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/*---------------------------------------------------------------------------*\
Original copyright FILE........: AKSLSPD.C TYPE........: Turbo C COMPANY.....: Voicetronix AUTHOR......: David Rowe DATE CREATED: 24/2/93
Modified by Jean-Marc Valin
This file contains functions for converting Linear Prediction Coefficients (LPC) to Line Spectral Pair (LSP) and back. Note that the LSP coefficients are not in radians format but in the x domain of the unit circle.
Speex License:
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: - Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. - Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. - Neither the name of the Xiph.org Foundation nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.*/
#include <math.h>
#include "lsp.h"
#include "stack_alloc.h"
#ifndef M_PI
#define M_PI 3.14159265358979323846 /* pi */
#endif
#ifndef NULL
#define NULL 0
#endif
/*---------------------------------------------------------------------------*\
FUNCTION....: cheb_poly_eva()
AUTHOR......: David Rowe DATE CREATED: 24/2/93
This function evaluates a series of Chebyshev polynomials
\*---------------------------------------------------------------------------*/
static float cheb_poly_eva(float *coef,float x,int m,char *stack)/* float coef[] coefficients of the polynomial to be evaluated *//* float x the point where polynomial is to be evaluated *//* int m order of the polynomial */{ int i; float *T,sum; int m2=m>>1;
/* Allocate memory for Chebyshev series formulation */ T=PUSH(stack, m2+1, float);
/* Initialise values */ T[0]=1; T[1]=x;
/* Evaluate Chebyshev series formulation using iterative approach */ /* Evaluate polynomial and return value also free memory space */ sum = coef[m2] + coef[m2-1]*x; x *= 2; for(i=2;i<=m2;i++) { T[i] = x*T[i-1] - T[i-2]; sum += coef[m2-i] * T[i]; } return sum;}
/*---------------------------------------------------------------------------*\
FUNCTION....: lpc_to_lsp()
AUTHOR......: David Rowe DATE CREATED: 24/2/93
This function converts LPC coefficients to LSP coefficients.
\*---------------------------------------------------------------------------*/
int lpc_to_lsp (float *a,int lpcrdr,float *freq,int nb,float delta, char *stack)/* float *a lpc coefficients *//* int lpcrdr order of LPC coefficients (10) *//* float *freq LSP frequencies in the x domain *//* int nb number of sub-intervals (4) *//* float delta grid spacing interval (0.02) */
{
float psuml,psumr,psumm,temp_xr,xl,xr,xm=0; float temp_psumr/*,temp_qsumr*/; int i,j,m,flag,k; float *Q; /* ptrs for memory allocation */ float *P; float *px; /* ptrs of respective P'(z) & Q'(z) */ float *qx; float *p; float *q; float *pt; /* ptr used for cheb_poly_eval()
whether P' or Q' */ int roots=0; /* DR 8/2/94: number of roots found */ flag = 1; /* program is searching for a root when,
1 else has found one */ m = lpcrdr/2; /* order of P'(z) & Q'(z) polynomials */
/* Allocate memory space for polynomials */ Q = PUSH(stack, (m+1), float); P = PUSH(stack, (m+1), float);
/* determine P'(z)'s and Q'(z)'s coefficients where
P'(z) = P(z)/(1 + z^(-1)) and Q'(z) = Q(z)/(1-z^(-1)) */
px = P; /* initialise ptrs */ qx = Q; p = px; q = qx; *px++ = 1.0; *qx++ = 1.0; for(i=1;i<=m;i++){ *px++ = a[i]+a[lpcrdr+1-i]-*p++; *qx++ = a[i]-a[lpcrdr+1-i]+*q++; } px = P; qx = Q; for(i=0;i<m;i++){ *px = 2**px; *qx = 2**qx; px++; qx++; } px = P; /* re-initialise ptrs */ qx = Q;
/* Search for a zero in P'(z) polynomial first and then alternate to Q'(z).
