/*---------------------------------------------------------------------------*\
FILE........: phase.c
AUTHOR......: David Rowe
DATE CREATED: 1/2/09
Functions for modelling and synthesising phase.
\*---------------------------------------------------------------------------*/
/*
Copyright (C) 2009 David Rowe
All rights reserved.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License version 2.1, as
published by the Free Software Foundation. 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 Lesser General Public License
along with this program; if not,see <http://www.gnu.org/licenses/>.
*/
#include "defines.h"
#include "phase.h"
#include "fft.h"
#include "comp.h"
#include "glottal.c"
#include <assert.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
#define GLOTTAL_FFT_SIZE 512
/*---------------------------------------------------------------------------*\
aks_to_H()
Samples the complex LPC synthesis filter spectrum at the harmonic
frequencies.
\*---------------------------------------------------------------------------*/
void aks_to_H(
MODEL *model, /* model parameters */
float aks[], /* LPC's */
float G, /* energy term */
COMP H[], /* complex LPC spectral samples */
int order
)
{
COMP Pw[FFT_DEC]; /* power spectrum */
int i,m; /* loop variables */
int am,bm; /* limits of current band */
float r; /* no. rads/bin */
float Em; /* energy in band */
float Am; /* spectral amplitude sample */
int b; /* centre bin of harmonic */
float phi_; /* phase of LPC spectra */
r = TWO_PI/(FFT_DEC);
/* Determine DFT of A(exp(jw)) ------------------------------------------*/
for(i=0; i<FFT_DEC; i++) {
Pw[i].real = 0.0;
Pw[i].imag = 0.0;
}
for(i=0; i<=order; i++)
Pw[i].real = aks[i];
fft(&Pw[0].real,FFT_DEC,-1);
/* Sample magnitude and phase at harmonics */
for(m=1; m<=model->L; m++) {
am = floor((m - 0.5)*model->Wo/r + 0.5);
bm = floor((m + 0.5)*model->Wo/r + 0.5);
b = floor(m*model->Wo/r + 0.5);
Em = 0.0;
for(i=am; i<bm; i++)
Em += G/(Pw[i].real*Pw[i].real + Pw[i].imag*Pw[i].imag);
Am = sqrt(fabs(Em/(bm-am)));
phi_ = -atan2(Pw[b].imag,Pw[b].real);
H[m].real = Am*cos(phi_);
H[m].imag = Am*sin(phi_);
}
}
/*---------------------------------------------------------------------------*\
phase_synth_zero_order()
Synthesises phases based on SNR and a rule based approach. No phase
parameters are required apart from the SNR (which can be reduced to a
1 bit V/UV decision per frame).
The phase of each harmonic is modelled as the phase of a LPC
synthesis filter excited by an impulse. Unlike the first order
model the position of the impulse is not transmitted, so we create
an excitation pulse train using a rule based approach.
Consider a pulse train with a pulse starting time n=0, with pulses
repeated at a rate of Wo, the fundamental frequency. A pulse train
in the time domain is equivalent to harmonics in the frequency
domain. We can make an excitation pulse train using a sum of
sinsusoids:
for(m=1; m<=L; m++)
ex[n] = cos(m*Wo*n)
Note: the Octave script ../octave/phase.m is an example of this if
you would like to try making a pulse train.
The phase of each excitation harmonic is:
arg(E[m]) = mWo
where E[m] are the complex excitation (freq domain) samples,
arg(x), just returns the phase of a complex sample x.
As we don't transmit the pulse position for this model, we need to
synthesise it. Now the excitation pulses occur at a rate of Wo.
This means the phase of the first harmonic advances by N samples
over a synthesis frame of N samples. For example if Wo is pi/20
(200 Hz), then over a 10ms frame (N=80 samples), the phase of the
first harmonic would advance (pi/20)*80 = 4*pi or two complete
cycles.
