1 /********************************************************************
3 * THIS FILE IS PART OF THE Ogg Vorbis SOFTWARE CODEC SOURCE CODE. *
4 * USE, DISTRIBUTION AND REPRODUCTION OF THIS SOURCE IS GOVERNED BY *
5 * THE GNU PUBLIC LICENSE 2, WHICH IS INCLUDED WITH THIS SOURCE. *
6 * PLEASE READ THESE TERMS DISTRIBUTING. *
8 * THE OggSQUISH SOURCE CODE IS (C) COPYRIGHT 1994-2000 *
9 * by Monty <monty@xiph.org> and The XIPHOPHORUS Company *
10 * http://www.xiph.org/ *
12 ********************************************************************
14 function: LSP (also called LSF) conversion routines
15 last mod: $Id: lsp.c,v 1.8 2000/05/08 20:49:49 xiphmont Exp $
17 The LSP generation code is taken (with minimal modification) from
18 "On the Computation of the LSP Frequencies" by Joseph Rothweiler
19 <rothwlr@altavista.net>, available at:
21 http://www2.xtdl.com/~rothwlr/lsfpaper/lsfpage.html
23 ********************************************************************/
25 /* Note that the lpc-lsp conversion finds the roots of polynomial with
26 an iterative root polisher (CACM algorithm 283). It *is* possible
27 to confuse this algorithm into not converging; that should only
28 happen with absurdly closely spaced roots (very sharp peaks in the
29 LPC f response) which in turn should be impossible in our use of
30 the code. If this *does* happen anyway, it's a bug in the floor
31 finder; find the cause of the confusion (probably a single bin
32 spike or accidental near-double-limit resolution problems) and
42 void vorbis_lsp_to_lpc(double *lsp,double *lpc,int m){
44 double *O=alloca(sizeof(double)*m2);
45 double *E=alloca(sizeof(double)*m2);
47 double *Ae=alloca(sizeof(double)*(m2+1));
48 double *Ao=alloca(sizeof(double)*(m2+1));
50 double *Be=alloca(sizeof(double)*(m2));
51 double *Bo=alloca(sizeof(double)*(m2));
54 /* even/odd roots setup */
56 O[i]=-2.*cos(lsp[i*2]);
57 E[i]=-2.*cos(lsp[i*2+1]);
60 /* set up impulse response */
70 /* run impulse response */
74 temp=O[j]*Ao[j]+Ae[j];
79 temp=E[j]*Bo[j]+Be[j];
84 lpc[i-1]=(A+Ao[j]+B-Ae[j])/2;
90 static void cheby(double *g, int ord) {
94 for(i=2; i<= ord; i++) {
95 for(j=ord; j >= i; j--) {
102 static int comp(const void *a,const void *b){
103 if(*(double *)a<*(double *)b)
109 /* CACM algorithm 283. */
110 static void cacm283(double *a,int ord,double *r){
112 double val, p, delta, error;
115 for(i=0; i<ord;i++) r[i] = 2.0 * (i+0.5) / ord - 1.0;
117 for(error=1 ; error > 1.e-12; ) {
119 for( i=0; i<ord; i++) { /* Update each point. */
123 for(k=ord-1; k>= 0; k--) {
124 val = val * rooti + a[k];
125 if (k != i) p *= rooti - r[k];
130 error += delta*delta;
134 /* Replaced the original bubble sort with a real sort. With your
135 help, we can eliminate the bubble sort in our lifetime. --Monty */
137 qsort(r,ord,sizeof(double),comp);
141 /* Convert lpc coefficients to lsp coefficients */
142 void vorbis_lpc_to_lsp(double *lpc,double *lsp,int m){
144 double *g1=alloca(sizeof(double)*(order2+1));
145 double *g2=alloca(sizeof(double)*(order2+1));
146 double *g1r=alloca(sizeof(double)*(order2+1));
147 double *g2r=alloca(sizeof(double)*(order2+1));
150 /* Compute the lengths of the x polynomials. */
151 /* Compute the first half of K & R F1 & F2 polynomials. */
152 /* Compute half of the symmetric and antisymmetric polynomials. */
153 /* Remove the roots at +1 and -1. */
156 for(i=0;i<order2;i++) g1[order2-i-1] = lpc[i]+lpc[m-i-1];
158 for(i=0;i<order2;i++) g2[order2-i-1] = lpc[i]-lpc[m-i-1];
160 for(i=0; i<order2;i++) g1[order2-i-1] -= g1[order2-i];
161 for(i=0; i<order2;i++) g2[order2-i-1] += g2[order2-i];
163 /* Convert into polynomials in cos(alpha) */
167 /* Find the roots of the 2 even polynomials.*/
169 cacm283(g1,order2,g1r);
170 cacm283(g2,order2,g2r);
173 lsp[i] = acos(g1r[i/2]);
174 lsp[i+1] = acos(g2r[i/2]);