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EXP_GAMMATONE - Creates various figures related to the Gammatone filters
Program code:
function exp_gammatone(varargin)
%EXP_GAMMATONE Creates various figures related to the Gammatone filters
% Usage: exp_gammatone(flags)
%
% EXP_GAMMATONE(flags) reproduces some figures from
% Patterson et al. (1987), Lyon (1997), and Hohmann (2002)
%
% The following flags can be specified;
%
% 'fig1_patterson1987'
%
% Reproduce Fig.1 from Patterson et al. (1987):
% The amplitude characteristics of three roex(p) filters
% centered at 427 Hz, 1000 Hz and 2089 Hz. The lower and
% upper filters are centered 6 ERBs below and above the
% 1000 Hz filter respectively. In each case, the range of
% the abscissa extends from an octave below to an octave
% above the centre frequency of the filter, on a linear
% frequency scale. The range of the ordinate is 40dB.
%
%
% 'fig2_patterson1987'
%
% Reproduce Fig.2 from Patterson et al. (1987):
% An array of 24 impulse responses for roex(p) filters
% whose centre frequencies ranges from 100 to 4000 Hz.
% The linear-phase assumption leads to symmetric impulse
% responses which have been aligned at their temporal
% mid-points.
%
%
% 'fig3_patterson1987'
%
% Reproduce Fig.3 similiar to Patterson et al. (1987):
% A cochleagram of four cycles of the [ae] in "past"
% produced by by a gammatone filterbank without phase
% compensation. The triangular objects are the upper
% three formants of the vowel. The duration of each
% period is ~8 ms. The ordinate is filter centre
% frequency of 189 equally spaced channels from 100 to
% 4000 Hz. Note the strong rightward skew induced by the
% phase lags of the low-frequency filters in the lower
% half of the figure.
%
%
% 'fig4_patterson1987'
%
% Reproduce Fig.4 similiar to Patterson et al. (1987):
% A cochleagram of four cycles of the [ae] in "past"
% produced by a gammatone filterbank with phase compensation.
% The coordinates are the same as for Figure 3. Note that
% the strong rightward skew produced by the phase lags of
% the lower frequency filters has been removed now.
%
%
% 'fig5_patterson1987'
%
% Reproduce Fig.5 from Patterson et al. (1987):
% An array of gamma impulse responses for a 24-channel
% auditory filterbank.(lower portion), and the equvalent
% array of gamma envelopes (upper portion). The range of
% abcissa is 25 ms; the filter centre frequencies range
% from 100 - 4,000 Hz.
%
%
% 'fig6_patterson1987'
%
% Reproduce Fig.6 from Patterson et al. (1987):
% A comparison of the gammatone(4,b) and roex(p) filters
% at three centre frequencies, 0.43, 1.00 and 2.09 kHz.
% In this case, the gammatone filter has been matched to
% the roex filter by equating the ERB, thus minimising
% the difference in the area under the curves. The range
% of the ordinate is 60 dB, the abscissa ranges from an
% octave below to an octave above the centre frequency in
% each case.
%
%
% 'fig7_patterson1987'
%
% Reproduce Fig.7 from Patterson et al. (1987):
% The comparison of the gammatone(4,b) and roex(p)
% filters at three centre frequencies (0.43, 1.00 and
% 2.09 kHz). In this case, the bandwidth of the gammatone
% filter has been increased by 10% to minimise the
% decibel difference between it and the roex filter. The
% range of the ordinate is 60 dB, and the abscissa ranges
% from an octave below to an octave above the centre
% frequency of the filter in each case.
%
%
% 'fig8_patterson1987'
%
% Reproduce Fig.8 from Patterson et al. (1987):
% A comparison of the gammatone(2,b) and the roex(p,w,t)
% filters at three centre frequencies (0.43, 1.00 and
% 2.09 kHz). The parameters for the roex filter are
% taken from Patterson et al (1982). The gammatone filter
% has been fitted to the roex by equating their ERBs.
% The range of the ordinate is 50dB, and the abscissa ranges
% from an octave below to an octave above the centren frequency,
% in each case.
%
%
% 'fig9_patterson1987'
%
% Reproduce Fig.9 from Patterson et al. (1987):
% A comparison of the gammatone(2,b) and the roex(p,w,t)
% filters at three centre frequencies (0.43, 1.00 and
% 2.09 kHz). In this case the roex parameters, w and t,
% have been adjusted to improve the fit to the
% gammatone(2,b) filter to show that the discrepancy can
% easily be minimised. The range of the ordinate is 50 dB,
% the abscissa shows a range from an octave below to an octave
% above the centre frequency of the filter in each case.
%
%
% 'fig10a_patterson1987'
%
% Reproduce Fig.10a from Patterson et al. (1987):
% The impulse responses for a gammatone auditory filterbank
% without phase compensation. The filterbank contains 37
% channels ranging from 100 to 5,000 Hz. The range of abcissa
% is 25 ms.
%
%
% 'fig10b_patterson1987'
%
% Reproduce Fig.10b from Patterson et al. (1987):
% The impulse responses for a gammatone auditory
% filterbank with envelope phase-compensation; that is,
% the peaks of the impulse-response envelopes have been
% aligned vertically. The filterbank contains 37 channels
% ranging from 100 to 5,000 Hz. The range of the abscissa
% is 25 ms.
%
%
% 'fig10c_patterson1987'
%
% Reproduce Fig.10c from Patterson et al. (1987):
% The impulse responses for a gammatone auditory filterbank
% with envelope and fine structure phase-compensation; that is,
% the envelope peaks have been aligned and then a fine structure
% peak has been aligned with the envelope peak. The filterbank
% contains 37 channels ranging from 100 to 5,000 Hz.
% The range of abcissa is 25 ms.
%
%
% 'fig11_patterson1987'
%
% Reproduce similiar to Fig.11 from Patterson et al. (1987):
% The impulse responses of a gammatone filterbank from a
% pulsetrain.
%
%
% 'fig1_lyon1997'
%
% Reproduce parts of Fig.1 from Lyon (1997) (no DAPGF):
% Comparison of GTF and APGF transfer function for two different
% values of the real part of the pole position. Notice that
% the ordering of gain near the peak for the classic gammatone
% filter is not maintained in the tail. The variation in the
% GTF tail is not accounted for by the usual phase-independent
% symetric GTF approximation.
%
%
% 'fig2_lyon1997'
%
% Reproduce parts of Fig.2 from Lyon (1997) (no DAPGF):
% Impulse responses of the APGF and sine-phased GTF from
% Figure 1. Note that the GTF's zero crossings are equally
% spaced in time, while those of the APGF are stretched out
% in early cycles.
%
%
% 'fig1_hohmann2002'
%
% Reproduce Fig.l from Hohmann (2002):
% Impulse response of the example Gammatone filter
% (center frequency fc = 1000 Hz; 3-db bandwidth fb = 100 Hz;
% sampling frequency fs = 10kHz). Solid and dashed lines
% show the real and imaginary part of the filter output,
% respectively. The absolute value of the filter output
% (dashdotted line) clearly represents the envelope.
%
%
% 'fig2_hohmann2002'
%
% Reproduce Fig.2 from Hohmann (2002):
% Frequency response of the example Gammatone filter
% (upper two panels) and of the real-to-imaginary
% response(lower two panels). Pi/2 was added to the phase
% of the latter (see text). The frequency axis goes up to
% half the sampling rate (z=pi).