We generate the excitation phase of the fundamental (first
harmonic):
arg[E[1]] = Wo*N;
We then relate the phase of the m-th excitation harmonic to the
phase of the fundamental as:
arg(E[m]) = m*arg(E[1])
This E[m] then gets passed through the LPC synthesis filter to
determine the final harmonic phase.
Comparing to speech synthesised using original phases:
- Through headphones speech synthesised with this model is not as
good. Through a loudspeaker it is very close to original phases.
- If there are voicing errors, the speech can sound clicky or
staticy. If V speech is mistakenly declared UV, this model tends to
synthesise impulses or clicks, as there is usually very little shift or
dispersion through the LPC filter.
- When combined with LPC amplitude modelling there is an additional
drop in quality. I am not sure why, theory is interformant energy
is raised making any phase errors more obvious.
NOTES:
1/ This synthesis model is effectively the same as a simple LPC-10
vocoders, and yet sounds much better. Why? Conventional wisdom
(AMBE, MELP) says mixed voicing is required for high quality
speech.
2/ I am pretty sure the Lincoln Lab sinusoidal coding guys (like xMBE
also from MIT) first described this zero phase model, I need to look
up the paper.
3/ Note that this approach could cause some discontinuities in
the phase at the edge of synthesis frames, as no attempt is made
to make sure that the phase tracks are continuous (the excitation
phases are continuous, but not the final phases after filtering
by the LPC spectra). Technically this is a bad thing. However
this may actually be a good thing, disturbing the phase tracks a
bit. More research needed, e.g. test a synthesis model that adds
a small delta-W to make phase tracks line up for voiced
harmonics.
\*---------------------------------------------------------------------------*/
void phase_synth_zero_order(
MODEL *model,
float aks[],
float *ex_phase, /* excitation phase of fundamental */
int order
)
{
int m;
float new_phi;
COMP Ex[MAX_AMP]; /* excitation samples */
COMP A_[MAX_AMP]; /* synthesised harmonic samples */
COMP H[MAX_AMP]; /* LPC freq domain samples */
float G;
float jitter = 0.0;
float r;
int b;
G = 1.0;
aks_to_H(model, aks, G, H, order);
/*
Update excitation fundamental phase track, this sets the position
of each pitch pulse during voiced speech. After much experiment
I found that using just this frame's Wo improved quality for UV
sounds compared to interpolating two frames Wo like this:
ex_phase[0] += (*prev_Wo+mode->Wo)*N/2;
*/
ex_phase[0] += (model->Wo)*N;
ex_phase[0] -= TWO_PI*floor(ex_phase[0]/TWO_PI + 0.5);
r = TWO_PI/GLOTTAL_FFT_SIZE;
for(m=1; m<=model->L; m++) {
/* generate excitation */
if (model->voiced) {
/* I think adding a little jitter helps improve low pitch
males like hts1a. This moves the onset of each harmonic
over at +/- 0.25 of a sample.
*/
jitter = 0.25*(1.0 - 2.0*rand()/RAND_MAX);
b = floor(m*model->Wo/r + 0.5);
if (b > ((GLOTTAL_FFT_SIZE/2)-1)) {
b = (GLOTTAL_FFT_SIZE/2)-1;
}
Ex[m].real = cos(ex_phase[0]*m - jitter*model->Wo*m + glottal[b]);
Ex[m].imag = sin(ex_phase[0]*m - jitter*model->Wo*m + glottal[b]);
}
else {
/* When a few samples were tested I found that LPC filter
phase is not needed in the unvoiced case, but no harm in
keeping it.
*/
float phi = TWO_PI*(float)rand()/RAND_MAX;
Ex[m].real = cos(phi);
Ex[m].imag = sin(phi);
}
/* filter using LPC filter */
A_[m].real = H[m].real*Ex[m].real - H[m].imag*Ex[m].imag;
A_[m].imag = H[m].imag*Ex[m].real + H[m].real*Ex[m].imag;
/* modify sinusoidal phase */
new_phi = atan2(A_[m].imag, A_[m].real+1E-12);
model->phi[m] = new_phi;
}
}