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Physiological mechanism behind critical bands?
> Date: Fri, 5 Nov 2004 01:42:12 -0500
> From: Woojay Jeon <wjjeon@ECE.GATECH.EDU>
> Subject: physiological mechanism behind critical bands?
> Can anybody refer me to any sources that discuss the physiological mechanism
> in the auditory system that gives rise to critical bands? Are critical bands
> due purely to the spectral integration effect in the basilar membrane (which
> is usually simulated by cochlear filterbanks), or is there more processing
> done in higher processing levels (such as in the central auditory system)
> that gives rise to the critical band effect? Exactly which parts of the
> auditory system are responsible for critical bands and how?
> Woojay Jeon.
The Critical Band description was originally derived from measurements by Harvey Fletcher and after a process of a quarter century refined by Greenwood into a frequency-position function which has common characteristics but different coefficients for all mammals. Last year I published an evolutionary argument for the shape of the map, which carries through to describing the origin of the critical band function. The spacing of critical bands appears equal for the higher frequencies but is spatially compressed for lower frequencies. The argument goes like this: Lower vertebrates with "archetypal" cochleas such as turtles do not hear above 1kHz. Evolution required higher frequencies and higher resolution of frequency content. In order to achieve that without sacrificing the pre-evolved performance, an evolutionary compromise had to be established. The article shows, by taking coefficient data from the smallest to the largest mammals, that the traditional way of describing the frequency-position map as "straight" with an end correction for low frequencies is conceptually limiting. It is generalised to being described as "warped" over its whole length. The concept has some remarkable corollaries. No theory had yet explained why the cochlea of any mammal should have any particular length; since that is not determined by the extent of high frequency reception or animal size. By contrast, the length of the cochlea, and the shape of the map appears fixed by the behavioural need for the extent of low frequency reception, e.g. in whales. The theory may find new resonance amongst those who are researching development and maturation and are able to manipulate the genetic information in its study.
The reference is:
LePage, E. L. The mammalian cochlear map is optimally warped. J. Acoust.SocAm. 2003 Aug; 114(2):896-906.
Abstract: The form of the mammalian cochlear frequency-position map has been well described by Greenwood and empirical values found for its coefficients for a number of species. The apical portion of the mammalian map is spatially compressed relative to the base, and this nonuniformity in the representation of frequency is evidently consistent across species. However, an evolutionary reason for this consistency, encompassing critical band behavior with respect to position, is conspicuously missing. Likewise, the length of the cochlea in any mammal, including echolocating species, is related to body size, but attempts to explain the length in terms of frequency limits, range, or resolution have no general explanation. New insight stems from a hypothesis in which the map curvature may be appreciated as an adaptation for optimal frequency resolution over the auditory range. It is demonstrated numerically that the mammalian curve may be considered a member of a family of curves which vary in their degree of warp. The ‘‘warp factor’’ found to be common across mammals is an optimal trade-off between four conflicting constraints: (1) enhancing high-frequency resolution; (2) setting a lower bound on loss of existing low-frequency resolution; (3) minimizing map nonuniformity; and (4) keeping the whole map smooth, thereby avoiding reflections.
I can supply a pdf of the article for anyone interested.
Eric LePage, Ph.D.