%
%
% 'fig3_hohmann2002'
%
% Reproduce Fig.3 from Hohmann (2002):
% Magnitude frequency response of the Gammatone
% filterbank. In this example, the filter channel density
% is 1 on the ERB scale and the filter bandwidth is 1
% ERBaud. The sampling frequency was 16276Hz and the
% lower and upper boundary for the center frequencies
% were 70Hz and 6.7kHz, respectively.
%
%
% 'fig4_hohmann2002'
%
% Treatment of an impulse response with envelope maximum
% to the left of the desired group delay (at sample 65).
% The original complex impulse response (real part and
% envelope plotted in the upper panel) is multiplied with
% a complex factor and delayed so that the envelope maximum
% and the maximum of the real part coincide with the desired
% group delay (lower panel).
%
%
% Examples:
% ---------
%
% To display Fig. 1 from Patterson et al. (1987) use :
%
% exp_gammatone('fig1_patterson1987');
%
% To display Fig. 2 Patterson et al. (1987) use :
%
% exp_gammatone('fig2_patterson1987');
%
% To display Fig. 3 Patterson et al. (1987) use :
%
% exp_gammatone('fig3_patterson1987');
%
% To display Fig. 4 Patterson et al. (1987) use :
%
% exp_gammatone('fig4_patterson1987');
%
% To display Fig. 5 Patterson et al. (1987) use :
%
% exp_gammatone('fig5_patterson1987');
%
% To display Fig. 6 Patterson et al. (1987) use :
%
% exp_gammatone('fig6_patterson1987');
%
% To display Fig. 7 Patterson et al. (1987) use :
%
% exp_gammatone('fig7_patterson1987');
%
% To display Fig. 8 Patterson et al. (1987) use :
%
% exp_gammatone('fig8_patterson1987');
%
% To display Fig. 9 Patterson et al. (1987) use :
%
% exp_gammatone('fig9_patterson1987');
%
% To display Fig. 10a Patterson et al. (1987) at use :
%
% exp_gammatone('fig10a_patterson1987');
%
% To display Fig. 10b Patterson et al. (1987) at use :
%
% exp_gammatone('fig10a_patterson1987');
%
% To display Fig. 10c Patterson et al. (1987) at use :
%
% exp_gammatone('fig10c_patterson1987');
%
% To display Fig. 11 Patterson et al. (1987) use :
%
% exp_gammatone('fig11_patterson1987');
%
% To display Fig. 1 Lyon (1997) use :
%
% exp_gammatone('fig1_lyon1997');
%
% To display Fig. 2 Lyon (1997) use :
%
% exp_gammatone('fig2_lyon1997');
%
% To display Fig. 1 Hohmann (2002) use :
%
% exp_gammatone('fig1_hohmann2002');
%
% To display Fig. 2 Hohmann (2002) use :
%
% exp_gammatone('fig2_hohmann2002');
%
% To display Fig. 3 Hohmann (2002) use :
%
% exp_gammatone('fig3_hohmann2002');
%
% To display Fig. 4 Hohmann (2002) use :
%
% exp_gammatone('fig4_hohmann2002');
%
% References:
% V. Hohmann. Frequency analysis and synthesis using a gammatone
% filterbank. Acta Acustica united with Acoustica, 88(3):433--442, 2002.
%
% R. Lyon. All pole models of auditory filtering. In E. R. Lewis, G. R.
% Long, R. F. Lyon, P. M. Narins, C. R. Steele, and E. Hecht-Poinar,
% editors, Diversity in auditory mechanics, pages 205--211. World
% Scientific Publishing, Singapore, 1997.
%
% B. Moore and B. Glasberg. Suggested formulae for calculating
% auditory-filter bandwidths and excitation patterns. J. Acoust. Soc.
% Am., 74:750--753, 1983.
%
% R. Patterson, I. Nimmo-Smith, J. Holdsworth, and P. Rice. An efficient
% auditory filterbank based on the gammatone function. APU report, 2341,
% 1987.
%
%
% See also: gammatone exp_hohmann2002 demo_gammatone demo_hohmann2002 hohmann2002 hohmann2002_process
%
% Url: http://amtoolbox.sourceforge.net/amt-0.10.0/doc/experiments/exp_gammatone.php
% Copyright (C) 2009-2020 Piotr Majdak and the AMT team.
% This file is part of Auditory Modeling Toolbox (AMT) version 0.10.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% AUTHOR: CK, 2014
%% ------ Check input options --------------------------------------------
definput.import={'amtredofile'};
definput.keyvals.FontSize = 12;
definput.keyvals.MarkerSize = 6;
definput.flags.type = {'missingflag', 'fig1_patterson1987', 'fig2_patterson1987', ...
'fig3_patterson1987', 'fig4_patterson1987', 'fig5_patterson1987', 'fig6_patterson1987', ...
'fig7_patterson1987', 'fig8_patterson1987', 'fig9_patterson1987', ...
'fig10a_patterson1987', 'fig10b_patterson1987', 'fig10c_patterson1987', ...
'fig11_patterson1987', 'fig1_lyon1997', 'fig2_lyon1997',...
'fig1_hohmann2002', 'fig2_hohmann2002', 'fig3_hohmann2002', 'fig4_hohmann2002'};
% Parse input options
[flags,~] = ltfatarghelper({'FontSize','MarkerSize'},definput,varargin);
if flags.do_missingflag
flagnames=[sprintf('%s, ',definput.flags.type{2:end-2}),...
