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Formants Detection via LPC Method
LPC
% NAME
% spLpc - The linear predictive coding (one-step finite observation
% wiener filter prediction)
% SYNOPSIS
% [a P e] = spLpc(x, fs, ncoef, show)
% DESCRIPTION
% Obtain LPC coefficients (AR model)
% INPUTS
% x (vector) of size Nx1 which contains signal
% fs (scalar) the sampling frequency
% [ncoef] (scalar) the number of coefficients. The default uses
% ncoef = 2 + fs / 1000;
% as a rule of thumb.
% OUTPUTS
% a (vector) of size ncoefx1 which contains LPC coefficients
% P (scalar) variance (power) of the prediction error
% e (vector) of size Nx1 which contains residual error signals
% AUTHOR
% Naotoshi Seo, April 2008
% USES
% lpc.m (Signal Processing toolbox)
function [a P e] = spLpc(x, fs, ncoef)
if ~exist('ncoef', 'var'
|| isempty(ncoef)
ncoef = 2 + round(fs / 1000); % rule of thumb for human speech
end
[a P] = lpc(x, ncoef);
if nargout > 2,
est_x = filter([0 -a(2:end)],1,x); % Estimated signal
e = x - est_x; % Residual signal
end
end[x, fs] = wavread('bee.wav'
a = spLpc(x, fs, [], 'plot'Formants Detection
% NAME
% spFormantsLpc - Formants Estimation via LPC Method
% SYNOPSIS
% [F] = spFormantsLpc(a, fs)
% DESCRIPTION
% Estimate formants frequencies
% INPUTS
% a (vector) of size ncoefx1 which contains the LPC coefficients
% of the original signal. Use spLpc.m
% fs (scalar) the sampling frequency of the original signal
% OUTPUTS
% F (vector) of size ncoefx1 which contains formants
% AUTHOR
% Naotoshi Seo, April 2008
% SEE ALSO
% spLpc.m
function [F] = spFormantsLpc(a, fs)
r = roots(a);
r = r(imag(r)>0.01);
F = sort(atan2(imag(r),real(r))*fs/(2*pi));
endFormants Tracking in Short-Time Frames
% NAME
% spFormantsTrackLpc: Formants Tracking via the LPC Method
% SYNOPSIS
% [F, T] = spFormantsTrackLpc(x, fs, ncoef,
% frame_length, frame_overlap, window, show)
% DESCRIPTION
% Formants Tracking via the LPC method
% INPUTS
% x (vector) of size Nx1.
% fs (scalar) the sampling rate in Hz.
% [ncoef](scalar) the number of LPC coefficients used for
% estimation. ncoef = 2 + fs / 1000 is the default.
% [frame_length]
% (scalar) the length of each frame in micro second.
% The default is 30ms.
% [frame_overlap]
% (scalar) the length of each frame overlaps in micro second.
% The default is frame_length / 2.
% [window]
% (string) the window function such as rectwin, hamming.
% if not specified, equivalent to hamming
% [show] (boolean) plot or not. The default is 0.
% OUTPUTS
% F (vector) formants (fm = F(find(T == 0.01))
% T (vector) formant times
% AUTHOR
% Naotoshi Seo, April 2006
function [F, T] = spFormantsTrackLpc(x, fs, ncoef, frame_length, frame_overlap, window, show)
%% Initialization
N = length(x);
if ~exist('frame_length', 'var' || isempty(frame_length)
frame_length = 30;
end
if ~exist('frame_overlap', 'var' || isempty(frame_overlap)
frame_overlap = 20;
end
if ~exist('window', 'var' || isempty(window)
window = 'hamming';
end
if ~exist('show', 'var' || isempty(show)
show = 0;
end
if ~exist('ncoef', 'var'
ncoef = [];
end
nsample = round(frame_length * fs / 1000); % convert ms to points
noverlap = round(frame_overlap * fs / 1000); % convert ms to points
window = eval(sprintf('%s(nsample)', window)); % e.g., hamming(nfft)
pos = 1; t = 1;
F = []; % formants
T = []; % time (s) at the frame
mid = round(nsample/2);
while (pos+nsample <= N)
frame = x(pos:pos+nsample-1);
frame = frame - mean(frame);
a = spLpc(frame, fs, ncoef);
fm = spFormantsLpc(a, fs);
for i=1:length(fm)
F = [F fm(i)]; % number of formants are not same for each frame
T = [T (pos+mid)/fs];
end
pos = pos + (nsample - noverlap);
t = t + 1;
end
if show
% plot waveform
t=(0:N-1)/fs;
subplot(2,1,1);
plot(t,x);
legend('Waveform'
xlabel('Time (s)'
ylabel('Amplitude'
xlim([t(1) t(end)]);
% plot formants trace
subplot(2,1,2);
plot(T, F, '.'
hold off;
legend('Formants'
xlabel('Time (s)'
ylabel('Frequency (Hz)'
xlim([t(1) t(end)]);
end[x, fs] = wavread('bee.wav'
[F, T] = spFormantsTrackLpc(x, fs, [], 30, 20, 'hamming', 'plot'
Formants Detection via LPC Method
LPC
% NAME
% spLpc - The linear predictive coding (one-step finite observation
% wiener filter prediction)
% SYNOPSIS
% [a P e] = spLpc(x, fs, ncoef, show)
% DESCRIPTION
% Obtain LPC coefficients (AR model)
% INPUTS
% x (vector) of size Nx1 which contains signal
% fs (scalar) the sampling frequency
% [ncoef] (scalar) the number of coefficients. The default uses
% ncoef = 2 + fs / 1000;
% as a rule of thumb.
