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657 lines
18 KiB
C
657 lines
18 KiB
C
/*---------------------------------------------------------------------------*\
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Original copyright
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FILE........: lsp.c
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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 (c) 2002-2006 (fixed-point,
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optimizations, 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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/*---------------------------------------------------------------------------*\
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Introduction to Line Spectrum Pairs (LSPs)
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------------------------------------------
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LSPs are used to encode the LPC filter coefficients {ak} for
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transmission over the channel. LSPs have several properties (like
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less sensitivity to quantisation noise) that make them superior to
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direct quantisation of {ak}.
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A(z) is a polynomial of order lpcrdr with {ak} as the coefficients.
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A(z) is transformed to P(z) and Q(z) (using a substitution and some
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algebra), to obtain something like:
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A(z) = 0.5[P(z)(z+z^-1) + Q(z)(z-z^-1)] (1)
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As you can imagine A(z) has complex zeros all over the z-plane. P(z)
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and Q(z) have the very neat property of only having zeros _on_ the
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unit circle. So to find them we take a test point z=exp(jw) and
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evaluate P (exp(jw)) and Q(exp(jw)) using a grid of points between 0
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and pi.
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The zeros (roots) of P(z) also happen to alternate, which is why we
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swap coefficients as we find roots. So the process of finding the
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LSP frequencies is basically finding the roots of 5th order
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polynomials.
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The root so P(z) and Q(z) occur in symmetrical pairs at +/-w, hence
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the name Line Spectrum Pairs (LSPs).
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To convert back to ak we just evaluate (1), "clocking" an impulse
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thru it lpcrdr times gives us the impulse response of A(z) which is
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{ak}.
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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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#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 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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#ifdef BFIN_ASM
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#include "lsp_bfin.h"
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#endif
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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 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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#ifndef OVERRIDE_CHEB_POLY_EVA
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static inline spx_word32_t cheb_poly_eva(
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spx_word16_t *coef, /* P or Q coefs in Q13 format */
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spx_word16_t x, /* cos of freq (-1.0 to 1.0) in Q14 format */
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int m, /* LPC order/2 */
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char *stack
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)
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{
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int i;
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spx_word16_t b0, b1;
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spx_word32_t sum;
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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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/* Initialise values */
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b1=16384;
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b0=x;
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/* Evaluate Chebyshev series formulation usin g iterative approach */
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sum = ADD32(EXTEND32(coef[m]), EXTEND32(MULT16_16_P14(coef[m-1],x)));
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for(i=2;i<=m;i++)
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{
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spx_word16_t tmp=b0;
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b0 = SUB16(MULT16_16_Q13(x,b0), b1);
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b1 = tmp;
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sum = ADD32(sum, EXTEND32(MULT16_16_P14(coef[m-i],b0)));
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}
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return sum;
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}
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#endif
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#else
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static float cheb_poly_eva(spx_word32_t *coef, spx_word16_t x, int m, char *stack)
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{
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int k;
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float b0, b1, tmp;
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/* Initial conditions */
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b0=0; /* b_(m+1) */
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b1=0; /* b_(m+2) */
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x*=2;
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/* Calculate the b_(k) */
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for(k=m;k>0;k--)
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{
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tmp=b0; /* tmp holds the previous value of b0 */
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b0=x*b0-b1+coef[m-k]; /* b0 holds its new value based on b0 and b1 */
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b1=tmp; /* b1 holds the previous value of b0 */
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}
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return(-b1+.5*x*b0+coef[m]);
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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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VARDECL(spx_word16_t *Q16); /* ptrs for memory allocation */
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VARDECL(spx_word16_t *P16);
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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_word16_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=0;i<m;i++){
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*px++ = SUB32(ADD32(EXTEND32(a[i]),EXTEND32(a[lpcrdr-i-1])), *p++);
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*qx++ = ADD32(SUB32(EXTEND32(a[i]),EXTEND32(a[lpcrdr-i-1])), *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=0;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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/* now that we have computed P and Q convert to 16 bits to
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speed up cheb_poly_eval */
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ALLOC(P16, m+1, spx_word16_t);
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ALLOC(Q16, m+1, spx_word16_t);
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for (i=0;i<m+1;i++)
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{
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P16[i] = P[i];
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Q16[i] = Q[i];
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}
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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 = Q16;
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else
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pt = P16;
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psuml = cheb_poly_eva(pt,xl,m,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,m,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,m,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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Converts LSP coefficients to LPC 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,xin;
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spx_word32_t mult, a;
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VARDECL(spx_word16_t *freqn);
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VARDECL(spx_word32_t **xp);
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VARDECL(spx_word32_t *xpmem);
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VARDECL(spx_word32_t **xq);
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VARDECL(spx_word32_t *xqmem);
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int m = lpcrdr>>1;
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/*
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Reconstruct P(z) and Q(z) by cascading second order polynomials
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in form 1 - 2cos(w)z(-1) + z(-2), where w is the LSP frequency.
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In the time domain this is:
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y(n) = x(n) - 2cos(w)x(n-1) + x(n-2)
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This is what the ALLOCS below are trying to do:
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int xp[m+1][lpcrdr+1+2]; // P matrix in QIMP
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int xq[m+1][lpcrdr+1+2]; // Q matrix in QIMP
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These matrices store the output of each stage on each row. The
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final (m-th) row has the output of the final (m-th) cascaded
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2nd order filter. The first row is the impulse input to the
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system (not written as it is known).