sprintf('%s or %s',definput.flags.type{end-1},definput.flags.type{end})];
error('%s: You must specify one of the following flags: %s.',upper(mfilename),flagnames);
end;
%% Pattersons Paper - Roex(p) Filter
% Figure 1;
if flags.do_fig1_patterson1987
% Global parameters:
fs = 25000; % Sampling frequency in Hz;
% Roex(p) at 1000 Hz;
% Parameters:
fc = 1000; % Center frequency in Hz;
df = 1/fc; % Distance on frequency scale in Hz;
g = (0:df:1-df); % Frequency scale;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape parameter;
% Equation 6 from paper Moore, 1983. (slopes are mirrored);
weight_l = (1+p.*g).*exp(-p.*g); % for lower slope;
weight_u = (1+p.*g).*exp(-p.*g); % for upper slope;
rp_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rp_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Plot;
figure('units','normalized','outerposition',[0 0.05 1 0.95])
subplot(1,3,2)
plot(rp_x, 10*log10(rp_y), 'b')
hold on
title('Roex(p) filters')
xlabel(['Roex(p) filter at ', num2str(fc), ' Hz center frequency'])
ylabel('Attenuation (dB) ')
xt = 0:0.2:2;
yt = -40:10:0;
axis([0 2 -40 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Roex(p) at 427 Hz;
% Parameters:
fc = 427; % Center frequency in Hz;
df = 1/fc; % Distance on frequency scale in Hz;
g = (0:df:1-df); % Frequency scale;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
% Equation 6 from paper Moore, 1983 (slopes are mirrored);
weight_l = (1+p.*g).*exp(-p.*g); % for lower slope;
weight_u = (1+p.*g).*exp(-p.*g); % for upper slope;
rp_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rp_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Plot;
subplot(1,3,1)
plot(rp_x, 10*log10(rp_y), 'b')
hold on
xlabel(['Roex(p) filter at ', num2str(fc), ' Hz center frequency'])
ylabel('Attenuation (dB) ')
xt = 0:0.2:2;
yt = -40:10:0;
axis([0 2 -40 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Roex(p) at 2089 Hz;
% Parameters:
fc = 2089; % Center frequency in Hz;
df = 1/fc; % Distance on frequency scale in Hz;
g = (0:df:1-df); % Frequency scale;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
% Equation 6 from paper Moore, 1983. (slopes are mirrored)
weight_l = (1+p.*g).*exp(-p.*g); % for lower slope;
weight_u = (1+p.*g).*exp(-p.*g); % for upper slope;
rp_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rp_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Plot;
subplot(1,3,3)
plot(rp_x, 10*log10(rp_y), 'b')
hold on
xlabel(['Roex(p) filter at ', num2str(fc), ' Hz center frequency'])
ylabel('Attenuation (dB) ')
xt = 0:0.2:2;
yt = -40:10:0;
axis([0 2 -40 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
end;
%% Pattersons Paper - Roex(p) Filter
% Figure 2
if flags.do_fig2_patterson1987
% Parameters:
fs = 20000; % Sampling frequency in Hz;
treal = 1:250; % Samples x-axis
fn = fs/2; % Nyquist frequency;
f = 0:fn; % Frequency vector
flow = 100; % ERB lowest center frequency Hz;
fhigh = 4000; % ERB highest center frequency Hz;
fc = erbspacebw(flow,fhigh); % 24 erb spaced channels;
nchannels = length(fc); % Number of channels
g = zeros(nchannels,fn+1);
erb = zeros(1,nchannels);
p = zeros(1,nchannels);
weight = zeros(nchannels,fn+1);
yfft = zeros(nchannels,fs);
yifft = zeros(nchannels,fs);
yshift = zeros(nchannels,fs);
for ii = 1:nchannels
g(ii,:) = abs(f(:)-fc(ii))./fc(ii); % Normalized distance from filter center
% Equation from paper Moore, 1983 found in text after Equation 6
erb(ii) = audfiltbw(fc(ii)); % Equivalent rectangular bandwidth;
p(ii) = 4*fc(ii)/erb(ii); % Filter shape
% Equation 6 from paper Moore, 1983 (slopes are mirrored);
weight(ii,:) = (1+p(ii).*g(ii,:)).*exp(-p(ii).*g(ii,:)); % Filter slope;
yfft(ii,:) = [weight(ii,:) fliplr(weight(ii,(2:end-1)))]; % Filter read for IFFT
yifft(ii,:) = (ifft(yfft(ii,:))); % IFFT
yshift(ii,:)= circshift(yifft(ii,:),[0 size(yifft,2)/2]); % Circular shift
end;
% Plot
figure ('units','normalized','outerposition',[0 0.05 1 0.95])
dy = 1;
for ii = 1:nchannels
plot(treal,25*yshift(ii,9875:10124)+dy);
hold on
dy = dy+1;
end;
title('Roex(p) filters')
xlabel('Sample')
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
yt = [1 4 8 12 16 20 24];
axis([0, 250, 0, 26]);
set(gca,'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz']})
box on
hold off
end;
%% Pattersons Paper - Classic Gammatone Filter
% Figure 3
% gammatone 'classic' (causalphase, real)
if flags.do_fig3_patterson1987
% Input parameters
x=amt_load('gammatone','a_from_past_uk.mat'); % Load mat-file with vowel a in variable insig and sampling frequency in variable fs;
fs=x.fs;
ts = 1/fs; % Time between sampling points in s;
insig = x.data(:,1).'; % Extract one channel from signal;
insig = insig(610:963); % Extract ~8 ms;
insig = insig-mean(insig); % Removes DC;
insig = [insig insig insig insig insig insig insig insig]; % 8 cycles;
nchannels = 189; % Number of channels in filterbank;
N=length(insig); % Length of signal;
treal = (1:N)*ts*1000; % Time axis in ms;
flow = 150; % Lowest center frequency in Hz;
fhigh = 4000; % Highest center frequency in Hz;
fc = erbspace(flow,fhigh,nchannels); % 189 erb-spaced channels;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'classic');
% Filters impulse signal with filter coefficients from above.
outsig = real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot;
figure ('units','normalized','outerposition',[0 0.05 1 0.95])
hold on
dy = 1;
for ii = 1:nchannels
plot(treal,24*outsig(ii,:)+dy)
dy = dy+1;
end;
title ([num2str(nchannels), ' channel array of gammatone impulse responses of vowel a from past'])
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
set(gca, 'Xlim', [20 56], 'Ylim', [1 189])
yt = [1 20 40 60 80 100 120 140 160 180 189];
set(gca, 'YTick', yt )
set(gca,'YTickLabel', {['#001: ' num2str(round(fc(1))) ' Hz'] ,['#020: ' num2str(round(fc(20))) ' Hz'] , ...
['#040: ' num2str(round(fc(40))) ' Hz'] , ['#060: ' num2str(round(fc(60))) ' Hz'], ...
['#080: ' num2str(round(fc(80))) ' Hz'], ['#100: ' num2str(round(fc(100))) ' Hz'], ...
['#120: ' num2str(round(fc(120))) ' Hz'], ['#140: ' num2str(round(fc(140))) ' Hz'], ...
['#160: ' num2str(round(fc(160))) ' Hz'], ['#180: ' num2str(round(fc(180))) ' Hz'],['#189: ' num2str(round(fc(189))) ' Hz']})
box on
hold off
end;
%% Pattersons Paper - Classic Gammatone Filter
% Figure 4
% gammatone 'classic' (causalphase, real)
if flags.do_fig4_patterson1987
% Input parameters
x=amt_load('gammatone','a_from_past_uk.mat'); % Load mat-file with vowel a in variable insig and sampling frequency in variable fs;
fs=x.fs;
ts = 1/fs; % Time between sampling points in s;
insig = x.data(:,1).'; % Extract one channel from signal;
insig = insig(610:963); % Extract ~8 ms;
insig = insig-mean(insig); % Removes DC;
insig = [insig insig insig insig insig insig insig insig]; % 8 cycles;
nchannels = 189; % Number of channels in filterbank;
N=length(insig); % Length of signal;
treal = (1:N)*ts*1000; % Time axis in ms;
flow = 150; % Lowest center frequency in Hz;
fhigh = 4000; % Highest center frequency in Hz;
fc = erbspace(flow,fhigh,nchannels); % 189 erb-spaced channels;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'classic','exppeakphase');
% Filters impulse signal with filter coefficients from above.
outsig = real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Impulse response of filter;
impulse = [1 zeros(1,352)];
outimp = real(ufilterbankz(b,a,impulse));
outimp = permute(outimp,[3 2 1]);
% Find impulse response envelopes maximums;
envmax = zeros(1,nchannels);
for ii = 1:nchannels
envmax(ii) = find( abs(outimp(ii,:)) == max(abs(outimp(ii,:))));
end;
% Delay output so the impulse response envelopes peak above each other;
for ii = 1:nchannels
% Time to delay
delay = zeros(1,(max(envmax(:))+1) - envmax(ii));
% Add delay
outsig(ii,:) = [delay outsig(ii,1:N - length(delay))];
end;
% Plot;
figure ('units','normalized','outerposition',[0 0.05 1 0.95])
hold on
dy = 1;
for ii = 1:nchannels
plot(treal,24*outsig(ii,:)+dy)
dy = dy+1;
end;
title ([num2str(nchannels), ' channel array of gammatone impulse responses of vowel a from past'])
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
set(gca, 'Xlim', [20 56], 'Ylim', [1 189])
yt = [1 20 40 60 80 100 120 140 160 180 189];
set(gca, 'YTick', yt )
set(gca,'YTickLabel', {['#001: ' num2str(round(fc(1))) ' Hz'] ,['#020: ' num2str(round(fc(20))) ' Hz'] , ...
