tom@516: % Copyright 2012, Google, Inc.
tom@516: % Author: Richard F. Lyon
tom@516: %
tom@516: % This Matlab file is part of an implementation of Lyon's cochlear model:
tom@516: % "Cascade of Asymmetric Resonators with Fast-Acting Compression"
tom@516: % to supplement Lyon's upcoming book "Human and Machine Hearing"
tom@516: %
tom@516: % Licensed under the Apache License, Version 2.0 (the "License");
tom@516: % you may not use this file except in compliance with the License.
tom@516: % You may obtain a copy of the License at
tom@516: %
tom@516: %     http://www.apache.org/licenses/LICENSE-2.0
tom@516: %
tom@516: % Unless required by applicable law or agreed to in writing, software
tom@516: % distributed under the License is distributed on an "AS IS" BASIS,
tom@516: % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
tom@516: % See the License for the specific language governing permissions and
tom@516: % limitations under the License.
tom@516: 
tom@516: function conductance = CARFAC_Detect(x_in)
tom@516: % function conductance = CARFAC_detect(x_in)
tom@516: % An IHC-like sigmoidal detection nonlinearity for the CARFAC.
tom@516: % Resulting conductance is in about [0...1.3405]
tom@516: 
tom@516: 
tom@516: a = 0.175;   % offset of low-end tail into neg x territory
tom@516: % this parameter is adjusted for the book, to make the 20% DC
tom@516: % response threshold at 0.1
tom@516: 
tom@516: set = x_in > -a;
tom@516: z = x_in(set) + a;
tom@516: 
tom@516: % zero is the final answer for many points:
tom@516: conductance = zeros(size(x_in));
tom@516: conductance(set) = z.^3 ./ (z.^3 + z.^2 + 0.1);
tom@516: 
tom@516: 
tom@516: %% other things I tried:
tom@516: %
tom@516: % % zero is the final answer for many points:
tom@516: % conductance = zeros(size(x_in));
tom@516: %
tom@516: % order = 4;  % 3 is a little cheaper; 4 has continuous second deriv.
tom@516: %
tom@516: % % thresholds and terms involving just a, b, s are scalar ops; x are vectors
tom@516: %
tom@516: % switch order
tom@516: %   case 3
tom@516: %     a = 0.15;  % offset of low-end tail into neg x territory
tom@516: %     b = 1; % 0.44;   % width of poly segment
tom@516: %     slope = 0.7;
tom@516: %
tom@516: %     threshold1 = -a;
tom@516: %     threshold2 = b - a;
tom@516: %
tom@516: %     set2 = x_in > threshold2;
tom@516: %     set1 = x_in > threshold1 & ~set2;
tom@516: %
tom@516: %     s = slope/(2*b - 3/2*b^2);  % factor to make slope at breakpoint
tom@516: %     t = s * (b^2 - (b^3) / 2);
tom@516: %
tom@516: %     x = x_in(set1) - threshold1;
tom@516: %     conductance(set1) = s * x .* (x - x .* x / 2);  % x.^2 - 0.5x.^3
tom@516: %
tom@516: %     x = x_in(set2) - threshold2;
tom@516: %     conductance(set2) = t + slope * x ./ (1 + x);
tom@516: %
tom@516: %
tom@516: %   case 4
tom@516: %     a = 0.24;  % offset of low-end tail into neg x territory
tom@516: %     b = 0.57;   % width of poly segment; 0.5 to end at zero curvature,
tom@516: %     a = 0.18;  % offset of low-end tail into neg x territory
tom@516: %     b = 0.57;   % width of poly segment; 0.5 to end at zero curvature,
tom@516: %     % 0.57 to approx. match curvature of the upper segment.
tom@516: %     threshold1 = -a;
tom@516: %     threshold2 = b - a;
tom@516: %
tom@516: %
tom@516: %     set2 = x_in > threshold2;
tom@516: %     set1 = x_in > threshold1 & ~set2;
tom@516: %
tom@516: %     s = 1/(3*b^2 - 4*b^3);  % factor to make slope 1 at breakpoint
tom@516: %     t = s * (b^3 - b^4);
tom@516: %
tom@516: %     x = x_in(set1) - threshold1;
tom@516: %     conductance(set1) = s * x .* x .* (x - x .* x);  % x.^3 - x.^4
tom@516: %
tom@516: %     x = x_in(set2) - threshold2;
tom@516: %     conductance(set2) = t + x ./ (1 + x);
tom@516: %
tom@516: % end
tom@516: %