```
function IC = verhulst2015_ic(CN,fs,Tex,Tin,dly,Aic,Sic)
% VERHULST2015_IC inferior-colliculus model
%
% Usage: IC = verhulst2015_ic(CN,fs,Tex,Tin,dly,Aic,Sic)
%
% Inferior Colliculus model based on the same-frequency excitatory-inhibitory
% (SFEI) from Nelson and Carney (2004). This function implements
% Eq. 13 from Verhulst et al. (2015).
%
% License:
% --------
%
% This model is licensed under the UGent Academic License. Further usage details are provided
% in the UGent Academic License which can be found in the AMT directory "licences" and at
% <https://raw.githubusercontent.com/HearingTechnology/Verhulstetal2018Model/master/license.txt>.
%
% References:
% P. C. Nelson and L. Carney. A phenomenological model of peripheral and
% central neural responses to amplitude-modulated tones. J. Acoust. Soc.
% Am., 116(4), 2004.
%
% S. Verhulst, H. Bharadwaj, G. Mehraei, C. Shera, and
% B. Shinn-Cunningham. Functional modeling of the human auditory
% brainstem response to broadband stimulation. jasa, 138(3):1637--1659,
% 2015.
%
%
% Url: http://amtoolbox.org/amt-1.3.0/doc/modelstages/verhulst2015_ic.php
% #License: ugent
% #StatusDoc: Good
% #StatusCode: Good
% #Verification: Unknown
% #Requirements: MATLAB M-Signal PYTHON C
% #Author: Alejandro Osses (2020): primary implementation
% #Author: Piotr Majdak (2021): adaptations for the AMT 1.0
% This file is licenced under the terms of the UGent Academic License, which details can be found in the AMT directory "licences" and at <https://raw.githubusercontent.com/HearingTechnology/Verhulstetal2018Model/master/license.txt>.
% For non-commercial academic research, you can use this file and/or modify it under the terms of that license. This file is distributed without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose.
% #License: ugent
% #StatusDoc: Good
% #StatusCode: Good
% #Verification: Unknown
% #Requirements: MATLAB M-Signal PYTHON C
% #Author: Alejandro Osses (2020): primary implementation based on https://github.com/HearingTechnology/Verhulstetal2018Model
% #Author: Piotr Majdak (2021): adaptations for the AMT 1.0
if nargin < 3
Tex=0.5e-3;
end
if nargin < 4
Tin=2e-3;
end
if nargin < 5
dly = 2e-3; % default in Verhulst 2018
end
if nargin < 6
Aic=1;
end
if nargin < 7
Sic=1.5;
end
N_Tau = length(Tex);
for i = 1:N_Tau
Tex_here = Tex(i);
Tin_here = Tin(i);
dly_IC = dly(i);
Aic_here = Aic(i);
Sic_here = Sic(i);
inhibition_delay_samples = round(dly_IC*fs);
if iscell(CN)
CN_here = CN{i};
else
CN_here = CN;
end
L = size(CN_here,1);
delayed_inhibition = zeros(size(CN_here));
delayed_inhibition(inhibition_delay_samples+1:end,:) = CN_here(1:L-inhibition_delay_samples,:);
[bEx,aEx] = local_irrcoeff(Tex_here,fs);
[bIn,aIn] = local_irrcoeff(Tin_here,fs);
IC_excitatory = filter(bEx,aEx,CN_here);
IC_inhibitory = filter(bIn,aIn,delayed_inhibition);
IC{i} = Aic_here*(IC_excitatory-Sic_here*IC_inhibitory);
end
if N_Tau == 1
IC = IC{i};
end
function [num,den] = local_irrcoeff(Tau,fs)
% The filter characterised by the transfer function with num and den as the
% coefficients of the numerator and denominator, respectively, is obtained
% as normalised alpha functions. The design of this filter was done applying
% a bilinear transformation. This filter design is equivalent to the alpha
% functions described by Nelson and Carney (2004).
factor = 1/(2*fs*Tau+1)^2;
m = (2*fs*Tau-1)/(2*fs*Tau+1);
a0 = 1;
a1 = -2*m;
a2 = m^2;
b0 = 1;
b1 = 2;
b2 = 1;
num = [b0 b1 b2]*factor;
den = [a0 a1 a2];
```