['#040: ' num2str(round(fc(40))) ' Hz'] , ['#060: ' num2str(round(fc(60))) ' Hz'], ...
['#080: ' num2str(round(fc(80))) ' Hz'], ['#100: ' num2str(round(fc(100))) ' Hz'], ...
['#120: ' num2str(round(fc(120))) ' Hz'], ['#140: ' num2str(round(fc(140))) ' Hz'], ...
['#160: ' num2str(round(fc(160))) ' Hz'], ['#180: ' num2str(round(fc(180))) ' Hz'],['#189: ' num2str(round(fc(189))) ' Hz']})
box on
hold off
end;
%% Pattersons Paper - Classic Gammatone Filter
% Figure 5
% gammatone 'classic' (causalphase, real)
if flags.do_fig5_patterson1987
% Input parameters
fs = 25000; % Sampling frequency in Hz;
ts = 1/fs; % Time between sampling points in s
N=4096; % Length of signal;
treal = (1:N)*ts*1000; % Time axis in ms;
flow = 100; % ERB lowest center frequency Hz;
fhigh = 4000; % ERB highest center frequency Hz;
fc = erbspacebw(flow,fhigh); % Array of centre frequencies in Hz;
nchannels = length(fc); % Number of channels
insig = zeros(1,N); % Impulse as input signal;
insig(1) = 1;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'classic');
% Filters impulse signal with filter coefficients from above.
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Lower figure;
figure('units','normalized','outerposition',[0.5 0.1 0.5 0.9])
subplot(2,1,2)
hold on
dy = 1;
for ii = 1:size(outsig,1)
plot(treal,14*outsig(ii,:) + dy)
dy = dy + 1;
end;
clear dy;
title ([ num2str(nchannels),' channel array of gamma impulse responses (classic)'])
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
xt = 0:5:27;
yt = [1 4 8 12 16 20 24];
axis([0, 25, 0, 26]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz']})
box on
hold off
% Upper figure;
subplot(2,1,1)
hold on
dy = 1;
for ii = 1:size(outsig,1)
env = abs(hilbert(outsig(ii,:),N));
plot(treal,(14*env)+dy)
dy = dy+1;
end;
title ([num2str(nchannels),' channel array of gamma impulse responses envelopes (classic)'])
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
xt = 0:5:25;
yt = [1 4 8 12 16 20 24];
axis([0, 25, 0, 26]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(fc(1),'%6.2f') ' Hz'] , ['#04: ' num2str(fc(4),'%6.2f') ' Hz'], ...
['#08: ' num2str(fc(8),'%6.2f') ' Hz'], ['#12: ' num2str(fc(12),'%6.2f') ' Hz'], ...
['#16: ' num2str(fc(16),'%6.2f') ' Hz'], ['#20: ' num2str(fc(20),'%6.2f') ' Hz'], ...
['#24: ' num2str(fc(24),'%6.2f') ' Hz']})
box on
hold off
end;
%% Pattersons Paper - Roex(pwt) Filter
% Figure 6
if flags.do_fig6_patterson1987
% Global parameters:
fs = 25000; % Sampling frequency in Hz;
df = 1/1000; % Frequency resolution roex(pwt);
g = 0:df:1-df; % Frequency axis roex(pwt);
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis gammatone;
% Roex(p) at 1000 Hz;
% Parameters:
fc = 1000; % Center frequency in Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.002; % Realtive weight for second exponatial;
t = 0.4*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency axis;
% Gammatone filter at 1000 Hz center frequency;
% Parameters:
fc = 1000; % Center frequency in Hz;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 4; % Filter order;
betamul = 1.02; % Filter bandwidth;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filter impulse signal;
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
% Normalize to 0;
outsigfft = (outsigfft)/max(outsigfft);
% Plot;
figure('units','normalized','outerposition',[0 0.05 1 0.95])
subplot(1,3,2)
plot(rpwt_x, 10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
title('Roex(pwt) filters in blue vs. Gammatone classic in red')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -60:10:0;
axis([0 2 -60 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Roex(p) at 427 Hz
% Parameters:
fc = 427; % Center frequency in Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.002; % Realtive weight for second exponatial;
t = 0.4*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency axis;
% Gammatone filter at 427 Hz center frequency;
% Parameters:
fc = 427; % Center frequency in Hz;
ind = find(f/fc > 2,1); % Index where Frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 4; % Filter order;
betamul = 1.02; % Filter bandwidth;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filter impulse signal;
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
% Normalize to 0;
outsigfft = (outsigfft)/max(outsigfft);
% Plot;
subplot(1,3,1)
plot(rpwt_x, 10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -60:10:0;
axis([0 2 -60 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Roex(p) at 2089 Hz;
% Parameters:
fc = 2089; % Center frequency in Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.002; % Realtive weight for second exponatial;
t = 0.4*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency axis;
% Gammatone filter at 2089 Hz center frequency;
% Parameters:
fc = 2089; % Center frequency in Hz;
ind = find(f/fc > 2,1); % Index where Frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 4; % Filter order;
betamul = 1.02; % Filter bandwidth;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filter impulse signal;
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
% Normalize to 0;
outsigfft = (outsigfft)/max(outsigfft);
% Plot;
subplot(1,3,3)
plot(rpwt_x, 10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -60:10:0;
axis([0 2 -60 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
end;
%% Pattersons Paper - Roex(pwt) Filter
% Figure 7
if flags.do_fig7_patterson1987
% Global parameters:
fs = 25000; % Sampling frequency in Hz;
df = 1/1000; % Frequency resolution roex(pwt);
g = 0:df:1-df; % Frequency axis roex(pwt);
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis gammatone;
% Roex(p) at 1000 Hz;
% Parameters:
fc = 1000; % Center frequency in Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.002; % Realtive weight for second exponatial;
t = 0.4*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency axis;
% Gammatone filter at 1000 Hz center frequency;
% Parameters:
fc = 1000; % Center frequency in Hz;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 4; % Filter order;
betamul = 1.02*1.1; % Filter bandwidth;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filter impulse signal;
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
% Normalize to 0;
outsigfft = (outsigfft)/max(outsigfft);
% Plot;
figure('units','normalized','outerposition',[0 0.05 1 0.95])
subplot(1,3,2)
plot(rpwt_x, 10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
title('Roex(pwt) filters in blue vs. Gammatone classic in red')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -60:10:0;
axis([0 2 -60 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Roex(p) at 427 Hz;
% Parameters:
fc = 427; % Center frequency in Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.002; % Realtive weight for second exponatial;
t = 0.4*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency axis;
% Gammatone filter at 427 Hz center frequency;
% Parameters:
fc = 427; % Center frequency in Hz;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 4; % Filter order;
betamul = 1.02*1.1; % Filter bandwidth;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
% Normalize to 0;
outsigfft = (outsigfft)/max(outsigfft);
% Plot;
subplot(1,3,1)
plot(rpwt_x, 10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -60:10:0;
axis([0 2 -60 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Roex(p) at 2089 Hz;
% Parameters:
fc = 2089; % Center frequency in Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.002; % Realtive weight for second exponatial;
t = 0.4*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency axis;
% Gammatone filter at 2089 Hz center frequency;
% Parameters:
fc = 2089; % Center frequency in Hz;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 4; % Filter order;
