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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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