitted to revcor data.
The name appears to have been adopted by de Boer and de Jongh (1978)".
However, I am not able to find the term "gammatone" in the de Boer and
de Jongh paper "On cochlear encoding: Potentialities and limitations of
the reverse-correlation technique" JASA 63(1), 1978.

Any ideas?
Thanks!
Tamas

--
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Dipl.-Ing. Tamás Harczos
PhD Student
Institute for Media Technology
Faculty of Electr. Eng. and Inf. Techn.
Ilmenau University of Technology
Tel.: +49 3677 467 225
Fax.: +49 3677 467 4225
E-Mail: tamas.harczos@xxxxxxxxxxxxxxxxxx
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