UHSDR/UHSDR-active-devel/mchf-eclipse/drivers/freedv/phase.c
2022-08-24 08:39:13 +02:00

290 lines
9.1 KiB
C
Executable File

/*---------------------------------------------------------------------------*\
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 "kiss_fft.h"
#include "comp.h"
#include "comp_prim.h"
#include "sine.h"
#include <assert.h>
#include <ctype.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
/*---------------------------------------------------------------------------*\
sample_phase()
Samples phase at centre of each harmonic from and array of FFT_ENC
DFT samples.
\*---------------------------------------------------------------------------*/
void sample_phase(MODEL *model,
COMP H[],
COMP A[] /* LPC analysis filter in freq domain */
)
{
int m, b;
float r;
r = TWO_PI/(FFT_ENC);
/* Sample phase at harmonics */
for(m=1; m<=model->L; m++) {
b = (int)(m*model->Wo/r + 0.5);
H[m] = cconj(A[b]); /* synth filter 1/A is opposite phase to analysis filter */
}
}
/*---------------------------------------------------------------------------*\
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 synthesis
filter excited by an impulse. In many Codec 2 modes the synthesis
filter is a LPC filter. 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_SAMP samples
over a synthesis frame of N_SAMP samples. For example if Wo is pi/20
(200 Hz), then over a 10ms frame (N_SAMP=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_SAMP;
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 synthesis 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(
int n_samp,
MODEL *model,
float *ex_phase, /* excitation phase of fundamental */
COMP H[] /* L synthesis filter freq domain samples */
)
{
int m;
float new_phi;
COMP Ex[MAX_AMP+1]; /* excitation samples */
COMP A_[MAX_AMP+1]; /* synthesised harmonic samples */
/*
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+model->Wo)*N_SAMP/2;
*/
ex_phase[0] += (model->Wo)*n_samp;
ex_phase[0] -= TWO_PI*floorf(ex_phase[0]/TWO_PI + 0.5);
for(m=1; m<=model->L; m++) {
/* generate excitation */
if (model->voiced) {
Ex[m].real = cosf(ex_phase[0]*m);
Ex[m].imag = sinf(ex_phase[0]*m);
}
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)codec2_rand()/CODEC2_RAND_MAX;
Ex[m].real = cosf(phi);
Ex[m].imag = sinf(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 = atan2f(A_[m].imag, A_[m].real+1E-12);
model->phi[m] = new_phi;
}
}
/*---------------------------------------------------------------------------*\
FUNCTION....: mag_to_phase
AUTHOR......: David Rowe
DATE CREATED: Jan 2017
Algorithm for http://www.dsprelated.com/showcode/20.php ported to C. See
also Octave function mag_to_phase.m
Given a magnitude spectrum in dB, returns a minimum-phase phase
spectra.
\*---------------------------------------------------------------------------*/
void mag_to_phase(float phase[], /* Nfft/2+1 output phase samples in radians */
float Gdbfk[], /* Nfft/2+1 postive freq amplitudes samples in dB */
int Nfft,
codec2_fft_cfg fft_fwd_cfg,
codec2_fft_cfg fft_inv_cfg
)
{
COMP Sdb[Nfft], c[Nfft], cf[Nfft], Cf[Nfft];
int Ns = Nfft/2+1;
int i;
/* install negative frequency components, 1/Nfft takes into
account kiss fft lack of scaling on ifft */
Sdb[0].real = Gdbfk[0];
Sdb[0].imag = 0.0;
for(i=1; i<Ns; i++) {
Sdb[i].real = Sdb[Nfft-i].real = Gdbfk[i];
Sdb[i].imag = Sdb[Nfft-i].imag = 0.0;
}
/* compute real cepstrum from log magnitude spectrum */
codec2_fft(fft_inv_cfg, Sdb, c);
for(i=0; i<Nfft; i++) {
c[i].real /= (float)Nfft;
c[i].imag /= (float)Nfft;
}
/* Fold cepstrum to reflect non-min-phase zeros inside unit circle */
cf[0] = c[0];
for(i=1; i<Ns-1; i++) {
cf[i] = cadd(c[i],c[Nfft-i]);
}
cf[Ns-1] = c[Ns-1];
for(i=Ns; i<Nfft; i++) {
cf[i].real = 0.0;
cf[i].imag = 0.0;
}
/* Cf = dB_magnitude + j * minimum_phase */
codec2_fft(fft_fwd_cfg, cf, Cf);
/* The maths says we are meant to be using log(x), not 20*log10(x),
so we need to scale the phase to account for this:
log(x) = 20*log10(x)/scale */
float scale = (20.0/logf(10.0));
for(i=0; i<Ns; i++) {
phase[i] = Cf[i].imag/scale;
}
}