# Adaptation (adaptationProc.m)¶

This processor corresponds to the adaptive response of the auditory nerve fibers, in which abrupt changes in the input result in emphasised overshoots followed by gradual decay to compressed steady-state level [Smith1977], [Smith1983]. The function is adopted from the Auditory Modeling Toolbox [Soendergaard2013]. The adaptation stage is modelled as a chain of five feedback loops in series. Each of the loops consists of a low-pass filter with its own time constant, and a division operator [Pueschel1988], [Dau1996], [Dau1997a]. At each stage, the input is divided by its low-pass filtered version. The time constant affects the charging / releasing state of the filter output at a given moment, and thus affects the amount of attenuation caused by the division. This implementation realises the characteristics of the process that input variations which are rapid compared to the time constants are linearly transformed, whereas stationary input signals go through logarithmic compression.

Table 21 List of parameters related to 'adaptation'.
Parameter Default Description
adpt_lim 10 Overshoot limiting ratio
adpt_mindB 0

Lowest audible threshold of the signal

in dB SPL

adpt_tau [0.005 0.050 0.129 0.253 0.500] Time constants of feedback loops
adpt_model ''(empty)

Implementation model 'adt_dau',

'adt_puschel', or 'adt_breebart'

can be used instead of the above three

parameters (See Table 22)

The adaptation processor uses three parameters to generate the output from the IHC representation: adpt_lim determines the maximum ratio of the onset response amplitude against the steady-state response, which sets a limit to the overshoot caused by the loops. adpt_mindB sets the lowest audible threshold of the input signal. adpt_tau are the time constants of the loops. Though the default model uses five loops and thus five time constants, variable number of elements of adpt_tau is supported which can vary the number of loops. Some specific sets of these parameters, as used in related studies, are also supported optionally with the adpt_model parameter. This can be given instead of the other three parameters, which will set them as used by the respective researchers. Table 21 lists the parameters and their default values, and Table 22 lists the supported models. The output signal is expressed in MU which deviates the input-output relation from a perfect logarithmic transform, such that the input level increment at low level range results in a smaller output level increment than the input increment at higher level range. This corresponds to a smaller just-noticeable level change at high levels than at low levels [Dau1996], [Jepsen2008], with the use of DRNL model for the BM stage, introduces an additional squaring expansion process between the IHC output and the adaptation stage, which transforms the input that comes through the DRNL-IHC processors into an intensity-like representation to be compatible with the adaptation implementation originally designed based on the use of gammatone filter bank. The adaptation processor recognises whether DRNL or gammatone processor is used in the chain and adjusts the input signal accordingly.

Table 22 List of supported models related to 'adaptation'.
adpt_model Description
'adt_dau'

Choose the parameters as in the models of [Dau1996], [Dau1997a].

This consists of 5 adaptation loops with an overshoot limit of 10 and

a minimum level of 0 dB. This is a correction in regard to the model

described in [Dau1996], which did not use overshoot limiting. The

adaptation loops have an exponentially spaced time constants

adpt_tau=[0.005 0.050 0.129 0.253 0.500]

'adt_puschel'

Choose the parameters as in the original model [Pueschel1988].

This consists of 5 adaptation loops without overshoot limiting

(adpt_lim=0). The adaptation loops have a linearly spaced time

constants adpt_tau=[0.0050 0.1288 0.2525 0.3762 0.5000].

'adt_breebaart' As 'adt_puschel', but with overshoot limiting

The effect of the adaptation processor - the exaggeration of rapid variations - is demonstrated in Fig. 24, where the output of the IHC model from the same input as used in the example of Inner hair-cell (ihcProc.m) (the right panel of Fig. 23) is compared to the adaptation output by running the script DEMO_Adaptation.m.

 [Dau1997a] (1, 2) Dau, T., Püschel, D., and Kohlrausch, A. (1997a), “Modeling auditory processing of amplitude modulation. I. Detection and masking with narrow-band carriers,” Journal of the Acoustical Society of America 102(5), pp. 2892–2905.
 [Pueschel1988] (1, 2) Püschel, D. (1988), “Prinzipien der zeitlichen Analyse beim Hören,” Ph.D. thesis, University of Göttingen.
 [Smith1977] Smith, R. L. (1977), “Short-term adaptation in single auditory nerve fibers: some poststimulatory effects,” J Neurophysiol 40(5), pp. 1098–1111.
 [Smith1983] Smith, R. L., Brachman, M. L., and Goodman, D. a. (1983), “Adaptation in the Auditory Periphery,” Annals of the New York Academy of Sciences 405(1 Cochlear Pros), pp. 79–93.