path: root/phase.c

/*---------------------------------------------------------------------------*\

  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;
    }

    
}