betamul = 1.02*1.1; % Filter bandwidth;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
% Normalize to 0;
outsigfft = (outsigfft)/max(outsigfft);
% Plot;
subplot(1,3,3)
plot(rpwt_x, 10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -60:10:0;
axis([0 2 -60 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
end;
%% Pattersons Paper - Roex(pwt)
% Figure 8
if flags.do_fig8_patterson1987
% Global parameters:
fs = 25000; % Sampling frequency in Hz;
df = 1/1000; % Frequency resolution roex(pwt);
g = 0:df:1-df; % Frequency axis roex(pwt);
% Roex(pwt) filters at 427 Hz;
% Parameters:
fc = 427; % Center frequency at 427 Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.0025; % Realtive weight for second exponatial;
t = 0.2*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Gammatone filter at 427 Hz center frequency;
% Parameters:
fc = 427; % Center frequency at 427 Hz;
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 2; % Filter order;
betamul = 0.6; % ERB multiplicator;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filter impulse signal;
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
%Normalize;
outsigfft = (outsigfft)/max((outsigfft));
% Plot;
figure('units','normalized','outerposition',[0 0.05 1 0.95])
subplot(1,3,1)
plot(rpwt_x,10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -50:10:0;
axis([0 2 -50 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Filters at 1000 Hz;
% Parameters:
fc = 1000; % Center frequency at 427 Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.0025; % Realtive weight for second exponatial;
t = 0.2*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Gammatone filter at 1000 Hz center frequency;
% Parameters:
fc = 1000; % Center frequency at 427 Hz;
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 2; % Filter order;
betamul = 0.6; % ERB multiplicator;
% Derives gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
outsigfft = (outsigfft)/max((outsigfft));
% Plot;
subplot(1,3,2)
plot(rpwt_x,10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
title('Roex(pwt) filters in blue vs. Gammatone classic in red')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -50:10:0;
axis([0 2 -50 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Filters at 2089 Hz;
% Parameters:
fc = 2089; % Center frequency at 427 Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.0025; % Realtive weight for second exponatial;
t = 0.2*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Gammatone filter at 2089 Hz center frequency;
% Parameters:
fc = 2089; % Center frequency at 427 Hz;
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 2; % Filter order;
betamul = 0.6; % ERB multiplicator;
% Derives gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
outsigfft = (outsigfft)/max((outsigfft));
% Plot;
subplot(1,3,3)
plot(rpwt_x,10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -50:10:0;
axis([0 2 -50 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
end;
%% Pattersons Paper - Roex(pwt)
% Figure 9
if flags.do_fig9_patterson1987
% Global parameters:
fs = 25000; % Sampling frequency in Hz;
df = 1/1000; % Frequency resolution roex(pwt);
g = 0:df:1-df; % Frequency axis roex(pwt);
% Roex(pwt) filters at 427 Hz;
% Parameters:
fc = 427; % Center frequency at 427 Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.005; % Realtive weight for second exponatial;
t = 0.24*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Gammatone filter at 427 Hz center frequency;
% Parameters:
fc = 427; % Center frequency at 427 Hz;
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 2; % Filter order;
betamul = 0.6; % ERB multiplicator;
% Derive gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filter impulse signal;
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
%Normalize;
outsigfft = (outsigfft)/max((outsigfft));
% Plot;
figure('units','normalized','outerposition',[0 0.05 1 0.95])
subplot(1,3,1)
plot(rpwt_x,10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -50:10:0;
axis([0 2 -50 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Filters at 1000 Hz;
% Parameters:
fc = 1000; % Center frequency at 427 Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.005; % Realtive weight for second exponatial;
t = 0.24*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Gammatone filter at 1000 Hz center frequency;
% Parameters:
fc = 1000; % Center frequency at 427 Hz;
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 2; % Filter order;
betamul = 0.6; % ERB multiplicator;
% Derives gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
outsigfft = (outsigfft)/max((outsigfft));
% Plot;
subplot(1,3,2)
plot(rpwt_x,10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
title('Roex(pwt) filters in blue vs. Gammatone classic in red')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -50:10:0;
axis([0 2 -50 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
% Filters at 2089 Hz;
% Parameters:
fc = 2089; % Center frequency at 427 Hz;
erb = audfiltbw(fc); % Equivalent rectangular bandwidth;
% Equation from paper Moore, 1983 found in text after Equation 6.
p = 4*fc/erb; % Filter shape;
w = 0.005; % Realtive weight for second exponatial;
t = 0.24*p; % Filter shape tail;
% Equation A8 from Patterson 1982 (slopes are mirrored).
weight_l = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for lower slope;
weight_u = (1-w).*(1+p.*g).*exp(-p.*g)+w*(1+t.*g).*exp(-t.*g); % for upper slope;
rpwt_y = [fliplr(weight_l) 1 weight_u]; % Filteramplitude;
rpwt_x = ([-fliplr(g) 0 g]+1); % Frequency-axis;
% Gammatone filter at 2089 Hz center frequency;
% Parameters:
fc = 2089; % Center frequency at 427 Hz;
N = 4178; % Signallength for gammatone filter;
f = (0:N-1)*fs/N; % Frequency axis;
ind = find(f/fc > 2,1); % Index where frequency axis is 2;
insig = zeros(1,N); % Input impulse signal;
insig(1) = 1; % with peak at 1;
n = 2; % Filter order;
betamul = 0.6; % ERB multiplicator;
% Derives gammatone filter coefficients;
[b,a] = gammatone(fc,fs,n,betamul,'classic');
outsig = 2*real(ufilterbankz(b,a,insig));
% FFT;
outsigfft = fft(outsig);
outsigfft = (outsigfft)/max((outsigfft));
% Plot;
subplot(1,3,3)
plot(rpwt_x,10*log10(rpwt_y), 'b')
hold on
plot(f(1:ind)/fc,20*log10(abs(outsigfft(1:ind))),'r')
xlabel(['Center frequency at ', num2str(fc), ' Hz'])
ylabel('Attenuation (dB) roex: 10*log10 vs. gammatone: 20*log10')
xt = 0:0.2:2;
yt = -50:10:0;
axis([0 2 -50 0])
set(gca,'XTick',xt)
set(gca,'YTick',yt)
box on
hold off
end;
%% Pattersons Paper
% Figure 10a
% gammatone 'classic' (causalphase, real)
if flags.do_fig10a_patterson1987
% Input parameters
fs = 25000; % Sampling frequency in Hz;
ts = 1/fs; % Time between sampling points in s;
N=4096; % Length of signal;
treal = (1:N)*ts*1000; % Time axis in ms;
nchannels = 37; % Number of channels in filterbank;
flow = 100; % ERB lowest center frequency in Hz;
fhigh = 5000; % ERB highest center frequency in Hz;
fc = erbspace(flow,fhigh,nchannels); % 37 erb-spaced channels
insig = zeros(1,N); % Impulse as input signal
insig(1) = 1;
% Derives filter coefficients for 37 erb spaced channels
[b,a] = gammatone(fc,fs,'classic');
% Filters impulse signal with filter coefficients from above
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot
figure
hold on
dy = 1;
for ii = 1:nchannels
plot(treal,14*outsig(ii,:) + dy)
dy = dy+1;
end;
clear dy;
title 'Gammatone impulse response filterbank without phase-compensation'
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
xt = 0:5:25;
yt = [1 4 8 12 16 20 24 28 32 37];
axis([0, 25, 0, 40]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz'], ['#28: ' num2str(round(fc(28))) ' Hz'], ...
