annotate matlab/bmm/carfac/CARFAC_Detect.m @ 610:01986636257a

Second check-in of Alex Brandmeyer's C++ implementation of CARFAC. Addressed style issues and completed implementation of remaining functions. Still needs proper testing of the output stages against the MATLAB version, and runtime functions need improvements in efficiency.

% Copyright 2012 Google Inc. All Rights Reserved.
% Author: Richard F. Lyon
%
% This Matlab file is part of an implementation of Lyon's cochlear model:
% "Cascade of Asymmetric Resonators with Fast-Acting Compression"
% to supplement Lyon's upcoming book "Human and Machine Hearing"
%
% Licensed under the Apache License, Version 2.0 (the "License");
% you may not use this file except in compliance with the License.
% You may obtain a copy of the License at
%
%     http://www.apache.org/licenses/LICENSE-2.0
%
% Unless required by applicable law or agreed to in writing, software
% distributed under the License is distributed on an "AS IS" BASIS,
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
% See the License for the specific language governing permissions and
% limitations under the License.

function conductance = CARFAC_Detect(x_in)
% function conductance = CARFAC_detect(x_in)
% An IHC-like sigmoidal detection nonlinearity for the CARFAC.
% Resulting conductance is in about [0...1.3405]


a = 0.175;   % offset of low-end tail into neg x territory
% this parameter is adjusted for the book, to make the 20% DC
% response threshold at 0.1

set = x_in > -a;
z = x_in(set) + a;

% zero is the final answer for many points:
conductance = zeros(size(x_in));
conductance(set) = z.^3 ./ (z.^3 + z.^2 + 0.1);


%% other things I tried:
%
% % zero is the final answer for many points:
% conductance = zeros(size(x_in));
%
% order = 4;  % 3 is a little cheaper; 4 has continuous second deriv.
%
% % thresholds and terms involving just a, b, s are scalar ops; x are vectors
%
% switch order
%   case 3
%     a = 0.15;  % offset of low-end tail into neg x territory
%     b = 1; % 0.44;   % width of poly segment
%     slope = 0.7;
%
%     threshold1 = -a;
%     threshold2 = b - a;
%
%     set2 = x_in > threshold2;
%     set1 = x_in > threshold1 & ~set2;
%
%     s = slope/(2*b - 3/2*b^2);  % factor to make slope at breakpoint
%     t = s * (b^2 - (b^3) / 2);
%
%     x = x_in(set1) - threshold1;
%     conductance(set1) = s * x .* (x - x .* x / 2);  % x.^2 - 0.5x.^3
%
%     x = x_in(set2) - threshold2;
%     conductance(set2) = t + slope * x ./ (1 + x);
%
%
%   case 4
%     a = 0.24;  % offset of low-end tail into neg x territory
%     b = 0.57;   % width of poly segment; 0.5 to end at zero curvature,
%     a = 0.18;  % offset of low-end tail into neg x territory
%     b = 0.57;   % width of poly segment; 0.5 to end at zero curvature,
%     % 0.57 to approx. match curvature of the upper segment.
%     threshold1 = -a;
%     threshold2 = b - a;
%
%
%     set2 = x_in > threshold2;
%     set1 = x_in > threshold1 & ~set2;
%
%     s = 1/(3*b^2 - 4*b^3);  % factor to make slope 1 at breakpoint
%     t = s * (b^3 - b^4);
%
%     x = x_in(set1) - threshold1;
%     conductance(set1) = s * x .* x .* (x - x .* x);  % x.^3 - x.^4
%
%     x = x_in(set2) - threshold2;
%     conductance(set2) = t + x ./ (1 + x);
%
% end
%