```
function CN = verhulst2015_cn(summedAN,fs,Tex,Tin,dly,Acn,Scn)
%VERHULST2015_CN cochlear-nucleus model
%
% Usage: CN = verhulst2015_cn(summedAN,fs,Tex,Tin,dly,Acn,Scn)
%
% Cochlear nucleus model based on the same-frequency inhibitory-excitatory
% (SFIE) design from Nelson and Carney (2004). This function implements
% Eq. 12 from Verhulst et al. (2015).
%
% Make sure that the variables Tex, Tin, dly, Acn, Scn have the same dimensions.
%
% 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_cn.php
% #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
% 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.
if nargin < 3
Tex=0.5e-3; % Tau excitation
end
if nargin < 4
Tin=2e-3; % Tau inhibition
end
if nargin < 5
dly = 1e-3;
end
if nargin < 6
Acn=1.5;
end
if nargin < 7
Scn=0.6;
end
N_Tau = length(Tex);
L = size(summedAN,1);
for i = 1:N_Tau
Tex_here = Tex(i);
Tin_here = Tin(i);
dly_CN = dly(i);
Acn_here = Acn(i);
Scn_here = Scn(i);
inhibition_delay_samples = round(dly_CN*fs);
delayed_inhibition = zeros(size(summedAN));
delayed_inhibition(inhibition_delay_samples+1:end,:) = summedAN(1:L-inhibition_delay_samples,:);
[bEx,aEx] = local_irrcoeff(Tex_here,fs);
[bIn,aIn] = local_irrcoeff(Tin_here,fs);
CN_excitatory = filter(bEx,aEx,summedAN);
CN_inhibitory = filter(bIn,aIn,delayed_inhibition);
CN{i} = Acn_here*(CN_excitatory-Scn_here*CN_inhibitory);
end
if N_Tau == 1
CN = CN{1};
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];
```