diff trunk/matlab/bmm/carfac/CARFAC_Detect.m @ 516:68c15d43fcc8

Added MATLAB code for Lyon's CAR-FAC filter cascade.

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/trunk/matlab/bmm/carfac/CARFAC_Detect.m	Wed Feb 15 21:26:40 2012 +0000
@@ -0,0 +1,92 @@
+% Copyright 2012, Google, Inc.
+% 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
+%