% OUTPUTS
% a (vector) of size ncoefx1 which contains LPC coefficients
% P (scalar) variance (power) of the prediction error
% e (vector) of size Nx1 which contains residual error signals
% AUTHOR
% Naotoshi Seo, April 2008
% USES
% lpc.m (Signal Processing toolbox)
function [a P e] = spLpc(x, fs, ncoef)
if ~exist('ncoef', 'var'
|| isempty(ncoef)ncoef = 2 + round(fs / 1000); % rule of thumb for human speech
end
[a P] = lpc(x, ncoef);
if nargout > 2,
est_x = filter([0 -a(2:end)],1,x); % Estimated signal
e = x - est_x; % Residual signal
end
end[x, fs] = wavread('bee.wav'
;a = spLpc(x, fs, [], 'plot'
;Formants Detection % NAME
% spFormantsLpc - Formants Estimation via LPC Method
% SYNOPSIS
% [F] = spFormantsLpc(a, fs)
% DESCRIPTION
% Estimate formants frequencies
% INPUTS
% a (vector) of size ncoefx1 which contains the LPC coefficients
% of the original signal. Use spLpc.m
% fs (scalar) the sampling frequency of the original signal
% OUTPUTS
% F (vector) of size ncoefx1 which contains formants
% AUTHOR
% Naotoshi Seo, April 2008
% SEE ALSO
% spLpc.m
function [F] = spFormantsLpc(a, fs)
r = roots(a);
r = r(imag(r)>0.01);
F = sort(atan2(imag(r),real(r))*fs/(2*pi));
endFormants Tracking in Short-Time Frames
% NAME
% spFormantsTrackLpc: Formants Tracking via the LPC Method
% SYNOPSIS
% [F, T] = spFormantsTrackLpc(x, fs, ncoef,
% frame_length, frame_overlap, window, show)
% DESCRIPTION
% Formants Tracking via the LPC method
% INPUTS
% x (vector) of size Nx1.
% fs (scalar) the sampling rate in Hz.
% [ncoef](scalar) the number of LPC coefficients used for
% estimation. ncoef = 2 + fs / 1000 is the default.
% [frame_length]
% (scalar) the length of each frame in micro second.
% The default is 30ms.
% [frame_overlap]
% (scalar) the length of each frame overlaps in micro second.
% The default is frame_length / 2.
% [window]
% (string) the window function such as rectwin, hamming.
% if not specified, equivalent to hamming
% [show] (boolean) plot or not. The default is 0.
% OUTPUTS
% F (vector) formants (fm = F(find(T == 0.01))
% T (vector) formant times
% AUTHOR
% Naotoshi Seo, April 2006
function [F, T] = spFormantsTrackLpc(x, fs, ncoef, frame_length, frame_overlap, window, show)
%% Initialization
N = length(x);
if ~exist('frame_length', 'var'
|| isempty(frame_length)frame_length = 30;
end
if ~exist('frame_overlap', 'var'
|| isempty(frame_overlap)frame_overlap = 20;
end
if ~exist('window', 'var'
|| isempty(window)window = 'hamming';
end
if ~exist('show', 'var'
|| isempty(show)show = 0;
end
if ~exist('ncoef', 'var'
ncoef = [];
end
nsample = round(frame_length * fs / 1000); % convert ms to points
noverlap = round(frame_overlap * fs / 1000); % convert ms to points
window = eval(sprintf('%s(nsample)', window)); % e.g., hamming(nfft)
pos = 1; t = 1;
F = []; % formants
T = []; % time (s) at the frame
mid = round(nsample/2);
while (pos+nsample <= N)
frame = x(pos:pos+nsample-1);
frame = frame - mean(frame);
a = spLpc(frame, fs, ncoef);
fm = spFormantsLpc(a, fs);
for i=1:length(fm)
F = [F fm(i)]; % number of formants are not same for each frame
T = [T (pos+mid)/fs];
end
pos = pos + (nsample - noverlap);
t = t + 1;
end
if show
% plot waveform
t=(0:N-1)/fs;
subplot(2,1,1);
plot(t,x);
legend('Waveform'
;xlabel('Time (s)'
;ylabel('Amplitude'
;xlim([t(1) t(end)]);
% plot formants trace
subplot(2,1,2);
plot(T, F, '.'
;hold off;
legend('Formants'
;xlabel('Time (s)'
;ylabel('Frequency (Hz)'
;xlim([t(1) t(end)]);
end[x, fs] = wavread('bee.wav'
;[F, T] = spFormantsTrackLpc(x, fs, [], 30, 20, 'hamming', 'plot'
;