['#32: ' num2str(round(fc(32))) ' Hz'], ['#37: ' num2str(round(fc(37))) ' Hz'], })
box on
hold off
end;
%% Pattersons Paper
% Figure 10b
% gammatone 'classic','peakphase','complex'
if flags.do_fig10b_patterson1987
% Input parameters
fs = 25000; % Sampling frequency;
ts = 1/fs; % Time between sampling points in s
N=4096; % Length of signal
treal = (1:N)*ts*1000; % Time axis in ms
nchannels = 37; % Number of channels in filterbank;
flow = 100; % ERB lowest center frequency in Hz;
fhigh = 5000; % ERB highest center frequency
fc = erbspace(flow,fhigh,nchannels); % 37 erb-spaced channels
insig = zeros(1,N); % Impulse as input signal
insig(1) = 1;
% Derives filter coefficients for 37 erb-spaced channels
[b,a] = gammatone(fc,fs,'classic');
% Filters impulse signal with filter coefficients from above
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Find peak at envelope maximum
envmax = zeros(1,nchannels);
for ii = 1:nchannels
% Envelope maximum per channel
envmax(ii) = find(abs(outsig(ii,:)) == max(abs(outsig(ii,:))));
end;
% Adding Delay
desiredpeak = max(envmax)+1;
for ii = 1:nchannels
% Time to delay
delay = zeros(1,desiredpeak - envmax(ii));
% Add delay
outsig(ii,:) = [delay outsig(ii,1:size(outsig,2) - length(delay))];
end;
%Plot
figure
hold on
dy = 1;
for ii = 1:nchannels
plot(treal,14*real(outsig(ii,:))+dy)
dy = dy+1;
end;
clear dy;
title 'Gammatone filterbank with envelope phase-compensation'
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
xt = 0:5:25;
yt = [1 4 8 12 16 20 24 28 32 37];
axis([0, 25, 0, 39]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz'], ['#28: ' num2str(round(fc(28))) ' Hz'], ...
['#32: ' num2str(round(fc(32))) ' Hz'], ['#37: ' num2str(round(fc(37))) ' Hz'], })
box on
hold off
end;
%% Pattersons Paper
% Figure 10c
% gammatone 'classic','peakphase','complex'
if flags.do_fig10c_patterson1987
% Input parameters
fs = 25000; % Sampling frequency;
ts = 1/fs; % Time between sampling points in s
N=4096; % Length of signal
treal = (1:N)*ts*1000; % Time axis in ms
nchannels = 37; % Number of channels in filterbank;
flow = 100; % ERB lowest center frequency in Hz;
fhigh = 5000; % ERB highest center frequency
fc = erbspace(flow,fhigh,nchannels); % 37 erb-spaced channels
insig = zeros(1,N); % Impulse as input signal
insig(1) = 1;
% Derives filter coefficients for 37 erb-spaced channels
[b,a] = gammatone(fc,fs,'classic', 'exppeakphase');
% Filters impulse signal with filter coefficients from above
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Find peak at envelope maximum
envmax = zeros(1,nchannels);
for ii = 1:nchannels
% Envelope maximum per channel
envmax(ii) = find(abs(outsig(ii,:)) == max(abs(outsig(ii,:))));
end;
% Adding Delay
desiredpeak = max(envmax)+1;
for ii = 1:nchannels
% Time to delay
delay = zeros(1,desiredpeak - envmax(ii));
% Add delay
outsig(ii,:) = [delay outsig(ii,1:size(outsig,2) - length(delay))];
end;
%Plot
figure
hold on
dy = 1;
for ii = 1:nchannels
plot(treal,14*real(outsig(ii,:))+dy)
dy = dy+1;
end;
clear dy;
title 'Gammatone filterbank with envelope phase-compensation and delayed channel'
xlabel 'Time (ms)'
ylabel('# Frequency Channel (ERB): Frequency (Hz)');
xt = 0:5:25;
yt = [1 4 8 12 16 20 24 28 32 37];
axis([0, 25, 0, 39]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz'], ['#28: ' num2str(round(fc(28))) ' Hz'], ...
['#32: ' num2str(round(fc(32))) ' Hz'], ['#37: ' num2str(round(fc(37))) ' Hz'], })
box on
hold off
end;
%% Pattersons Paper
% Figure 11
% gammatone 'classic' (causalphase, real) pulsetrain
% Warning: Not sure if b=3 or b=1/3 // b=2 or b=1/2
if flags.do_fig11_patterson1987
% Input parameters
fs = 10000; % Sampling frequency in Hz;
ts = 1/fs; % Time between sampling points in s;
N=4096; % Length of signal;
treal = (1:N)*ts*1000; % Time axis in ms;
nchannels = 37; % Number of channels in filterbank;
flow = 100; % ERB lowest center frequency in Hz;
fhigh = 5000; % ERB highest center frequency in Hz;
fc = erbspace(flow,fhigh,nchannels); % 37 erb-spaced channels
insig = zeros(1,N); % Impulse as input signal
insig(160) = 1; % at 16 ms,
insig(240) = 1; % at 24 ms,
insig(320) = 1; % at 32 ms;
% Derives filter coefficients for erb spaced channels
[b,a] = gammatone(fc,fs,'classic');
% Filters impulse signal with filter coefficients from above
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot
figure('units','normalized','outerposition',[0 0.05 1 0.95])
hta1 = subplot(3,1,1);
posAxes1 = get(hta1, 'Position');
posAxes1(2) = posAxes1(2) + (1 - posAxes1(2))*5/8;
posAxes1(4) = posAxes1(4)/4;
set(hta1, 'Position',posAxes1);
plot(treal,insig);
title 'Pulsetrain'
ylabel 'Amplitude'
set(gca, 'XLim',[14.5 39],'YLim',[0 1])
dy = 1;
hta2 = subplot(3,1,2);
posAxes2 = get(hta2, 'Position');
posAxes2(2) = posAxes1(2)- posAxes2(2);
posAxes2(4) = posAxes1(4)*6;
set(hta2, 'Position',posAxes2);
hold on
for ii = 1:size(outsig,1)
plot(treal,4*outsig(ii,:)+dy)
dy = dy+1;
end;
title 'Gammatone impulse response filterbank but without envelope phase-compensation'
ylabel('# Channel (ERB) : Frequency (Hz)');
xt = 0:5:25;
yt = [1 4 8 12 16 20 24 28 32 37];
axis([14.5, 39, 0, 38]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz'], ['#28: ' num2str(round(fc(28))) ' Hz'], ...
