Bastian,
That's an interesting distinction that needs to be made, between the peripheral and "whole system" auditory filter, whether gammatone or otherwise. In my book, I say this about that (in Part III – The Auditory Periphery):
13.1 What Is an Auditory Filter?
The auditory filters that we consider here include both those motivated by psychoacoustic experiments, such
as detection of tones in noise maskers, and those motivated by reproducing the observed mechanical response
of the basilar membrane or neural response of the auditory nerve. One thesis of this work is that a single
model can do a good job for both of these, and thereby provide a good basis for a machine hearing system.
Since there are several stages of neural processing between the cochlea and our psychoacoustic perceptions,
it would not be surprising if the best parameters were different between these types of models, but it seems
likely that the linear and nonlinear filtering due to the cochlea plays a sufficient role in perception that we may
find one set of parameters is adequate, at least for a range of machine hearing applications.
And to be fair, the gammatone was originally proposed as a model of frog hearing physiology, and is widely used in cochlear models, even though Patterson popularized it in the psychoacoustic domain.
Quibbles:
1. "The gammatoneFilterBank follows the algorithm described in [1] and first proposed by [2]." [1] is Slaney's method, a simple filter cascade based on analyzing the Laplace transform of the gammatone. [2] is Patterson et al.'s "Complex Sounds and Auditory Images", a great paper but it doesn't say one word about how to implement the gammatone (they did have other implementation papers elsewhere, but not this method and not here).
2. Ref 2 says "the shape of the magnitude characteristic of the gammatone filter is very similar to that of the roex(p) filter commonly used to represent the magnitude characteristic of the human auditory filter." Mathworks says "The gammatone filter is similar to the roex filter derived from the notched-noise
experiment." A cursory look at more recent literature on auditory filters, including Patterson's, would suggest omitting or at least tempering this claim. See my book Chapter 13 or this paper:
https://storage.googleapis.com/pub-tools-public-publication-data/pdf/36895.pdf
3. Error where it says b –– bandwidth, set to 1.019*erb2hz(fc). Either the documentation is wrong, or the functionality is wrong. Hopefully the former.
4. The parameterization by only FrequencyRange, NumFilters, and SampleRate is rather impoverished. It is not documented whether the filters match the ERB bandwidth if some of these parameters are changed, or whether adjacent filters continue to cross over about 3 dB down; you can't have both, but you might want one or the other, and there's not enough control to say what you want. With a few more parameters one could do useful comparisons, tradeoffs, and tunings of filter numbers, orders, bandwidths, and phases for example. With just a few more one could include better auditory filter variants (that differ only in the locations of the zeros of the cascaded second-order filters), including APGF and OZGF.
R2019a also adds gtcc (gammatone cepstral coefficients). Their algorithm uses log(energy) before the DCT, instead of the cube root proposed by the Shao et al. reference, which also uses a slightly different acronym: GFCC (gammatone frequency cepstral coefficients). Not clear why. The referenced paper did not really investigate whether their improvement over mfcc was due to the different frequency scale (700 Hz mel vs 229 Hz ERB break point between linear and exponential spacing), or the filter shape (triangle vs gammatone), or the nonlinearity (log vs cube root), or the domain of implementation (frequency vs time). With the impoverished parameterizations of these functions in the audio toolboxes, it's hard to further compare such things (though the gtcc does allow some of that). The other gtcc ref (Rabiner and Schafer) has nothing on gammatone or gtcc or gfcc.
I could go on...
Dick