/*---------------------------------------------------------------------------*\ 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: This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library 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 Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ #include #include #include #include "lsp.h" #include "stack_alloc.h" #ifndef M_PI #define M_PI 3.14159265358979323846 /* pi */ #endif /*---------------------------------------------------------------------------*\ FUNCTION....: cheb_poly_eva() AUTHOR......: David Rowe DATE CREATED: 24/2/93 This function evalutes a series of chebyshev polynomials \*---------------------------------------------------------------------------*/ float cheb_poly_eva(float *coef,float x,int m,float *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,*t,*u,*v,sum; /* Allocate memory for chebyshev series formulation */ T=PUSH(stack, m/2+1); /* Initialise pointers */ t = T; /* T[i-2] */ *t++ = 1.0; u = t--; /* T[i-1] */ *u++ = x; v = u--; /* T[i] */ /* Evaluate chebyshev series formulation using iterative approach */ for(i=2;i<=m/2;i++) *v++ = (2*x)*(*u++) - *t++; /* T[i] = 2*x*T[i-1] - T[i-2] */ sum=0.0; /* initialise sum to zero */ t = T; /* reset pointer */ /* Evaluate polynomial and return value also free memory space */ for(i=0;i<=m/2;i++) sum+=coef[(m/2)-i]**t++; POP(stack); 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, float *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) polynimials */ /* Allocate memory space for polynomials */ Q = PUSH(stack, (m+1)); P = PUSH(stack, (m+1)); /* 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; /* initilaise 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= -1.0)){ xr = xl - delta ; /* 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; } } } POP(stack); POP(stack); 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, float *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); 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++){ for(i=0;iM_PI-margin) lsp[len]=margin; for (i=1;ilsp[i+1]-margin) lsp[i]= .5* (lsp[i] + lsp[i+1]-margin); } }