['#32: ' num2str(round(fc(32))) ' Hz'], ['#37: ' num2str(round(fc(37))) ' Hz'], })
box on
hta3 = subplot(3,1,3);
posAxes3 = get(hta3, 'Position');
posAxes3(2) = posAxes3(2) - (1 - posAxes1(2))*1/8; % *3/8
posAxes3(4) = posAxes1(4)*6;
set(hta3, 'Position',posAxes3);
% title 'test'
xlabel 'Time (ms)'
ylabel('# Channel (ERB) : Frequency (Hz)');
xt = 15:5:40;
yt = [1 4 8 12 16 20 24 28 32 37];
axis([14.5, 39, 0, 38]);
set(gca,'XTick',xt, 'YTick', yt)
set(gca,'YTickLabel', {['#01: ' num2str(round(fc(1))) ' Hz'] , ['#04: ' num2str(round(fc(4))) ' Hz'], ...
['#08: ' num2str(round(fc(8))) ' Hz'], ['#12: ' num2str(round(fc(12))) ' Hz'], ...
['#16: ' num2str(round(fc(16))) ' Hz'], ['#20: ' num2str(round(fc(20))) ' Hz'], ...
['#24: ' num2str(round(fc(24))) ' Hz'], ['#28: ' num2str(round(fc(28))) ' Hz'], ...
['#32: ' num2str(round(fc(32))) ' Hz'], ['#37: ' num2str(round(fc(37))) ' Hz'], })
hold off
end
%% Lyons Paper - Allpole Gammatone Filter
% Figure 1
% gammatone (allpole,causalphase,real')
% gammatone 'classic' (causalphase, real)
% Warning: Not sure if b should be: b=3 or b=1/3 // b=2 or b=1/2;
if flags.do_fig1_lyon1997
% Input parameters
fs = 24000; % Sampling frequency in Hz;
flow = 100; % ERB lowest center frequency in Hz;
fhigh = 4000; % ERB highest center frequency in Hz;
fc = erbspacebw(flow,fhigh); % 24 ERB spaced channels;
channel = 20; % Channel
n = 6; % Filter order;
betamul = 3; % Betamul
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,n,betamul); % default = APGF
% Returns frequency response vector 'h' and the corresponding
% angular frequency vector 'w' for channel 13.
[h,w] = freqz(b(channel,:), a(channel,:));
% Scale first value to zero.
h = h(:)/h(1);
% For scaling of following transfer function (peak on peak).
nor = real(max(h));
% Plot
figure
semilogx(w/(fc(channel)/fs*2*pi), 10*log10(abs(h)),'r-');
title 'Transfer functions of classic and allpole gammatone filters for b = \omega_r/3 and b = \omega_r/2'
xlabel '\omega/\omega_r'
ylabel 'Magnitude gain (db)'
set(gca,'XLim',[0.03 3],'YLim',[-40, 35])
box on
hold on
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,n,betamul,'classic'); % GTF
% Returns frequency response vector 'h' and the corresponding
% angular frequency vector 'w' for channel 13.
[h,w] = freqz(b(20,:), a(20,:));
% Scale tranfer function to previous transfer fuction.
h=abs(h) * nor;
% Plot
semilogx(w/(fc(channel)/fs*2*pi), 10*log10(abs(h)),'b--');
% Change betamul;
betamul = 2;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,n,betamul);
% Returns frequency response vector 'h' and the corresponding
% angular frequency vector 'w' for channel 13.
[h,w] = freqz(b(channel,:), a(channel,:));
% Scale first value to zero;
h = h(:)/h(1);
% For scaling of following transfer function (peak on peak).
nor = real(max(h));
% Plot
semilogx(w/(fc(channel)/fs*(2*pi)), 10*log10(abs(h)),'r-');
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Returns frequency response vector 'h' and the corresponding
% angular frequency vector 'w' for channel 13.
[h,w] = freqz(b(channel,:), a(channel,:));
% Scale tranfer function to previous transfer fuction.
h=abs(h) * nor;
% Plot
semilogx(w/(fc(channel)/fs*2*pi), 10*log10(abs(h)),'b--');
legend('APGF, b=3', 'GTF, b=3', 'APGF, b=2', 'GTF, b=2', 'Location', 'NorthWest')
box on
hold off
warning('Not sure if b should be: b=3 or b=1/3 // b=2 or b=1/2');
end;
%% Lyons Paper
% Figure 2
% gammatone 'classic' (causalphase, real)
% gammatone (allpole,causalphase) 'complex'
% Warning: Not sure if b should be: b=3 or b=1/3 // b=2 or b=1/2;
if flags.do_fig2_lyon1997
% Input parameters
fs = 24000; % Sampling frequency in Hz;
flow = 100; % ERB lowest center frequency in Hz;
fhigh = 4000; % ERB highest center frequency in Hz;
fc = erbspacebw(flow,fhigh); % 24 ERB spaced channels;
N = 512; % Signal length;
insig = zeros(1,N); % Input signal;
insig(1) = 1; % Impulse at sample 1024;
channel = 12; % Channel
n = 6; % Filter order 6;
betamul = 1/3; % Betamul;
treal = (0:N-1)*((2*pi*fc(channel))/fs/pi);
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filters impulse signal with filter coefficients from above.
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot
figure
subplot(2,1,1)
plot(treal, outsig(channel,:),'b--')
title 'Impulse responses for b = \omega_r / 3 (low damping, low BW, high gain)'
xlabel 't * \omega_r / pi'
ylabel 'Amplitude'
set(gca,'XLim',[0 16], 'YLim',[-0.25 0.25])
box on
hold on
%'XLim',[1020 1084],'
% Derives filter coefficients for erb spaced channels.
%[b,a] = gammatone(erb,fs,n,betamul);
[b,a] = gammatone(fc,fs,n,betamul);
% Filters impulse signal with filter coefficients from above.
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot
plot(treal,outsig(channel,:),'r-')
legend('GTF','APGF')
hold off
% Change filter order
n = 6;
% Change betamul
betamul = 1/2;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,n,betamul,'classic');
% Filters impulse signal with filter coefficients from above.
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot
subplot(2,1,2)
plot(treal, outsig(channel,:),'b--')
title 'Impulse responses for b = \omega_r / 2 (high damping, high BW, low gain)'
xlabel 't * \omega_r / pi'
ylabel 'Amplitude'
set(gca, 'XLim',[0 16],'YLim',[-0.25 0.25])
box on
hold on
% Derives filter coefficients for erb spaced channels.
