%DEMO_FILTERBANKS CQT, ERBLET and AUDLET filterbanks
%
% This demo shows CQT (Constant Quality Transform), ERBLET (Equivalent
% Rectangular Bandwidth -let transform), and AUDLET (Auditory -let)
% representations acting as filterbanks with high and low redundancies.
% Note that ERBLET and AUDLET are similar concepts. The main difference
% is that ERBlet uses only the perceptual ERB scale while AUDlet allows
% for various perceptual scales like Bark or Mel scales. In short,
% ERBFILTERS is a wrapper of AUDFILTERS for the ERB scale.
% Filterbanks are build such that the painless condition is always satisfied.
% Real input signal and filters covering only the positive frequency range
% are used. The redundancy is calculated as a ratio of the number of (complex)
% coefficients and the input length times two to account for the storage
% requirements of complex numbers.
%
% The high redundancy representation uses 'uniform' subsampling i.e.
% all channels are subsampled with the same subsampling factor which
% is the lowest from the filters according to the painless condition
% rounded towards zero.
%
% The low redundancy representation uses 'fractional' subsampling
% which results in the least redundant representation still
% satisfying the painless condition. Actual time positions of atoms
% can be non-integer, hence the word fractional.
%
% Figure 1: ERBLET representations
%
% The high-redundancy plot (top) consists of 400 channels (~9 filters
% per ERB) and the low-redundancy plot (bottom) consists of 44 channels
% (1 filter per ERB).
%
% Figure 2: CQT representations
%
% Both representations consist of 280 channels (32 channels per octave,
% frequency range 50Hz-20kHz). The high-redundany represention is on
% the top and the low-redundancy repr. is on the bottom.
%
% Figure 3: AUDLET representations
%
% The first representation consists of 72 channels BARKlet FB (3 filters
% per Bark in the frequency range 100Hz-16kHz using fractional subsampling.
% The second representation consists of 40 channels MELlet FB using
% uniform subsampling and triangular windows.
%
%
% See also: audfilters, erbfilters, cqtfilters
%
% Url: http://ltfat.github.io/doc/demos/demo_filterbanks.html
% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% 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/>.
% Read the test signal and crop it to the range of interest
[f,fs]=gspi;
f=f(10001:100000);
dr=50;
figure(1);
subplot(2,1,1);
% Create the ERB filterbank using 400 filters linearly spaced in the
% ERB scale and using uniform subsampling.
[g,a,fc]=erbfilters(fs,numel(f),'M',400,'uniform');
% Compute the filterbank response
c1=filterbank(f,g,a);
% Compute redundancy
erb1_redundancy = 2*sum(1./a);
% Plot the representation
plotfilterbank(c1,a,fc,fs,dr,'audtick');
title('ERBLET representations')
subplot(2,1,2);
% Create the ERB filterbank using 44 filters linearly spaced in the
% ERB scale and using fractional subsampling.
[g,a,fc]=erbfilters(fs,numel(f),'fractional');
% Compute the filterbank response
c2=filterbank(f,g,a);
% Compute redundancy
erb2_redundancy = 2*sum(a(:,2)./a(:,1));
% Plot the representation
plotfilterbank(c2,a,fc,fs,dr,'audtick');
fprintf('ERBLET high redundancy %.2f, low redundany %.2f.\n',...
erb1_redundancy,erb2_redundancy);
figure(2);
subplot(2,1,1);
% Create the CQT filterbank using 32 channels per octave in frequency
% range 50Hz-20kHz using uniform subsampling.
[g,a,fc] = cqtfilters(fs,50,20000,32,numel(f),'uniform');
% Compute the filterbank response
c3=filterbank(f,g,a);
% Compute redundancy
cqt1_redundancy = 2*sum(1./a);
% Plot the representation
plotfilterbank(c3,a,fc,fs,'dynrange',dr);
title('CQT representations')
subplot(2,1,2);
% Create the CQT filterbank using 32 channels per octave in frequency
% range 50Hz-20kHz using fractional subsampling.
[g,a,fc] = cqtfilters(fs,50,20000,32,numel(f),'fractional');
% Compute the filterbank response
c4=filterbank(f,g,a);
% Compute redundancy
cqt2_redundancy = 2*sum(a(:,2)./a(:,1));
% Plot the representation
plotfilterbank(c4,a,fc,fs,'dynrange',dr);
fprintf('CQT high redundancy %.2f, low redundany %.2f.\n',...
cqt1_redundancy,cqt2_redundancy);
% Finally two settings of AUDFILTERS are illustrated, namely an analysis on
% the Bark scale (top) and one on the Mel scale using triangular windows (bottom).
figure(3);
subplot(2,1,1);
% Create a Barklet FB with 3 filters per Bark in the
% frequency range 100Hz-16kHz using fractional subsampling.
[g,a,fc]=audfilters(fs,numel(f),100,16000,'bark','fractional','spacing',1/3);
% Compute the filterbank response
c5=filterbank(f,{'realdual',g},a);
% Compute redundancy
bark_redundancy = 2*sum(a(:,2)./a(:,1));
% Plot the representation
plotfilterbank(c5,a,fc,fs,dr,'audtick');
title('AUDLET representations: Bark scale (top) and Mel scale (bottom)')
fprintf('BARKLET redundancy %.2f\n',bark_redundancy);
subplot(2,1,2);
% Create a MELlet FB with 40 filters and a triangular window using
% uniform subsampling.
[g,a,fc]=audfilters(fs,numel(f),'mel','uniform','M',40,'tria');
% Compute the filterbank response
c6=filterbank(f,{'realdual',g},a);
% Compute redundancy
mel_redundancy = 2*sum(a.^-1);
% Plot the representation
plotfilterbank(c6,a,fc,fs,dr,'audtick');
title('MELlet representation')
fprintf('MELLET redundancy %.2f\n',mel_redundancy);