255 lines
8.4 KiB
C
255 lines
8.4 KiB
C
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/*---------------------------------------------------------------------------*\
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FILE........: phase.c
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AUTHOR......: David Rowe
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DATE CREATED: 1/2/09
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Functions for modelling and synthesising phase.
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\*---------------------------------------------------------------------------*/
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/*
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Copyright (C) 2009 David Rowe
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All rights reserved.
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License version 2.1, as
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published by the Free Software Foundation. This program is
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distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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*/
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#include "defines.h"
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#include "phase.h"
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#include "four1.h"
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#include <assert.h>
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#include <math.h>
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#include <string.h>
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#include <stdlib.h>
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#define VTHRESH 4.0
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/*---------------------------------------------------------------------------*\
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aks_to_H()
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Samples the complex LPC synthesis filter spectrum at the harmonic
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frequencies.
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\*---------------------------------------------------------------------------*/
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void aks_to_H(
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MODEL *model, /* model parameters */
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float aks[], /* LPC's */
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float G, /* energy term */
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COMP H[], /* complex LPC spectral samples */
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int order
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)
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{
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COMP Pw[FFT_DEC]; /* power spectrum */
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int i,m; /* loop variables */
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int am,bm; /* limits of current band */
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float r; /* no. rads/bin */
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float Em; /* energy in band */
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float Am; /* spectral amplitude sample */
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int b; /* centre bin of harmonic */
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float phi_; /* phase of LPC spectra */
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r = TWO_PI/(FFT_DEC);
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/* Determine DFT of A(exp(jw)) ------------------------------------------*/
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for(i=0; i<FFT_DEC; i++) {
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Pw[i].real = 0.0;
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Pw[i].imag = 0.0;
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}
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for(i=0; i<=order; i++)
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Pw[i].real = aks[i];
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four1(&Pw[-1].imag,FFT_DEC,-1);
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/* Sample magnitude and phase at harmonics */
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for(m=1; m<=model->L; m++) {
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am = floor((m - 0.5)*model->Wo/r + 0.5);
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bm = floor((m + 0.5)*model->Wo/r + 0.5);
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b = floor(m*model->Wo/r + 0.5);
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Em = 0.0;
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for(i=am; i<bm; i++)
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Em += G/(Pw[i].real*Pw[i].real + Pw[i].imag*Pw[i].imag);
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Am = sqrt(fabs(Em/(bm-am)));
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phi_ = -atan2(Pw[b].imag,Pw[b].real);
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H[m].real = Am*cos(phi_);
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H[m].imag = Am*sin(phi_);
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}
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}
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/*---------------------------------------------------------------------------*\
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phase_synth_zero_order()
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Synthesises phases based on SNR and a rule based approach. No phase
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parameters are required apart from the SNR (which can be reduced to a
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1 bit V/UV decision per frame).
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The phase of each harmonic is modelled as the phase of a LPC
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synthesis filter excited by an impulse. Unlike the first order
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model the position of the impulse is not transmitted, so we create
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an excitation pulse train using a rule based approach.
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Consider a pulse train with a pulse starting time n=0, with pulses
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repeated at a rate of Wo, the fundamental frequency. A pulse train
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in the time domain is equivalent to harmonics in the frequency
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domain. We can make an excitation pulse train using a sum of
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sinsusoids:
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for(m=1; m<=L; m++)
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ex[n] = cos(m*Wo*n)
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Note: the Octave script ../octave/phase.m is an example of this if
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you would like to try making a pulse train.
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The phase of each excitation harmonic is:
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arg(E[m]) = mWo
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where E[m] are the complex excitation (freq domain) samples,
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arg(x), just returns the phase of a complex sample x.
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As we don't transmit the pulse position for this model, we need to
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synthesise it. Now the excitation pulses occur at a rate of Wo.
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This means the phase of the first harmonic advances by N samples
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over a synthesis frame of N samples. For example if Wo is pi/20
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(200 Hz), then over a 10ms frame (N=80 samples), the phase of the
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first harmonic would advance (pi/20)*80 = 4*pi or two complete
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cycles.
