# Re: Roots of the term "gammatone" ("Richard F. Lyon" )

Subject: Re: Roots of the term "gammatone"
From:    "Richard F. Lyon"  <DickLyon@xxxxxxxx>
Date:    Wed, 28 Mar 2012 12:22:41 -0700
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

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: @xxxxxxxx{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} } @xxxxxxxx{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 >> >>-- >>*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* >>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@xxxxxxxx >>*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*

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