621 lines
16 KiB
C
621 lines
16 KiB
C
/*---------------------------------------------------------------------------*\
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Original copyright
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FILE........: AKSLSPD.C
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TYPE........: Turbo C
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COMPANY.....: Voicetronix
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AUTHOR......: David Rowe
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DATE CREATED: 24/2/93
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Heavily modified by Jean-Marc Valin (fixed-point, optimizations,
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additional functions, ...)
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This file contains functions for converting Linear Prediction
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Coefficients (LPC) to Line Spectral Pair (LSP) and back. Note that the
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LSP coefficients are not in radians format but in the x domain of the
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unit circle.
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Speex License:
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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- Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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- Neither the name of the Xiph.org Foundation nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#ifdef _MSC_VER
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#include "winpoop.h"
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#endif
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#include <math.h>
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#include "lsp.h"
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#include "stack_alloc.h"
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#include "math_approx.h"
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#ifndef M_PI
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#define M_PI 3.14159265358979323846 /* pi */
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#endif
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#ifndef NULL
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#define NULL 0
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#endif
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#ifdef FIXED_POINT
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#define C1 8192
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#define C2 -4096
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#define C3 340
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#define C4 -10
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static spx_word16_t spx_cos(spx_word16_t x)
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{
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spx_word16_t x2;
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if (x<12868)
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{
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x2 = MULT16_16_P13(x,x);
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return ADD32(C1, MULT16_16_P13(x2, ADD32(C2, MULT16_16_P13(x2, ADD32(C3, MULT16_16_P13(C4, x2))))));
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} else {
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x = SUB16(25736,x);
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x2 = MULT16_16_P13(x,x);
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return SUB32(-C1, MULT16_16_P13(x2, ADD32(C2, MULT16_16_P13(x2, ADD32(C3, MULT16_16_P13(C4, x2))))));
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/*return SUB32(-C1, MULT16_16_Q13(x2, ADD32(C2, MULT16_16_Q13(C3, x2))));*/
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}
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}
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#define FREQ_SCALE 16384
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/*#define ANGLE2X(a) (32768*cos(((a)/8192.)))*/
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#define ANGLE2X(a) (SHL16(spx_cos(a),2))
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/*#define X2ANGLE(x) (acos(.00006103515625*(x))*LSP_SCALING)*/
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#define X2ANGLE(x) (spx_acos(x))
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#else
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/*#define C1 0.99940307
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#define C2 -0.49558072
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#define C3 0.03679168*/
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#define C1 0.9999932946f
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#define C2 -0.4999124376f
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#define C3 0.0414877472f
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#define C4 -0.0012712095f
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#define SPX_PI_2 1.5707963268
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static inline spx_word16_t spx_cos(spx_word16_t x)
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{
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if (x<SPX_PI_2)
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{
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x *= x;
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return C1 + x*(C2+x*(C3+C4*x));
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} else {
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x = M_PI-x;
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x *= x;
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return NEG16(C1 + x*(C2+x*(C3+C4*x)));
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}
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}
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#define FREQ_SCALE 1.