%[b,a] = gammatone(erb,fs,n,betamul);
[b,a] = gammatone(fc,fs,n,betamul);
% Filters impulse signal with filter coefficients from above.
outsig = 2*real(ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Plot
plot(treal,outsig(channel,:),'r-')
legend('GTF', 'APGF')
box on
hold off
warning('Not sure if b should be: b=3 or b=1/3 // b=2 or b=1/2');
end;
%% Hohmanns paper
% Figure 1
% gammatone (allpole,causalphase) 'complex'
if flags.do_fig1_hohmann2002
% Input parameters
fs = 10000; % Sampling frequency in Hz;
fc = 1000; % Center frequency at 1000 Hz;
N = 4096; % Signal length;
% n = 4; % Filter order
% betamul = 0.75; % Bandwidth multiplicator
insig = zeros(1,N); % Input signal with
insig(1) = 1; % impulse at 1;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'complex');
% Filters impulse signal with filter coefficients from above.
outsig = (ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Envelope of impulse response of gammatone filter at 1000 Hz
outsigenv = hilbert(real(outsig),fs);
% Plot
figure
plot(abs(outsigenv),'b-.')
xlabel('Sample')
ylabel('Amplitude')
set(gca, 'XLim',[0 200],'YLim',[-0.04 0.04])
box on
hold on
plot(real(outsig),'r-')
plot(imag(outsig),'g--')
hold off
end;
%% Hohmanns paper
% Figure 2
% gammatone (allpole,causalphase) 'complex'
if flags.do_fig2_hohmann2002
% Input parameters
fs = 10000; % Sampling frequency in Hz;
fc = 1000; % Center frequency at 1000 Hz;
fn = fs/2; % Nyquist frequency in Hz
Tn = 1/fn; % Time between samples for Nyquist frequency
N = 4096; % Signal length;
df = fs/N; % Distance frequency of fft
xfn = (0:df:fn-df)*Tn; % Frequency vector for fft
insig = zeros(1,N); % Input signal with
insig(1) = 1; % impulse at one;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'complex');
% Filters impulse signal with filter coefficients from above.
outsig = (ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Upper two panels
% FFT of real part of output signal
outfftr = fft(2*real(outsig));
% Returns unwrapped phase response vectors evaluated at n equally-spaced points
% around the unit circle from 0 to 2? radians/sample.
[phi] = phasez(b,a,2048);
phi = phi+2*pi;
phi = phi.';
% Lower two panels
% The real-to-imaginary transfer function is calculated by
% dividing the FFT-spectra of imaginary and real part of the
% impulse response.
outffti = fft(2*imag(outsig));
outsigrtoi = outffti./outfftr;
% Extract phase angle of signal.
theta = angle(outsigrtoi);
% Add Pi/2 to phase.
phirtoi = theta+ pi/2;
% Plot
figure
subplot(4,1,1)
plot(xfn, 20*log10(abs(outfftr(1:N/2))))
set(gca,'Xlim',[0 1], 'YLim',[-70 0])
ylabel('Magnitude/db')
box on
subplot(4,1,2)
plot(xfn,phi)
ylabel('Phase/rad')
set(gca,'Xlim',[0 1],'Ylim',[-5 5])
box on
subplot(4,1,3)
plot(xfn, 20*log10(abs(outsigrtoi(1:N/2))))
set(gca,'Xlim',[0 1],'Ylim',[-10 10])
ylabel('Magnitude/db')
box on
subplot(4,1,4)
plot(xfn, phirtoi(1:N/2))
set(gca,'Xlim',[0 1],'Ylim',[-2 2])
xlabel('Frequency / \pi')
ylabel('Phase + \pi / 2 / rad')
box on
grid
end;
%% Hohmanns paper
% Figure 3
% gammatone (allpole,causalphase) 'complex'
if flags.do_fig3_hohmann2002
fs = 16276; % Sampling frequency in Hz;
flow = 70; % ERB lowest center frequency in Hz;
fhigh = 6700; % ERB highest center frequency in Hz;
fc = erbspacebw(flow,fhigh); % 24 ERB spaced channels;
fn = fs/2; % Nyquist frequency in Hz
N = 2048; % Signal length
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'complex');
% Frequency response per channel
h = zeros(length(fc),N/4);
w = zeros(length(fc),N/4);
for ii=1:length(fc)
[h(ii,:),w(ii,:)] = freqz(b(ii,:),a(ii,:));
end;
% Normalize peak to zero
h(:) = abs(h(:));
% Plot
figure
hold on
for ii = 1:length(fc)
plot(w(ii,:)/(2*pi)*fs, 20*log10(h(ii,:)))
end;
xlabel('Frequency / Hz')
ylabel('Level / dB')
set(gca,'Xlim',[0 fn],'Ylim',[-40 0])
box on
hold off
end;
%% Hohmanns paper
% Figure 4
% gammatone (allpole,causalphase) 'complex'
% Result is delayed and peakphased.
% Case 2a: envelope maximum before desired peak;
if flags.do_fig4_hohmann2002
fs = 16276; % Sampling frequency in Hz;
flow = 70; % ERB lowest center frequency in Hz;
fhigh = 6700; % ERB highest center frequency in Hz;
fc = erbspacebw(flow,fhigh); % 24 ERB spaced channels;
insig = zeros(1,fs); % Input signal with
insig(1) = 1; % impulse at one
% The envelope maximum envmax is earlier in time than the desired
% peak at channels 13 to 30.
channel = 20;
desiredpeak = 65;
% Derives filter coefficients for erb spaced channels.
[b,a] = gammatone(fc,fs,'complex');
% Filters impulse signal with filter coefficients from above.
outsig = (ufilterbankz(b,a,insig));
outsig = permute(outsig,[3 2 1]);
% Envelope maximum
outenv = hilbert(real(outsig(channel,:)),fs);
envmax = find(abs(outenv(1,:)) == max(abs(outenv(1,:))));
% Signal maximum
sigmax = find(real(outsig(channel,:)) == max(real(outsig(channel,:))));
% Phase delay between envelope maximum and signal maximum
% Equation 18 Phi_k
phi = fc(channel)*(-2*pi)*(envmax - sigmax)/fs;
% Derives signal with envelope maximum at signal maximum
% Equation 19
outsignew = real(outsig(channel,:)) * cos(phi) - imag(outsig(channel,:)) * sin(phi);
% For testing purpose
% outenvnew = hilbert(real(outsignew(1,:)),fs);
% envmaxnew = find(abs(outenvnew(1,:)) == max(abs(outenvnew(1,:))));
% sigmaxnew = find(real(outsignew(1,:)) == max(real(outsignew(1,:))));
%
% warning(['FIXME: The maximum of the real part of the impulse response ' ...
% 'misses the maximum of the envelope in channel ' num2str(channel)...
% ' by ' num2str(envmaxnew - sigmaxnew) ' sample(s).']);
% Derives time delay
% Equation 20
delay = outsignew(end-desiredpeak+envmax+1:end);
% Delay signal
% Equation 21
outsigdelay= [delay outsignew(1:length(outsignew) - delay)];
outsigdelay = outsigdelay(1:length(outsignew) - delay);
% Envelope of delayed signal
outsigdelayenv = hilbert(real(outsigdelay),fs);
% Plot
figure
subplot(2,1,1)
plot(real(outsig(channel,:)),'b-')
hold on
set(gca, 'XLim',[0 200],'YLim',[-0.04 0.04])
line([65 65], [-0.05 0.05])
xlabel('Sample')
ylabel('Amplitude')
box on
plot(abs(outenv),'r-')
hold off
subplot(2,1,2)
plot (real(outsigdelay),'b-')
hold on
set(gca, 'XLim',[0 200],'YLim',[-0.04 0.04])
xlabel('Sample')
ylabel('Amplitude')
line([65 65], [-0.05 0.05])
plot(abs(outsigdelayenv),'r-')
box on
hold off
end;
end
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