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The version below takes advantage of the fact that a lot of the
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outputs are zero or known, for example if we put an inpulse
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into the first section the "clock" it 10 times only the first 3
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outputs samples are non-zero (it's an FIR filter).
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*/
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ALLOC(xp, (m+1), spx_word32_t*);
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ALLOC(xpmem, (m+1)*(lpcrdr+1+2), spx_word32_t);
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ALLOC(xq, (m+1), spx_word32_t*);
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ALLOC(xqmem, (m+1)*(lpcrdr+1+2), spx_word32_t);
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for(i=0; i<=m; i++) {
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xp[i] = xpmem + i*(lpcrdr+1+2);
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xq[i] = xqmem + i*(lpcrdr+1+2);
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}
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/* work out 2cos terms in Q14 */
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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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#define QIMP 21 /* scaling for impulse */
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xin = SHL32(EXTEND32(1), (QIMP-1)); /* 0.5 in QIMP format */
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/* first col and last non-zero values of each row are trivial */
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for(i=0;i<=m;i++) {
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xp[i][1] = 0;
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xp[i][2] = xin;
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xp[i][2+2*i] = xin;
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xq[i][1] = 0;
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xq[i][2] = xin;
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xq[i][2+2*i] = xin;
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}
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/* 2nd row (first output row) is trivial */
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xp[1][3] = -MULT16_32_Q14(freqn[0],xp[0][2]);
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xq[1][3] = -MULT16_32_Q14(freqn[1],xq[0][2]);
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xout1 = xout2 = 0;
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/* now generate remaining rows */
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for(i=1;i<m;i++) {
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for(j=1;j<2*(i+1)-1;j++) {
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mult = MULT16_32_Q14(freqn[2*i],xp[i][j+1]);
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xp[i+1][j+2] = ADD32(SUB32(xp[i][j+2], mult), xp[i][j]);
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mult = MULT16_32_Q14(freqn[2*i+1],xq[i][j+1]);
|
|
xq[i+1][j+2] = ADD32(SUB32(xq[i][j+2], mult), xq[i][j]);
|
|
}
|
|
|
|
/* for last col xp[i][j+2] = xq[i][j+2] = 0 */
|
|
|
|
mult = MULT16_32_Q14(freqn[2*i],xp[i][j+1]);
|
|
xp[i+1][j+2] = SUB32(xp[i][j], mult);
|
|
mult = MULT16_32_Q14(freqn[2*i+1],xq[i][j+1]);
|
|
xq[i+1][j+2] = SUB32(xq[i][j], mult);
|
|
}
|
|
|
|
/* process last row to extra a{k} */
|
|
|
|
for(j=1;j<=lpcrdr;j++) {
|
|
int shift = QIMP-13;
|
|
|
|
/* final filter sections */
|
|
a = PSHR32(xp[m][j+2] + xout1 + xq[m][j+2] - xout2, shift);
|
|
xout1 = xp[m][j+2];
|
|
xout2 = xq[m][j+2];
|
|
|
|
/* hard limit ak's to +/- 32767 */
|
|
|
|
if (a < -32767) a = -32767;
|
|
if (a > 32767) a = 32767;
|
|
ak[j-1] = (short)a;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
#else
|
|
|
|
void lsp_to_lpc(spx_lsp_t *freq,spx_coef_t *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;
|
|
VARDECL(float *Wp);
|
|
float *pw,*n1,*n2,*n3,*n4=NULL;
|
|
VARDECL(float *x_freq);
|
|
int m = lpcrdr>>1;
|
|
|
|
ALLOC(Wp, 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;
|
|
|
|
ALLOC(x_freq, lpcrdr, float);
|
|
for (i=0;i<lpcrdr;i++)
|
|
x_freq[i] = ANGLE2X(freq[i]);
|
|
|
|
/* 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.f*x_freq[i2] * *n1 + *n2;
|
|
xout2 = xin2 - 2.f*x_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);
|
|
if (j>0)
|
|
ak[j-1] = (xout1 + xout2)*0.5f;
|
|
*(n4+1) = xin1;
|
|
*(n4+2) = xin2;
|
|
|
|
xin1 = 0.0;
|
|
xin2 = 0.0;
|
|
}
|
|
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef FIXED_POINT
|
|
|
|
/*Makes sure the LSPs are stable*/
|
|
void lsp_enforce_margin(spx_lsp_t *lsp, int len, spx_word16_t margin)
|
|
{
|
|
int i;
|
|
spx_word16_t m = margin;
|
|
spx_word16_t m2 = 25736-margin;
|
|
|
|
if (lsp[0]<m)
|
|
lsp[0]=m;
|
|
if (lsp[len-1]>m2)
|
|
lsp[len-1]=m2;
|
|
for (i=1;i<len-1;i++)
|
|
{
|
|
if (lsp[i]<lsp[i-1]+m)
|
|
lsp[i]=lsp[i-1]+m;
|
|
|
|
if (lsp[i]>lsp[i+1]-m)
|
|
lsp[i]= SHR16(lsp[i],1) + SHR16(lsp[i+1]-m,1);
|
|
}
|
|
}
|
|
|
|
|
|
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;
|
|
spx_word16_t tmp = DIV32_16(SHL32(EXTEND32(1 + subframe),14),nb_subframes);
|
|
spx_word16_t tmp2 = 16384-tmp;
|
|
for (i=0;i<len;i++)
|
|
{
|
|
interp_lsp[i] = MULT16_16_P14(tmp2,old_lsp[i]) + MULT16_16_P14(tmp,new_lsp[i]);
|
|
}
|
|
}
|
|
|
|
#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
|