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#define ANGLE2X(a) (spx_cos(a))
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#define X2ANGLE(x) (acos(x))
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#endif
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/*---------------------------------------------------------------------------*\
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FUNCTION....: cheb_poly_eva()
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AUTHOR......: David Rowe
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DATE CREATED: 24/2/93
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This function evaluates a series of Chebyshev polynomials
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\*---------------------------------------------------------------------------*/
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#ifdef FIXED_POINT
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static inline spx_word32_t cheb_poly_eva(spx_word32_t *coef,spx_word16_t x,int m,char *stack)
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/* float coef[] coefficients of the polynomial to be evaluated */
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/* float x the point where polynomial is to be evaluated */
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/* int m order of the polynomial */
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{
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int i;
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VARDECL(spx_word16_t *T);
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spx_word32_t sum;
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int m2=m>>1;
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VARDECL(spx_word16_t *coefn);
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/*Prevents overflows*/
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if (x>16383)
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x = 16383;
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if (x<-16383)
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x = -16383;
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/* Allocate memory for Chebyshev series formulation */
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ALLOC(T, m2+1, spx_word16_t);
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ALLOC(coefn, m2+1, spx_word16_t);
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for (i=0;i<m2+1;i++)
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{
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coefn[i] = coef[i];
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/*printf ("%f ", coef[i]);*/
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}
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/*printf ("\n");*/
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/* Initialise values */
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T[0]=16384;
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T[1]=x;
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/* Evaluate Chebyshev series formulation using iterative approach */
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/* Evaluate polynomial and return value also free memory space */
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sum = ADD32(coefn[m2], MULT16_16_P14(coefn[m2-1],x));
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/*x *= 2;*/
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for(i=2;i<=m2;i++)
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{
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T[i] = SUB16(MULT16_16_Q13(x,T[i-1]), T[i-2]);
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sum = ADD32(sum, MULT16_16_P14(coefn[m2-i],T[i]));
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/*printf ("%f ", sum);*/
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}
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/*printf ("\n");*/
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return sum;
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}
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#else
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static float cheb_poly_eva(spx_word32_t *coef,float x,int m,char *stack)
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/* float coef[] coefficients of the polynomial to be evaluated */
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/* float x the point where polynomial is to be evaluated */
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/* int m order of the polynomial */
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{
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int i;
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VARDECL(float *T);
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float sum;
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int m2=m>>1;
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/* Allocate memory for Chebyshev series formulation */
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ALLOC(T, m2+1, float);
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/* Initialise values */
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T[0]=1;
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T[1]=x;
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/* Evaluate Chebyshev series formulation using iterative approach */
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/* Evaluate polynomial and return value also free memory space */
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sum = coef[m2] + coef[m2-1]*x;
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x *= 2;
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for(i=2;i<=m2;i++)
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{
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T[i] = x*T[i-1] - T[i-2];
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sum += coef[m2-i] * T[i];
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}
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return sum;
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}
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#endif
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/*---------------------------------------------------------------------------*\
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FUNCTION....: lpc_to_lsp()
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AUTHOR......: David Rowe
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DATE CREATED: 24/2/93
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This function converts LPC coefficients to LSP
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coefficients.
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\*---------------------------------------------------------------------------*/
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#ifdef FIXED_POINT
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#define SIGN_CHANGE(a,b) (((a)&0x70000000)^((b)&0x70000000)||(b==0))
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#else
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#define SIGN_CHANGE(a,b) (((a)*(b))<0.0)
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#endif
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int lpc_to_lsp (spx_coef_t *a,int lpcrdr,spx_lsp_t *freq,int nb,spx_word16_t delta, char *stack)
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/* float *a lpc coefficients */
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/* int lpcrdr order of LPC coefficients (10) */
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/* float *freq LSP frequencies in the x domain */
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/* int nb number of sub-intervals (4) */
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/* float delta grid spacing interval (0.02) */
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{
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spx_word16_t temp_xr,xl,xr,xm=0;
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spx_word32_t psuml,psumr,psumm,temp_psumr/*,temp_qsumr*/;
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int i,j,m,flag,k;
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VARDECL(spx_word32_t *Q); /* ptrs for memory allocation */
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VARDECL(spx_word32_t *P);
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spx_word32_t *px; /* ptrs of respective P'(z) & Q'(z) */
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spx_word32_t *qx;
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spx_word32_t *p;
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spx_word32_t *q;
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spx_word32_t *pt; /* ptr used for cheb_poly_eval()
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whether P' or Q' */
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int roots=0; /* DR 8/2/94: number of roots found */
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flag = 1; /* program is searching for a root when,
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1 else has found one */
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m = lpcrdr/2; /* order of P'(z) & Q'(z) polynomials */
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/* Allocate memory space for polynomials */
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ALLOC(Q, (m+1), spx_word32_t);
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ALLOC(P, (m+1), spx_word32_t);
