vorbis/lib/lsp.c

/********************************************************************
 *                                                                  *
 * THIS FILE IS PART OF THE Ogg Vorbis SOFTWARE CODEC SOURCE CODE.  *
 * USE, DISTRIBUTION AND REPRODUCTION OF THIS SOURCE IS GOVERNED BY *
 * THE GNU PUBLIC LICENSE 2, WHICH IS INCLUDED WITH THIS SOURCE.    *
 * PLEASE READ THESE TERMS DISTRIBUTING.                            *
 *                                                                  *
 * THE OggSQUISH SOURCE CODE IS (C) COPYRIGHT 1994-2000             *
 * by Monty <monty@xiph.org> and The XIPHOPHORUS Company            *
 * http://www.xiph.org/                                             *
 *                                                                  *
 ********************************************************************

  function: LSP (also called LSF) conversion routines
  last mod: $Id: lsp.c,v 1.9.2.3 2000/09/02 09:39:19 xiphmont Exp $

  The LSP generation code is taken (with minimal modification) from
  "On the Computation of the LSP Frequencies" by Joseph Rothweiler
  <rothwlr@altavista.net>, available at:
  
  http://www2.xtdl.com/~rothwlr/lsfpaper/lsfpage.html 

 ********************************************************************/

/* Note that the lpc-lsp conversion finds the roots of polynomial with
   an iterative root polisher (CACM algorithm 283).  It *is* possible
   to confuse this algorithm into not converging; that should only
   happen with absurdly closely spaced roots (very sharp peaks in the
   LPC f response) which in turn should be impossible in our use of
   the code.  If this *does* happen anyway, it's a bug in the floor
   finder; find the cause of the confusion (probably a single bin
   spike or accidental near-float-limit resolution problems) and
   correct it. */

#include <math.h>
#include <string.h>
#include <stdlib.h>
#include "lsp.h"
#include "os.h"
#include "misc.h"

void vorbis_lsp_to_curve(float *curve,int n,float *lsp,int m,float amp,
			 float *w){
  int i,j,k;
  float *coslsp=alloca(m*sizeof(float));
  for(i=0;i<m;i++)coslsp[i]=2*cos(lsp[i]);

  for(k=0;k<n;k++){
    double p=.5;
    double q=.5;
    for(j=0;j<m;j+=2){
      p*= w[k]-coslsp[j];
      q*= w[k]-coslsp[j+1];
    }
    curve[k]=amp/sqrt(p*p*(2.+ w[k])+q*q*(2.- w[k]));
  }
}

static void cheby(float *g, int ord) {
  int i, j;

  g[0] *= 0.5;
  for(i=2; i<= ord; i++) {
    for(j=ord; j >= i; j--) {
      g[j-2] -= g[j];
      g[j] += g[j]; 
    }
  }
}

static int comp(const void *a,const void *b){
  if(*(float *)a<*(float *)b)
    return(1);
  else
    return(-1);
}

/* CACM algorithm 283. */
/* we require doubles here due to the huge spread between val/p and
   the required max error of 1.e-12, which is beyond the capabilities
   of floats */
static void cacm283(float *a,int ord,float *r){
  int i, k;
  double val, p, delta, error;
  double rooti;

  for(i=0; i<ord;i++) r[i] = 2.0 * (i+0.5) / ord - 1.0;
  
  for(error=1 ; error > 1.e-12; ) {
    error = 0;
    for( i=0; i<ord; i++) {  /* Update each point. */
      rooti = r[i];
      val = a[ord];
      p = a[ord];
      for(k=ord-1; k>= 0; k--) {
	val = val * rooti + a[k];
	if (k != i) p *= rooti - r[k];
      }
      delta = val/p;
      r[i] -= delta;

      error += delta*delta;
    }
  }
  
  /* Replaced the original bubble sort with a real sort.  With your
     help, we can eliminate the bubble sort in our lifetime. --Monty */
  
  qsort(r,ord,sizeof(float),comp);

}

/* Convert lpc coefficients to lsp coefficients */
void vorbis_lpc_to_lsp(float *lpc,float *lsp,int m){
  int order2=m/2;
  float *g1=alloca(sizeof(float)*(order2+1));
  float *g2=alloca(sizeof(float)*(order2+1));
  float *g1r=alloca(sizeof(float)*(order2+1));
  float *g2r=alloca(sizeof(float)*(order2+1));
  int i;

  /* Compute the lengths of the x polynomials. */
  /* Compute the first half of K & R F1 & F2 polynomials. */
  /* Compute half of the symmetric and antisymmetric polynomials. */
  /* Remove the roots at +1 and -1. */
  
  g1[order2] = 1.0;
  for(i=0;i<order2;i++) g1[order2-i-1] = lpc[i]+lpc[m-i-1];
  g2[order2] = 1.0;
  for(i=0;i<order2;i++) g2[order2-i-1] = lpc[i]-lpc[m-i-1];
  
  for(i=0; i<order2;i++) g1[order2-i-1] -= g1[order2-i];
  for(i=0; i<order2;i++) g2[order2-i-1] += g2[order2-i];

  /* Convert into polynomials in cos(alpha) */
  cheby(g1,order2);
  cheby(g2,order2);

  /* Find the roots of the 2 even polynomials.*/
  
  cacm283(g1,order2,g1r);
  cacm283(g2,order2,g2r);
  
  for(i=0;i<m;i+=2){
    lsp[i] = acos(g1r[i/2]);
    lsp[i+1] = acos(g2r[i/2]);
  }
}