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EXP_HOHMANN2002 - figures from Hohmann (2012)
Program code:
function exp_hohmann2002(varargin)
%EXP_HOHMANN2002 figures from Hohmann (2012)
% Usage: exp_hohmann(flags)
%
% `exp_hohmann2002(flags)` reproduces figures of the paper from
% Hohmann (2002).
%
% The following flags can be specified:
%
% 'fig1' Reproduce Fig. 1:
% Impulse response of the example Gammatone filter (center
% frequency fc = 1000 Hz: 3-dB bandwidth fb = 100 Hz;
% sampling frequency fs = 10 kHz. 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' Reproduce Fig.2:
% 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' Reproduce Fig.3:
% 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' Reproduce Fig.4:
% 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).
%
% 'fig5' Reproduce Fig.5:
% Treatment of an impulse response with envelope maximum
% to the right of the desired group delay (vertical line at
% sampling 65). The original complex impulse response ( real
% part and envelope plotted in the upper panel) is multiplied
% with a complex factor so that the maximum of the real part
% coincides with the desired group delay (lower panel).
%
% 'fig6' Reproduce Fig.6:
% Impulse response of the analysis-synthesis system using
% the filterbank design from section 3.1 (upper pannel). A
% peaked impulse is achieved at the desired group delay of
% 4 ms (65 samples at fs = 16276 Hz). The lower panel shows
% the main part of the response on a larger scale.
%
% 'fig7' Reproduce Fig.7:
% Magnitude and group delay of the transfer function of the
% analysis-synthesis system using the filterbank design from
% section 3.1.
%
%
% Examples:
% ---------
%
% To display Fig. 1, use :::
%
% exp_hohmann2002('fig1');
%
% To display Fig. 2, use :::
%
% exp_hohmann2002('fig2');
%
% To display Fig. 3, use :::
%
% exp_hohmann2002('fig3');
%
% To display Fig. 4, use :::
%
% exp_hohmann2002('fig4');
%
% To display Fig. 5, use :::
%
% exp_hohmann2002('fig5');
%
% To display Fig. 6, use :::
%
% exp_hohmann2002('fig6');
%
% To display Fig. 7, use :::
%
% exp_hohmann2002('fig7');
%
%
% References: hohmann2002
%
% See also: demo_hohmann2002 hohmann2002 hohmann2002_process hohmann2002_delay hohmann2002_synth hohmann2002_mixer
% AUTHOR: CK, 2014
%% ------ Check input options --------------------------------------------
definput.import={'amt_cache'};
definput.keyvals.FontSize = 12;
definput.keyvals.MarkerSize = 6;
definput.flags.type = {'missingflag', 'fig1', 'fig2', 'fig3', 'fig4', ...
'fig5', 'fig6', 'fig7', 'fig8'};
% 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;
%% Figure 1
if flags.do_fig1
fs = 10000; % Sampling rate in Hz;
fc = 1000; % Center frequency in Hz;
bw = 100; % Bandwidth of 100 Hz
attenuation_db = 3; % Attenuation of the filter at the bandwidth
gamma_order= 4; % Filter order;
% Construct new analyzer object;
filter = hohmann2002_filter (fs, fc, bw, attenuation_db, gamma_order);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
impulse_response = hohmann2002_process(filter, impulse);
%Plot;
figure;
plot(real(impulse_response));
hold on
plot(imag(impulse_response),'--g');
plot(abs(impulse_response),'r');
xt = 0:50:200;
axis([0, 200, -0.04, 0.04]);
set(gca,'XTick',xt)
title('Real part, imaginary part and envelope of impulse response at fc = 1000 Hz ');
xlabel('Sample/ 1');
ylabel('Amplitude/ 1');
box on;
end;
%% Figure 2
if flags.do_fig2
fs = 10000; % Sampling rate in Hz;
fc = 1000; % Center frequency in Hz;
bw = 100; % Bandwidth of 100 Hz
attenuation_db = 3; % Attenuation of the filter at the bandwidth
gamma_order= 4; % Filter order;
% Construct new analyzer object;
filter = hohmann2002_filter (fs, fc, bw, attenuation_db, gamma_order);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
impulse_response = hohmann2002_process(filter, impulse)';
% Frequency response;
frequency_response = fft(real(impulse_response)');
% Normalized frequency vector;
frequency = (0:8191) * fs / 8192 * 2/fs;
% Phase response;
phi = angle(frequency_response);
% Unwrap phase;
phi = unwrap(phi);