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/* determine P'(z)'s and Q'(z)'s coefficients where
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P'(z) = P(z)/(1 + z^(-1)) and Q'(z) = Q(z)/(1-z^(-1)) */
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px = P; /* initialise ptrs */
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qx = Q;
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p = px;
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q = qx;
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#ifdef FIXED_POINT
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*px++ = LPC_SCALING;
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*qx++ = LPC_SCALING;
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for(i=1;i<=m;i++){
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*px++ = SUB32(ADD32(EXTEND32(a[i]),EXTEND32(a[lpcrdr+1-i])), *p++);
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*qx++ = ADD32(SUB32(EXTEND32(a[i]),EXTEND32(a[lpcrdr+1-i])), *q++);
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}
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px = P;
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qx = Q;
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for(i=0;i<m;i++)
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{
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/*if (fabs(*px)>=32768)
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speex_warning_int("px", *px);
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if (fabs(*qx)>=32768)
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speex_warning_int("qx", *qx);*/
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*px = PSHR32(*px,2);
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*qx = PSHR32(*qx,2);
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px++;
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qx++;
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}
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/* The reason for this lies in the way cheb_poly_eva() is implemented for fixed-point */
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P[m] = PSHR32(P[m],3);
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Q[m] = PSHR32(Q[m],3);
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#else
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*px++ = LPC_SCALING;
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*qx++ = LPC_SCALING;
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for(i=1;i<=m;i++){
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*px++ = (a[i]+a[lpcrdr+1-i]) - *p++;
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*qx++ = (a[i]-a[lpcrdr+1-i]) + *q++;
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}
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px = P;
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qx = Q;
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for(i=0;i<m;i++){
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*px = 2**px;
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*qx = 2**qx;
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px++;
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qx++;
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}
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#endif
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px = P; /* re-initialise ptrs */
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qx = Q;
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/* Search for a zero in P'(z) polynomial first and then alternate to Q'(z).
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Keep alternating between the two polynomials as each zero is found */
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xr = 0; /* initialise xr to zero */
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xl = FREQ_SCALE; /* start at point xl = 1 */
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for(j=0;j<lpcrdr;j++){
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if(j&1) /* determines whether P' or Q' is eval. */
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pt = qx;
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else
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pt = px;
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psuml = cheb_poly_eva(pt,xl,lpcrdr,stack); /* evals poly. at xl */
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flag = 1;
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while(flag && (xr >= -FREQ_SCALE)){
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spx_word16_t dd;
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/* Modified by JMV to provide smaller steps around x=+-1 */
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#ifdef FIXED_POINT
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dd = MULT16_16_Q15(delta,SUB16(FREQ_SCALE, MULT16_16_Q14(MULT16_16_Q14(xl,xl),14000)));
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if (psuml<512 && psuml>-512)
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dd = PSHR16(dd,1);
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#else
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dd=delta*(1-.9*xl*xl);
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if (fabs(psuml)<.2)
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dd *= .5;
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#endif
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xr = SUB16(xl, dd); /* interval spacing */
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psumr = cheb_poly_eva(pt,xr,lpcrdr,stack);/* poly(xl-delta_x) */
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temp_psumr = psumr;
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temp_xr = xr;
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/* if no sign change increment xr and re-evaluate poly(xr). Repeat til
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sign change.
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if a sign change has occurred the interval is bisected and then
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checked again for a sign change which determines in which
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interval the zero lies in.
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If there is no sign change between poly(xm) and poly(xl) set interval
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between xm and xr else set interval between xl and xr and repeat till
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root is located within the specified limits */
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if(SIGN_CHANGE(psumr,psuml))
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{
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roots++;
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psumm=psuml;
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for(k=0;k<=nb;k++){
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#ifdef FIXED_POINT
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xm = ADD16(PSHR16(xl,1),PSHR16(xr,1)); /* bisect the interval */
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#else
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xm = .5*(xl+xr); /* bisect the interval */
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#endif
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psumm=cheb_poly_eva(pt,xm,lpcrdr,stack);
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/*if(psumm*psuml>0.)*/
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if(!SIGN_CHANGE(psumm,psuml))
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{
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psuml=psumm;
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xl=xm;
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} else {
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psumr=psumm;
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xr=xm;
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}
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}
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/* once zero is found, reset initial interval to xr */
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freq[j] = X2ANGLE(xm);
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xl = xm;
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flag = 0; /* reset flag for next search */
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}
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else{
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psuml=temp_psumr;
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xl=temp_xr;
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}
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}
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}
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return(roots);
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}
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/*---------------------------------------------------------------------------*\
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FUNCTION....: lsp_to_lpc()
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AUTHOR......: David Rowe
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DATE CREATED: 24/2/93
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lsp_to_lpc: This function converts LSP coefficients to LPC
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coefficients.