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We generate the excitation phase of the fundamental (first
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harmonic):
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arg[E[1]] = Wo*N;
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We then relate the phase of the m-th excitation harmonic to the
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phase of the fundamental as:
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arg(E[m]) = m*arg(E[1])
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This E[m] then gets passed through the LPC synthesis filter to
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determine the final harmonic phase.
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For a while there were prolems with low pitched males like hts1
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sounding "clicky". The synthesied time domain waveform also looked
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clicky. Many methods were tried to improve the sounds quality of
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low pitched males. Finally adding a small amount of jitter to each
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harmonic worked.
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The current result sounds very close to the original phases, with
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only 1 voicing bit per frame. For example hts1a using original
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amplitudes and this phase model produces speech hard to distinguish
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from speech synthesise with the orginal phases. The sound quality
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of this patrtiallyuantised codec (nb original amplitudes) is higher
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than g729, even though all the phase information has been
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discarded.
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NOTES:
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1/ This synthesis model is effectvely the same as simple LPC-10
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vocoders, and yet sounds much better. Why?
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2/ I am pretty sure the Lincoln Lab sinusoidal coding guys (like xMBE
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also from MIT) first described this zero phase model, I need to look
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up the paper.
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3/ Note that this approach could cause some discontinuities in
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the phase at the edge of synthesis frames, as no attempt is made
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to make sure that the phase tracks are continuous (the excitation
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phases are continuous, but not the final phases after filtering
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by the LPC spectra). Technically this is a bad thing. However
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this may actually be a good thing, disturbing the phase tracks a
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bit. More research needed, e.g. test a synthesis model that adds
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a small delta-W to make phase tracks line up for voiced
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harmonics.
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4/ Why does this sound so great with 1 V/UV decision? Conventional
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wisdom says mixed voicing is required for high qaulity speech.
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\*---------------------------------------------------------------------------*/
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void phase_synth_zero_order(
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MODEL *model,
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float aks[],
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float *ex_phase /* excitation phase of fundamental */
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)
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{
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int m;
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float new_phi;
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COMP Ex[MAX_AMP]; /* excitation samples */
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COMP A_[MAX_AMP]; /* synthesised harmonic samples */
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COMP H[MAX_AMP]; /* LPC freq domain samples */
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float G;
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float jitter;
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G = 1.0;
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aks_to_H(model,aks,G,H,LPC_ORD);
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/*
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Update excitation fundamental phase track, this sets the position
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of each pitch pulse during voiced speech. After much experiment
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I found that using just this frame Wo improved quality for UV
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sounds compared to interpolating two frames Wo like this:
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ex_phase[0] += (*prev_Wo+mode->Wo)*N/2;
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*/
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ex_phase[0] += (model->Wo)*N;
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ex_phase[0] -= TWO_PI*floor(ex_phase[0]/TWO_PI + 0.5);
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for(m=1; m<=model->L; m++) {
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/* generate excitation */
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if (model->voiced) {
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/* This method of adding jitter really helped remove the clicky
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sound in low pitched makes like hts1a. This moves the onset
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of each harmonic over at +/- 0.25 of a sample.
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*/
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jitter = 0.25*(1.0 - 2.0*rand()/RAND_MAX);
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Ex[m].real = cos(ex_phase[0]*m - jitter*model->Wo*m);
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Ex[m].imag = sin(ex_phase[0]*m - jitter*model->Wo*m);
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}
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else {
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/* When a few samples were tested I found that LPC filter
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phase is not needed in the unvoiced case, but no harm in
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keeping it.
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*/
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float phi = TWO_PI*(float)rand()/RAND_MAX;
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Ex[m].real = cos(phi);
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Ex[m].imag = sin(phi);
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}
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/* filter using LPC filter */
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A_[m].real = H[m].real*Ex[m].real - H[m].imag*Ex[m].imag;
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A_[m].imag = H[m].imag*Ex[m].real + H[m].real*Ex[m].imag;
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/* modify sinusoidal phase */
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new_phi = atan2(A_[m].imag, A_[m].real+1E-12);
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model->phi[m] = new_phi;
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}
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}
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