% Division of imaginary frequency reponse by real frequency response;
divspectra = fft(imag(impulse_response)')./frequency_response;
% Phase response from division above;
theta = angle(divspectra)+pi/2;
% Plot;
figure('units','normalized','outerposition',[0.25 0.05 0.5 0.9])
subplot(4,1,1)
plot(frequency(1:end/2), 20*log10(abs(frequency_response(1:end/2))))
xt = 0:0.2:1;
yt = -60:20:0;
axis([0, 1, -70, 0]);
set(gca,'XTick',xt, 'YTick', yt)
ylabel('Magnitude/dB')
box on
subplot(4,1,2)
plot(frequency(1:end/2),phi(1:end/2))
ylabel('Phase/rad')
xt = 0:0.2:1;
yt = -5:5:5;
axis([0, 1, -5, 5]);
set(gca,'XTick',xt, 'YTick', yt)
box on
subplot(4,1,3)
plot(frequency(1:end/2), 20*log10(abs(divspectra(1:end/2))))
xt = 0:0.2:1;
yt = -10:5:10;
axis([0, 1, -10, 10]);
set(gca,'XTick',xt, 'YTick', yt)
ylabel('Magnitude/db')
box on
subplot(4,1,4)
plot(frequency(1:end/2), theta(1:end/2))
xt = 0:0.2:1;
yt = -2:1:2;
axis([0, 1, -2, 2]);
set(gca,'XTick',xt, 'YTick', yt)
xlabel('Frequency / \pi')
ylabel('Phase + \pi / 2 /rad')
box on
end;
%% Figure 3
if flags.do_fig3
fs = 16276; % Sampling rate in Hz;
flow = 70; % Lowest center frequency in Hz;
basef = 1000; % Base center frequency in Hz;
fhigh = 6700; % Highest center frequency in Hz;
filters_per_ERBaud = 1.0; % Filterband density on ERB scale;
% Construct new analyzer object;
analyzer = hohmann2002 (fs,flow,basef,fhigh,filters_per_ERBaud);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
impulse_response = hohmann2002_process(analyzer, impulse)';
% Frequency response;
frequency_response = fft(real(impulse_response)');
% Frequency vector;
frequency = [0:8191] * fs / 8192;
% Plot;
figure
plot(frequency, 20 * log10(abs(frequency_response)));
axis([0,fs/2, -40, 0]);
title('Frequency response of the individual filters in this filterbank.');
xlabel('Frequency / Hz');
ylabel('Level / dB');
box on
end;
%% Figure 4
if flags.do_fig4
fs = 16276; % Sampling rate in Hz;
flow = 2160; % Lowest center frequency in Hz;
basef = 2160; % Base center frequency in Hz;
fhigh = 2160; % Highest center frequency in Hz;
filters_per_ERBaud = 1; % Filterband density on ERB scale;
delay_samples = 65; % Desired delay in Samples;
% Construct new analyzer object;
analyzer = hohmann2002 (fs,flow,basef,fhigh,filters_per_ERBaud);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
[impulse_response, analyzer] = hohmann2002_process(analyzer, impulse);
% Construct new delay object, which holds samples to delay and phase factors.
delay = hohmann2002_delay(analyzer,delay_samples);
% Delay filtered signal;
insig = impulse_response; % Impulse response as input signal;
outsig = hohmann2002_process(delay, insig);
outsigdelayenv = hilbert(real(outsig),fs);
% Plot;
figure('units','normalized','outerposition',[0.25 0.05 0.5 0.9])
subplot(2,1,1)
plot(real(impulse_response),'b-')
hold on
xt = 0:20:200;
yt = -0.05:0.01:0.05;
axis([0, 200, -0.05, 0.05]);
set(gca,'XTick',xt, 'YTick', yt)
title(['Impulse response with center frequency at ', num2str(basef), ' Hz'])
xlabel('Sample')
ylabel('Amplitude')
line([65 65], [-0.05 0.05])
plot(abs(impulse_response),'r-')
box on
hold off
subplot(2,1,2)
plot (real(outsig),'b-')
hold on
xt = 0:20:200;
yt = -0.05:0.01:0.05;
axis([0, 200, -0.05, 0.05]);
set(gca,'XTick',xt, 'YTick', yt)
title(['Delayed impulse response with peak at desired delay at sample ', num2str(delay_samples) ])
xlabel('Sample')
ylabel('Amplitude')
line([65 65], [-0.05 0.05])
plot(abs(outsigdelayenv),'r-')
box on
hold off
end;
%% Figure 5
if flags.do_fig5
fs = 16276; % Sampling rate in Hz;
flow = 73; % Lowest center frequency in Hz;
basef = 73; % Base center frequency in Hz;
fhigh = 73; % Highest center frequency in Hz;
filters_per_ERBaud = 1.0; % Filterband density on ERB scale;
delay_samples = 65; % Desired delay in Samples;
% Construct new analyzer object;
analyzer = hohmann2002 (fs,flow,basef,fhigh,filters_per_ERBaud);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
[impulse_response, analyzer] = hohmann2002_process(analyzer, impulse);
% Construct new delay object, which holds samples to delay and phase factors.