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\*---------------------------------------------------------------------------*/
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#ifdef FIXED_POINT
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void lsp_to_lpc(spx_lsp_t *freq,spx_coef_t *ak,int lpcrdr, char *stack)
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/* float *freq array of LSP frequencies in the x domain */
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/* float *ak array of LPC coefficients */
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/* int lpcrdr order of LPC coefficients */
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{
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int i,j;
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spx_word32_t xout1,xout2,xin1,xin2;
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VARDECL(spx_word32_t *Wp);
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spx_word32_t *pw,*n1,*n2,*n3,*n4=NULL;
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VARDECL(spx_word16_t *freqn);
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int m = lpcrdr>>1;
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ALLOC(freqn, lpcrdr, spx_word16_t);
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for (i=0;i<lpcrdr;i++)
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freqn[i] = ANGLE2X(freq[i]);
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ALLOC(Wp, 4*m+2, spx_word32_t);
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pw = Wp;
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/* initialise contents of array */
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for(i=0;i<=4*m+1;i++){ /* set contents of buffer to 0 */
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*pw++ = 0;
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}
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/* Set pointers up */
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pw = Wp;
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xin1 = 1048576;
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xin2 = 1048576;
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/* reconstruct P(z) and Q(z) by cascading second order
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polynomials in form 1 - 2xz(-1) +z(-2), where x is the
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LSP coefficient */
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for(j=0;j<=lpcrdr;j++){
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spx_word16_t *fr=freqn;
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for(i=0;i<m;i++){
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n1 = pw+(i<<2);
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n2 = n1 + 1;
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n3 = n2 + 1;
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n4 = n3 + 1;
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xout1 = ADD32(SUB32(xin1, MULT16_32_Q14(*fr,*n1)), *n2);
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fr++;
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xout2 = ADD32(SUB32(xin2, MULT16_32_Q14(*fr,*n3)), *n4);
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fr++;
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*n2 = *n1;
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*n4 = *n3;
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*n1 = xin1;
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*n3 = xin2;
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xin1 = xout1;
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xin2 = xout2;
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}
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xout1 = xin1 + *(n4+1);
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xout2 = xin2 - *(n4+2);
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/* FIXME: perhaps apply bandwidth expansion in case of overflow? */
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/*FIXME: Is it OK to have a long constant? */
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if (xout1 + xout2>SHL(32766,8))
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ak[j] = 32767;
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else if (xout1 + xout2 < -SHL(32766,8))
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ak[j] = -32767;
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else
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ak[j] = EXTRACT16(PSHR32(ADD32(xout1,xout2),8));
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*(n4+1) = xin1;
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*(n4+2) = xin2;
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xin1 = 0;
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xin2 = 0;
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}
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}
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#else
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void lsp_to_lpc(spx_lsp_t *freq,spx_coef_t *ak,int lpcrdr, char *stack)
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/* float *freq array of LSP frequencies in the x domain */
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/* float *ak array of LPC coefficients */
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/* int lpcrdr order of LPC coefficients */
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{
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int i,j;
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float xout1,xout2,xin1,xin2;
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VARDECL(float *Wp);
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float *pw,*n1,*n2,*n3,*n4=NULL;
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VARDECL(float *x_freq);
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int m = lpcrdr>>1;
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ALLOC(Wp, 4*m+2, float);
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pw = Wp;
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/* initialise contents of array */