Keep alternating between the two polynomials as each zero is found */
xr = 0; /* initialise xr to zero */ xl = 1.0; /* start at point xl = 1 */
for(j=0;j<lpcrdr;j++){ if(j%2) /* determines whether P' or Q' is eval. */ pt = qx; else pt = px;
psuml = cheb_poly_eva(pt,xl,lpcrdr,stack); /* evals poly. at xl */ flag = 1; while(flag && (xr >= -1.0)){ float dd; /* Modified by JMV to provide smaller steps around x=+-1 */ dd=(delta*(1-.9*xl*xl)); if (fabs(psuml)<.2) dd *= .5;
xr = xl - dd; /* interval spacing */ psumr = cheb_poly_eva(pt,xr,lpcrdr,stack);/* poly(xl-delta_x) */ temp_psumr = psumr; temp_xr = xr;
/* if no sign change increment xr and re-evaluate poly(xr). Repeat til
sign change. if a sign change has occurred the interval is bisected and then checked again for a sign change which determines in which interval the zero lies in. If there is no sign change between poly(xm) and poly(xl) set interval between xm and xr else set interval between xl and xr and repeat till root is located within the specified limits */
if((psumr*psuml)<0.0){ roots++;
psumm=psuml; for(k=0;k<=nb;k++){ xm = (xl+xr)/2; /* bisect the interval */ psumm=cheb_poly_eva(pt,xm,lpcrdr,stack); if(psumm*psuml>0.){ psuml=psumm; xl=xm; } else{ psumr=psumm; xr=xm; } }
/* once zero is found, reset initial interval to xr */ freq[j] = (xm); xl = xm; flag = 0; /* reset flag for next search */ } else{ psuml=temp_psumr; xl=temp_xr; } } } return(roots);}
/*---------------------------------------------------------------------------*\
FUNCTION....: lsp_to_lpc()
AUTHOR......: David Rowe DATE CREATED: 24/2/93
lsp_to_lpc: This function converts LSP coefficients to LPC coefficients.
\*---------------------------------------------------------------------------*/
void lsp_to_lpc(float *freq,float *ak,int lpcrdr, char *stack)/* float *freq array of LSP frequencies in the x domain *//* float *ak array of LPC coefficients *//* int lpcrdr order of LPC coefficients */
{ int i,j; float xout1,xout2,xin1,xin2; float *Wp; float *pw,*n1,*n2,*n3,*n4=NULL; int m = lpcrdr/2;
Wp = PUSH(stack, 4*m+2, float); pw = Wp;
/* initialise contents of array */
for(i=0;i<=4*m+1;i++){ /* set contents of buffer to 0 */ *pw++ = 0.0; }
/* Set pointers up */
pw = Wp; xin1 = 1.0; xin2 = 1.0;
/* reconstruct P(z) and Q(z) by cascading second order
polynomials in form 1 - 2xz(-1) +z(-2), where x is the LSP coefficient */
for(j=0;j<=lpcrdr;j++){ int i2=0; for(i=0;i<m;i++,i2+=2){ n1 = pw+(i*4); n2 = n1 + 1; n3 = n2 + 1; n4 = n3 + 1; xout1 = xin1 - 2*(freq[i2]) * *n1 + *n2; xout2 = xin2 - 2*(freq[i2+1]) * *n3 + *n4; *n2 = *n1; *n4 = *n3; *n1 = xin1; *n3 = xin2; xin1 = xout1; xin2 = xout2; } xout1 = xin1 + *(n4+1); xout2 = xin2 - *(n4+2); ak[j] = (xout1 + xout2)*0.5; *(n4+1) = xin1; *(n4+2) = xin2;
xin1 = 0.0; xin2 = 0.0; }
}
/*Added by JMV
Makes sure the LSPs are stable*/void lsp_enforce_margin(float *lsp, int len, float margin){ int i; if (lsp[0]<margin) lsp[0]=margin; if (lsp[len-1]>M_PI-margin) lsp[len-1]=M_PI-margin; for (i=1;i<len-1;i++) { if (lsp[i]<lsp[i-1]+margin) lsp[i]=lsp[i-1]+margin;
if (lsp[i]>lsp[i+1]-margin) lsp[i]= .5* (lsp[i] + lsp[i+1]-margin); }}
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