delay = hohmann2002_delay(analyzer,delay_samples);
% Delay filtered signal;
insig = impulse_response; % Impulse response as input signal;
outsig = hohmann2002_process(delay, insig);
outsigdelayenv = hilbert(real(outsig),fs);
% Plot;
figure('units','normalized','outerposition',[0.25 0.05 0.5 0.9])
subplot(2,1,1)
plot(real(impulse_response),'b-')
hold on
set(gca, 'XLim',[0 1000],'YLim',[-0.007 0.007])
title(['Impulse response with center frequency at ', num2str(basef), ' Hz'])
xlabel('Sample')
ylabel('Amplitude')
line([65 65], [-0.07 0.07])
plot(abs(impulse_response),'r-')
box on
hold off
subplot(2,1,2)
plot (real(outsig),'b-')
hold on
set(gca, 'XLim',[0 1000],'YLim',[-0.007 0.007])
title(['Delayed impulse response with a peak at desired delay at sample ', num2str(delay_samples) ])
xlabel('Sample')
ylabel('Amplitude')
line([65 65], [-0.07 0.07])
plot(abs(outsigdelayenv),'r-')
box on
hold off
end;
%% Figure 6
if flags.do_fig6
fs = 16276; % Sampling rate in Hz;
flow = 70; % Lowest center frequency in Hz;
basef = 1000; % Base center frequency in Hz;
fhigh = 6700; % Highest center frequency in Hz;
filters_per_ERBaud = 1.0; % Filterband density on ERB scale;
desired_delay = 0.004; % Desired delay in seconds;
% Construct new analyzer object;
analyzer = hohmann2002 (fs,flow,basef,fhigh,filters_per_ERBaud);
% Build synthesizer for an analysis-synthesis delay of desired_delay in seconds.
synthesizer = hohmann2002_synth(analyzer, desired_delay);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
[analyzed_impulse, analyzer] = hohmann2002_process(analyzer, impulse);
% Resynthesize filtered impulse response from above.
[resynthesized_impulse, synthesizer] = hohmann2002_process(synthesizer, analyzed_impulse);
% Plot;
figure('units','normalized','outerposition',[0.25 0.05 0.5 0.9])
subplot(2,1,1)
plot(real(resynthesized_impulse),'b-')
hold on
plot(zeros(1,length(resynthesized_impulse)),'r')
hold off
xt = -200:200:1199;
yt = -0.2:0.2:1.2;
axis([-199 1200 -0.2 1.2])
set(gca,'XTick',xt, 'YTick',yt)
title('Analysis of resynthesized impulse response')
xlabel('Sample')
ylabel('Amplitude')
box on
subplot(2,1,2)
plot (real(resynthesized_impulse),'b-')
hold on
plot(zeros(1,length(resynthesized_impulse)),'r')
hold off
xt = 40:10:120;
yt = -0.2:0.1:0.8;
axis([40 120 -0.15 0.85])
set(gca,'XTick',xt, 'YTick',yt)
title('Analysis of resynthesized impulse response on a larger scale')
xlabel('Sample')
ylabel('Amplitude')
box on
end;
%% Figure 7
if flags.do_fig7
fs = 16276; % Sampling rate in Hz;
flow = 70; % Lowest center frequency in Hz;
basef = 1000; % Base center frequency in Hz;
fhigh = 6700; % Highest center frequency in Hz;
filters_per_ERBaud = 1.0; % Filterband density on ERB scale;
desired_delay = 0.004; % Desired delay in seconds;
% Construct new analyzer object;
analyzer = hohmann2002 (fs,flow,basef,fhigh,filters_per_ERBaud);
% Build synthesizer for an analysis-synthesis delay of desired_delay in seconds.
synthesizer = hohmann2002_synth(analyzer, desired_delay);
% Impulse signal;
impulse = [1; zeros(8191,1)];
% Filter signal;
analyzed_impulse = hohmann2002_process(analyzer, impulse);
% Resynthesize filtered impulse response from above.
resynthesized_impulse = hohmann2002_process(synthesizer, analyzed_impulse);
% Normalized frequency vector;
frequency = (0:8191) * fs / 8192;
% Transfer function;
resynthesized_spectra = fft(resynthesized_impulse');
% Group delay;
[spectra_grpdelay, w] = grpdelay(resynthesized_impulse',1,8192);
% Plot;
figure('units','normalized','outerposition',[0.25 0.05 0.5 0.9])
subplot(2,1,1)
plot(w/(2*pi)*fs, spectra_grpdelay/fs*1000)
hold on
plot(zeros(1,length(frequency)),'r')
xt = 0:1000:8000;
yt = -15:5:20;
axis([0 8000 -15 20])
set(gca,'XTick',xt, 'YTick',yt)
title('Group delay of transfer function')
xlabel('Frequency [Hz]')
ylabel('Group delay / ms')
box on
subplot(2,1,2)
plot (frequency, 20*log10(abs(resynthesized_spectra)),'b-')
hold on
plot (zeros(1,length(frequency)),'r')
hold off
xt = 0:1000:8000;
yt = -40:5:5;
axis([0 8000 -40 5])
set(gca,'XTick',xt, 'YTick',yt)
title('Magnitude of transfer function')
xlabel('Frequency / Hz')
ylabel('Magnitude / dB')
box on
end;
%% Figure 8
if flags.do_fig8
amt_disp('Figure not implemented yet');
end
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