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for(i=0;i<=4*m+1;i++){ /* set contents of buffer to 0 */
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*pw++ = 0.0;
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}
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/* Set pointers up */
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pw = Wp;
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xin1 = 1.0;
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xin2 = 1.0;
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ALLOC(x_freq, lpcrdr, float);
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for (i=0;i<lpcrdr;i++)
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x_freq[i] = ANGLE2X(freq[i]);
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/* reconstruct P(z) and Q(z) by cascading second order
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polynomials in form 1 - 2xz(-1) +z(-2), where x is the
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LSP coefficient */
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for(j=0;j<=lpcrdr;j++){
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int i2=0;
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for(i=0;i<m;i++,i2+=2){
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n1 = pw+(i*4);
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n2 = n1 + 1;
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n3 = n2 + 1;
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n4 = n3 + 1;
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xout1 = xin1 - 2.f*x_freq[i2] * *n1 + *n2;
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xout2 = xin2 - 2.f*x_freq[i2+1] * *n3 + *n4;
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*n2 = *n1;
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*n4 = *n3;
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*n1 = xin1;
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*n3 = xin2;
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xin1 = xout1;
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xin2 = xout2;
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}
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xout1 = xin1 + *(n4+1);
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xout2 = xin2 - *(n4+2);
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ak[j] = (xout1 + xout2)*0.5f;
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*(n4+1) = xin1;
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*(n4+2) = xin2;
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xin1 = 0.0;
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xin2 = 0.0;
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}
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}
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#endif
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#ifdef FIXED_POINT
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/*Makes sure the LSPs are stable*/
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void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
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{
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int i;
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spx_word16_t m = margin;
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spx_word16_t m2 = 25736-margin;
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|
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if (lsp[0]<m)
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lsp[0]=m;
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if (lsp[len-1]>m2)
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lsp[len-1]=m2;
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for (i=1;i<len-1;i++)
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{
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if (lsp[i]<lsp[i-1]+m)
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lsp[i]=lsp[i-1]+m;
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|
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if (lsp[i]>lsp[i+1]-m)
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lsp[i]= SHR16(lsp[i],1) + SHR16(lsp[i+1]-m,1);
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}
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}
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|
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void lsp_interpolate(spx_lsp_t *old_lsp, spx_lsp_t *new_lsp, spx_lsp_t *interp_lsp, int len, int subframe, int nb_subframes)
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{
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|
int i;
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spx_word16_t tmp = DIV32_16(SHL32(1 + subframe,14),nb_subframes);
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|
spx_word16_t tmp2 = 16384-tmp;
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for (i=0;i<len;i++)
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{
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|
interp_lsp[i] = MULT16_16_P14(tmp2,old_lsp[i]) + MULT16_16_P14(tmp,new_lsp[i]);
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|
}
|
|
}
|
|
|
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#else
|
|
|
|
/*Makes sure the LSPs are stable*/
|
|
void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
|
|
{
|
|
int i;
|
|
if (lsp[0]<LSP_SCALING*margin)
|
|
lsp[0]=LSP_SCALING*margin;
|
|
if (lsp[len-1]>LSP_SCALING*(M_PI-margin))
|
|
lsp[len-1]=LSP_SCALING*(M_PI-margin);
|
|
for (i=1;i<len-1;i++)
|
|
{
|
|
if (lsp[i]<lsp[i-1]+LSP_SCALING*margin)
|
|
lsp[i]=lsp[i-1]+LSP_SCALING*margin;
|
|
|
|
if (lsp[i]>lsp[i+1]-LSP_SCALING*margin)
|
|
lsp[i]= .5f* (lsp[i] + lsp[i+1]-LSP_SCALING*margin);
|
|
}
|
|
}
|
|
|
|
|
|
void lsp_interpolate(spx_lsp_t *old_lsp, spx_lsp_t *new_lsp, spx_lsp_t *interp_lsp, int len, int subframe, int nb_subframes)
|
|
{
|
|
int i;
|
|
float tmp = (1.0f + subframe)/nb_subframes;
|
|
for (i=0;i<len;i++)
|
|
{
|
|
interp_lsp[i] = (1-tmp)*old_lsp[i] + tmp*new_lsp[i];
|
|
}
|
|
}
|
|
|
|
#endif
|