/* | |
** Copyright 2003-2010, VisualOn, Inc. | |
** | |
** Licensed under the Apache License, Version 2.0 (the "License"); | |
** you may not use this file except in compliance with the License. | |
** You may obtain a copy of the License at | |
** | |
** http://www.apache.org/licenses/LICENSE-2.0 | |
** | |
** Unless required by applicable law or agreed to in writing, software | |
** distributed under the License is distributed on an "AS IS" BASIS, | |
** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
** See the License for the specific language governing permissions and | |
** limitations under the License. | |
*/ | |
/*********************************************************************** | |
* File: az_isp.c | |
* | |
* Description: | |
*-----------------------------------------------------------------------* | |
* Compute the ISPs from the LPC coefficients (order=M) * | |
*-----------------------------------------------------------------------* | |
* * | |
* The ISPs are the roots of the two polynomials F1(z) and F2(z) * | |
* defined as * | |
* F1(z) = A(z) + z^-m A(z^-1) * | |
* and F2(z) = A(z) - z^-m A(z^-1) * | |
* * | |
* For a even order m=2n, F1(z) has M/2 conjugate roots on the unit * | |
* circle and F2(z) has M/2-1 conjugate roots on the unit circle in * | |
* addition to two roots at 0 and pi. * | |
* * | |
* For a 16th order LP analysis, F1(z) and F2(z) can be written as * | |
* * | |
* F1(z) = (1 + a[M]) PRODUCT (1 - 2 cos(w_i) z^-1 + z^-2 ) * | |
* i=0,2,4,6,8,10,12,14 * | |
* * | |
* F2(z) = (1 - a[M]) (1 - z^-2) PRODUCT (1 - 2 cos(w_i) z^-1 + z^-2 ) * | |
* i=1,3,5,7,9,11,13 * | |
* * | |
* The ISPs are the M-1 frequencies w_i, i=0...M-2 plus the last * | |
* predictor coefficient a[M]. * | |
*-----------------------------------------------------------------------* | |
************************************************************************/ | |
#include "typedef.h" | |
#include "basic_op.h" | |
#include "oper_32b.h" | |
#include "stdio.h" | |
#include "grid100.tab" | |
#define M 16 | |
#define NC (M/2) | |
/* local function */ | |
static __inline Word16 Chebps2(Word16 x, Word16 f[], Word32 n); | |
void Az_isp( | |
Word16 a[], /* (i) Q12 : predictor coefficients */ | |
Word16 isp[], /* (o) Q15 : Immittance spectral pairs */ | |
Word16 old_isp[] /* (i) : old isp[] (in case not found M roots) */ | |
) | |
{ | |
Word32 i, j, nf, ip, order; | |
Word16 xlow, ylow, xhigh, yhigh, xmid, ymid, xint; | |
Word16 x, y, sign, exp; | |
Word16 *coef; | |
Word16 f1[NC + 1], f2[NC]; | |
Word32 t0; | |
/*-------------------------------------------------------------* | |
* find the sum and diff polynomials F1(z) and F2(z) * | |
* F1(z) = [A(z) + z^M A(z^-1)] * | |
* F2(z) = [A(z) - z^M A(z^-1)]/(1-z^-2) * | |
* * | |
* for (i=0; i<NC; i++) * | |
* { * | |
* f1[i] = a[i] + a[M-i]; * | |
* f2[i] = a[i] - a[M-i]; * | |
* } * | |
* f1[NC] = 2.0*a[NC]; * | |
* * | |
* for (i=2; i<NC; i++) Divide by (1-z^-2) * | |
* f2[i] += f2[i-2]; * | |
*-------------------------------------------------------------*/ | |
for (i = 0; i < NC; i++) | |
{ | |
t0 = a[i] << 15; | |
f1[i] = vo_round(t0 + (a[M - i] << 15)); /* =(a[i]+a[M-i])/2 */ | |
f2[i] = vo_round(t0 - (a[M - i] << 15)); /* =(a[i]-a[M-i])/2 */ | |
} | |
f1[NC] = a[NC]; | |
for (i = 2; i < NC; i++) /* Divide by (1-z^-2) */ | |
f2[i] = add1(f2[i], f2[i - 2]); | |
/*---------------------------------------------------------------------* | |
* Find the ISPs (roots of F1(z) and F2(z) ) using the * | |
* Chebyshev polynomial evaluation. * | |
* The roots of F1(z) and F2(z) are alternatively searched. * | |
* We start by finding the first root of F1(z) then we switch * | |
* to F2(z) then back to F1(z) and so on until all roots are found. * | |
* * | |
* - Evaluate Chebyshev pol. at grid points and check for sign change.* | |
* - If sign change track the root by subdividing the interval * | |
* 2 times and ckecking sign change. * | |
