annotate matlab/bmm/carfac/CARFAC_Transfer_Functions.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.
% 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 [complex_transfns_freqs, ...
  stage_numerators, stage_denominators, group_delays] = ...
  CARFAC_Transfer_Functions(CF, freqs, to_channels, from_channels)
% function [complex_transfns_freqs, ...
%   stage_numerators, stage_denominators, group_delays] = ...
%   CARFAC_Transfer_Functions(CF, freqs, to_channels, from_channels)
%
% Return transfer functions as polynomials in z (nums & denoms);
% And evaluate them at freqs if it's given, to selected output,
%   optionally from selected starting points (from 0, input, by default).
%   complex_transfns_freqs has a row of complex gains per to_channel.

% always start with the rational functions, whether we want to return
% them or not; this defaults to ear 1 only:
[stage_numerators, stage_denominators] = CARFAC_Rational_Functions(CF);

if nargin >= 2
  % Evaluate at the provided list of frequencies.
  if ~isrow(freqs)
    if iscolumn(freqs)
      freqs = freqs';
    else
      error('Bad freqs_row in CARFAC_Transfer_Functions');
    end
  end
  if any(freqs < 0)
    error('Negatives in freqs_row in CARFAC_Transfer_Functions');
  end
  z_row = exp((i * 2 * pi / CF.fs) * freqs);  % z = exp(sT)
  gains = Rational_Eval(stage_numerators, stage_denominators, z_row);
  
  % Now multiply gains from input to output places; use logs?
  log_gains = log(gains);
  cum_log_gains = cumsum(log_gains);  % accum across cascaded stages
  
  % And figure out which cascade products we want:
  n_ch = CF.n_ch;
  if nargin < 3
    to_channels = 1:n_ch;
  end
  if isempty(to_channels) || any(to_channels < 1 | to_channels > n_ch)
    error('Bad to_channels in CARFAC_Transfer_Functions');
  end
  if nargin < 4 || isempty(from_channels)
    from_channels = 0;  % tranfuns from input, called channel 0.
  end
  if length(from_channels) == 1
    from_channels = from_channels * ones(1,length(to_channels));
  end
  % Default to cum gain of 1 (log is 0), from input channel 0:
  from_cum = zeros(length(to_channels), length(z_row));
  not_input = from_channels > 0;
  from_cum(not_input, :) = cum_log_gains(from_channels(not_input), :);
  log_transfns = cum_log_gains(to_channels, :) - from_cum;
  complex_transfns_freqs = exp(log_transfns);
  
  if nargout >= 4
    phases = imag(log_gains);  % no wrapping problem on single stages
    cum_phases = cumsum(phases);  % so no wrapping here either
    group_delays = -diff(cum_phases')';  % diff across frequencies
    group_delays = group_delays ./ (2*pi*repmat(diff(freqs), n_ch, 1));
  end
else
  % If no freqs are provided, do nothing but return the stage info above:
  complex_transfns_freqs = [];
end



function gains = Rational_Eval(numerators, denominators, z_row)
% function gains = Rational_Eval(numerators, denominators, z_row)
% Evaluate rational function at row of z values.

zz = [z_row .* z_row; z_row; ones(size(z_row))];
% dot product of each poly row with each [z2; z; 1] col:
gains = (numerators * zz) ./ (denominators * zz);



function [stage_numerators, stage_denominators] = ...
  CARFAC_Rational_Functions(CF, ear)
% function [stage_z_numerators, stage_z_denominators] = ...
%   CARFAC_Rational_Functions(CF, ear)
% Return transfer functions of all stages as rational functions.

if nargin < 2
  ear = 1;
end

n_ch = CF.n_ch;
coeffs = CF.ears(ear).CAR_coeffs;

a0 = coeffs.a0_coeffs;
c0 = coeffs.c0_coeffs;
zr = coeffs.zr_coeffs;

% get r, adapted if we have state:
r1 =  coeffs.r1_coeffs;  % max-damping condition
if isfield(CF.ears(ear), 'CAR_state')
  state = CF.ears(ear).CAR_state;
  zB = state.zB_memory; % current delta-r from undamping
  r = r1 + zB;
else
  zB = 0;  % HIGH-level linear condition by default
end

relative_undamping = zB ./ zr;
g = CARFAC_Stage_g(coeffs, relative_undamping);
a = a0 .* r;
c = c0 .* r;
r2 = r .* r;
h = coeffs.h_coeffs;

stage_denominators = [ones(n_ch, 1), -2 * a, r2];
stage_numerators = [g .* ones(n_ch, 1), g .* (-2 * a + h .* c), g .* r2];


%% example
% CF = CARFAC_Design
% f = (0:100).^2;  % frequencies to 10 kHz, unequally spaced
% to_ch = 10:10:96;  % selected output channels
% from_ch = to_ch - 10;  % test the inclusion of 0 in from list
% tf = CARFAC_Transfer_Functions(CF, f, to_ch, from_ch);
% figure
% plot(f, 20*log(abs(tf)')/log(10));  % dB vs lin. freq for 10 taps