georgid
commented
8 years ago Function to create_filter
[x, fs] = audioread('piano.wav');
no_filters = 720; %
lo_fq = 164; % E3
hi_fq = 10548; % E9
R = [lo_fq hi_fq ];
spectrum_size = 1025;
hz2scale = @( hz )(120*log2(hz/440));
scale2hz = @( scale )(power(2, ((scale)/120))*440);
[H, freq, C] = trifbank(no_filters, spectrum_size, R, fs, hz2scale, scale2hz);
% Plot all filters
figure
for i = 1 : no_filters
plot(H(i,:))
hold on
end
% center bins
center_f = C(2:end-1);
where trifbank is from htk_mfcc :
`function [ H, f, c ] = trifbank( M, K, R, fs, h2w, w2h )
% TRIFBANK Triangular filterbank.
%
% [H,F,C]=TRIFBANK(M,K,R,FS,H2W,W2H) returns matrix of M triangular filters
% (one per row), each K coefficients long along with a K coefficient long
% frequency vector F and M+2 coefficient long cutoff frequency vector C.
% The triangular filters are between limits given in R (Hz) and are
% uniformly spaced on a warped scale defined by forward (H2W) and backward
% (W2H) warping functions.
%
% Inputs
% M is the number of filters, i.e., number of rows of H
%
% K is the length of frequency response of each filter
% i.e., number of columns of H
%
% R is a two element vector that specifies frequency limits (Hz),
% i.e., R = [ low_frequency high_frequency ];
%
% FS is the sampling frequency (Hz)
%
% H2W is a Hertz scale to warped scale function handle
%
% W2H is a wared scale to Hertz scale function handle
%
% Outputs
% H is a M by K triangular filterbank matrix (one filter per row)
%
% F is a frequency vector (Hz) of 1xK dimension
%
% C is a vector of filter cutoff frequencies (Hz),
% note that C(2:end) also represents filter center frequencies,
% and the dimension of C is 1x(M+2)
%
% Example
% fs = 16000; % sampling frequency (Hz)
% nfft = 2^12; % fft size (number of frequency bins)
% K = nfft/2+1; % length of each filter
% M = 23; % number of filters
%
% hz2mel = @(hz)(1127_log(1+hz/700)); % Hertz to mel warping function
% mel2hz = @(mel)(700_exp(mel/1127)-700); % mel to Hertz warping function
%
% % Design mel filterbank of M filters each K coefficients long,
% % filters are uniformly spaced on the mel scale between 0 and Fs/2 Hz
% [ H1, freq ] = trifbank( M, K, [0 fs/2], fs, hz2mel, mel2hz );
%
% % Design mel filterbank of M filters each K coefficients long,
% % filters are uniformly spaced on the mel scale between 300 and 3750 Hz
% [ H2, freq ] = trifbank( M, K, [300 3750], fs, hz2mel, mel2hz );
%
% % Design mel filterbank of 18 filters each K coefficients long,
% % filters are uniformly spaced on the Hertz scale between 4 and 6 kHz
% [ H3, freq ] = trifbank( 18, K, [4 6]*1E3, fs, @(h)(h), @(h)(h) );
%
% hfig = figure('Position', [25 100 800 600], 'PaperPositionMode', ...
% 'auto', 'Visible', 'on', 'color', 'w'); hold on;
% subplot( 3,1,1 );
% plot( freq, H1 );
% xlabel( 'Frequency (Hz)' ); ylabel( 'Weight' ); set( gca, 'box', 'off' );
%
% subplot( 3,1,2 );
% plot( freq, H2 );
% xlabel( 'Frequency (Hz)' ); ylabel( 'Weight' ); set( gca, 'box', 'off' );
%
% subplot( 3,1,3 );
% plot( freq, H3 );
% xlabel( 'Frequency (Hz)' ); ylabel( 'Weight' ); set( gca, 'box', 'off' );
%
% Reference
% [1] Huang, X., Acero, A., Hon, H., 2001. Spoken Language Processing:
% A guide to theory, algorithm, and system development.
% Prentice Hall, Upper Saddle River, NJ, USA (pp. 314-315).
% Author Kamil Wojcicki, UTD, June 2011
if( nargin~= 6 ), help trifbank; return; end; % very lite input validation
f_min = 0; % filter coefficients start at this frequency (Hz)
f_low = R(1); % lower cutoff frequency (Hz) for the filterbank
f_high = R(2); % upper cutoff frequency (Hz) for the filterbank
f_max = 0.5*fs; % filter coefficients end at this frequency (Hz)
f = linspace( f_min, f_max, K ); % frequency range (Hz), size 1xK
fw = h2w( f );
% filter cutoff frequencies (Hz) for all filters, size 1x(M+2)
c = w2h( h2w(f_low)+[0:M+1]*((h2w(f_high)-h2w(f_low))/(M+1)) );
cw = h2w( c );
H = zeros( M, K ); % zero otherwise
for m = 1:M
% implements Eq. (6.140) on page 314 of [1]
% k = f>=c(m)&f<=c(m+1); % up-slope
% H(m,k) = 2*(f(k)-c(m)) / ((c(m+2)-c(m))*(c(m+1)-c(m)));
% k = f>=c(m+1)&f<=c(m+2); % down-slope
% H(m,k) = 2*(c(m+2)-f(k)) / ((c(m+2)-c(m))*(c(m+2)-c(m+1)));
% implements Eq. (6.141) on page 315 of [1]
k = f>=c(m)&f<=c(m+1); % up-slope
H(m,k) = (f(k)-c(m))/(c(m+1)-c(m));
k = f>=c(m+1)&f<=c(m+2); % down-slope
H(m,k) = (c(m+2)-f(k))/(c(m+2)-c(m+1));end
% H = H./repmat(max(H,[],2),1,K); % normalize to unit height (inherently done) % H = H./repmat(trapz(f,H,2),1,K); % normalize to unit area
% EOF `
dbogdanov
palonso
Triangular filterbank to compute cent-scale from frequency bands: python code to compute it:
NOTE: Each bin has 10 cents as in the implementation in [(https://github.com/MTG/essentia/blob/528c57494ae3322ffed4442f44082ef0608c0ee8/src/algorithms/tonal/pitchsaliencefunction.cpp)] However in the pitch salience, a frequency's magnitude content is distributed to 1) its corresponding bin + 2) the bins within one semitone up and one semitone below e.g. in the range
(h_bin-_binsInSemitone ; h_bin + binsInSemitone)with weigths_nearestBinsWeightsUnlike that this implementation maps a couple of freq bins with weights given by the triangular bands to one freq bin. Note that spectrum has big zero-padding to get a very big window for good resolution.ported from the implementation from MATLAB of the fluctogram feature 2.1 from the paper https://www.researchgate.net/publication/262259403_On_the_reduction_of_false_positives_in_singing_voice_detection