*---------------------------------------------------------------------*/ | |
nf = 0; /* number of found frequencies */ | |
ip = 0; /* indicator for f1 or f2 */ | |
coef = f1; | |
order = NC; | |
xlow = vogrid[0]; | |
ylow = Chebps2(xlow, coef, order); | |
j = 0; | |
while ((nf < M - 1) && (j < GRID_POINTS)) | |
{ | |
j ++; | |
xhigh = xlow; | |
yhigh = ylow; | |
xlow = vogrid[j]; | |
ylow = Chebps2(xlow, coef, order); | |
if ((ylow * yhigh) <= (Word32) 0) | |
{ | |
/* divide 2 times the interval */ | |
for (i = 0; i < 2; i++) | |
{ | |
xmid = (xlow >> 1) + (xhigh >> 1); /* xmid = (xlow + xhigh)/2 */ | |
ymid = Chebps2(xmid, coef, order); | |
if ((ylow * ymid) <= (Word32) 0) | |
{ | |
yhigh = ymid; | |
xhigh = xmid; | |
} else | |
{ | |
ylow = ymid; | |
xlow = xmid; | |
} | |
} | |
/*-------------------------------------------------------------* | |
* Linear interpolation * | |
* xint = xlow - ylow*(xhigh-xlow)/(yhigh-ylow); * | |
*-------------------------------------------------------------*/ | |
x = xhigh - xlow; | |
y = yhigh - ylow; | |
if (y == 0) | |
{ | |
xint = xlow; | |
} else | |
{ | |
sign = y; | |
y = abs_s(y); | |
exp = norm_s(y); | |
y = y << exp; | |
y = div_s((Word16) 16383, y); | |
t0 = x * y; | |
t0 = (t0 >> (19 - exp)); | |
y = vo_extract_l(t0); /* y= (xhigh-xlow)/(yhigh-ylow) in Q11 */ | |
if (sign < 0) | |
y = -y; | |
t0 = ylow * y; /* result in Q26 */ | |
t0 = (t0 >> 10); /* result in Q15 */ | |
xint = vo_sub(xlow, vo_extract_l(t0)); /* xint = xlow - ylow*y */ | |
} | |
isp[nf] = xint; | |
xlow = xint; | |
nf++; | |
if (ip == 0) | |
{ | |
ip = 1; | |
coef = f2; | |
order = NC - 1; | |
} else | |
{ | |
ip = 0; | |
coef = f1; | |
order = NC; | |
} | |
ylow = Chebps2(xlow, coef, order); | |
} | |
} | |
/* Check if M-1 roots found */ | |
if(nf < M - 1) | |
{ | |
for (i = 0; i < M; i++) | |
{ | |
isp[i] = old_isp[i]; | |
} | |
} else | |
{ | |
isp[M - 1] = a[M] << 3; /* From Q12 to Q15 with saturation */ | |
} | |
return; | |
} | |
/*--------------------------------------------------------------* | |
* function Chebps2: * | |
* ~~~~~~~ * | |
* Evaluates the Chebishev polynomial series * | |
*--------------------------------------------------------------* | |
* * | |
* The polynomial order is * | |
* n = M/2 (M is the prediction order) * | |
* The polynomial is given by * | |
* C(x) = f(0)T_n(x) + f(1)T_n-1(x) + ... +f(n-1)T_1(x) + f(n)/2 * | |
* Arguments: * | |
* x: input value of evaluation; x = cos(frequency) in Q15 * | |
* f[]: coefficients of the pol. in Q11 * | |
* n: order of the pol. * | |
* * | |
* The value of C(x) is returned. (Satured to +-1.99 in Q14) * | |
* * | |
*--------------------------------------------------------------*/ | |
static __inline Word16 Chebps2(Word16 x, Word16 f[], Word32 n) | |
{ | |
Word32 i, cheb; | |
Word16 b0_h, b0_l, b1_h, b1_l, b2_h, b2_l; | |
Word32 t0; | |
/* Note: All computation are done in Q24. */ | |
t0 = f[0] << 13; | |
b2_h = t0 >> 16; | |
b2_l = (t0 & 0xffff)>>1; | |
t0 = ((b2_h * x)<<1) + (((b2_l * x)>>15)<<1); | |
t0 <<= 1; | |
t0 += (f[1] << 13); /* + f[1] in Q24 */ | |
b1_h = t0 >> 16; | |
b1_l = (t0 & 0xffff) >> 1; | |
for (i = 2; i < n; i++) | |
{ | |
t0 = ((b1_h * x)<<1) + (((b1_l * x)>>15)<<1); | |
t0 += (b2_h * (-16384))<<1; | |
t0 += (f[i] << 12); | |
t0 <<= 1; | |
t0 -= (b2_l << 1); /* t0 = 2.0*x*b1 - b2 + f[i]; */ | |
b0_h = t0 >> 16; | |
b0_l = (t0 & 0xffff) >> 1; | |
b2_l = b1_l; /* b2 = b1; */ | |
b2_h = b1_h; | |
b1_l = b0_l; /* b1 = b0; */ | |
b1_h = b0_h; | |
} | |
t0 = ((b1_h * x)<<1) + (((b1_l * x)>>15)<<1); | |
t0 += (b2_h * (-32768))<<1; /* t0 = x*b1 - b2 */ | |
t0 -= (b2_l << 1); | |
t0 += (f[n] << 12); /* t0 = x*b1 - b2 + f[i]/2 */ | |
t0 = L_shl2(t0, 6); /* Q24 to Q30 with saturation */ | |
cheb = extract_h(t0); /* Result in Q14 */ | |
if (cheb == -32768) | |
{ | |
cheb = -32767; /* to avoid saturation in Az_isp */ | |
} | |
return (cheb); | |
} | |