/* ITU-T G.729A Speech Coder ANSI-C Source Code Version 1.1 Last modified: September 1996 Copyright (c) 1996, AT&T, France Telecom, NTT, Universite de Sherbrooke All rights reserved. */ /*-----------------------------------------------------* * Function Autocorr() * * * * Compute autocorrelations of signal with windowing * * * *-----------------------------------------------------*/ #include "g729_typedef.h" #include "g729_basic_op.h" #include "g729_oper_32b.h" #include "g729_ld8a.h" #include "g729_tab_ld8a.h" void Autocorr (Word16 x[], /* (i) : Input signal */ Word16 m, /* (i) : LPC order */ Word16 r_h[], /* (o) : Autocorrelations (msb) */ Word16 r_l[] /* (o) : Autocorrelations (lsb) */ ) { Word16 i, j, norm; Word16 y[L_WINDOW]; Word32 sum; Flag Overflow; /* Windowing of signal */ for (i = 0; i < L_WINDOW; i++) { y[i] = mult_r (x[i], hamwindow[i]); } /* Compute r[0] and test for overflow */ do { Overflow = 0; sum = 1; /* Avoid case of all zeros */ for (i = 0; i < L_WINDOW; i++) sum = L_mac_o (sum, y[i], y[i], &Overflow); /* If overflow divide y[] by 4 */ if (Overflow != 0) { for (i = 0; i < L_WINDOW; i++) { y[i] = shr (y[i], 2); } } } while (Overflow != 0); /* Normalization of r[0] */ norm = norm_l (sum); sum = L_shl (sum, norm); L_Extract (sum, &r_h[0], &r_l[0]); /* Put in DPF format (see oper_32b) */ /* r[1] to r[m] */ for (i = 1; i <= m; i++) { sum = 0; for (j = 0; j < L_WINDOW - i; j++) sum = L_mac (sum, y[j], y[j + i]); sum = L_shl (sum, norm); L_Extract (sum, &r_h[i], &r_l[i]); } return; } /*-------------------------------------------------------* * Function Lag_window() * * * * Lag_window on autocorrelations. * * * * r[i] *= lag_wind[i] * * * * r[i] and lag_wind[i] are in special double precision.* * See "oper_32b.c" for the format * * * *-------------------------------------------------------*/ void Lag_window (Word16 m, /* (i) : LPC order */ Word16 r_h[], /* (i/o) : Autocorrelations (msb) */ Word16 r_l[] /* (i/o) : Autocorrelations (lsb) */ ) { Word16 i; Word32 x; for (i = 1; i <= m; i++) { x = Mpy_32 (r_h[i], r_l[i], lag_h[i - 1], lag_l[i - 1]); L_Extract (x, &r_h[i], &r_l[i]); } return; } /*___________________________________________________________________________ | | | LEVINSON-DURBIN algorithm in double precision | | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | |---------------------------------------------------------------------------| | | | Algorithm | | | | R[i] autocorrelations. | | A[i] filter coefficients. | | K reflection coefficients. | | Alpha prediction gain. | | | | Initialization: | | A[0] = 1 | | K = -R[1]/R[0] | | A[1] = K | | Alpha = R[0] * (1-K**2] | | | | Do for i = 2 to M | | | | S = SUM ( R[j]*A[i-j] ,j=1,i-1 ) + R[i] | | | | K = -S / Alpha | | | | An[j] = A[j] + K*A[i-j] for j=1 to i-1 | | where An[i] = new A[i] | | An[i]=K | | | | Alpha=Alpha * (1-K**2) | | | | END | | | | Remarks on the dynamics of the calculations. | | | | The numbers used are in double precision in the following format : | | A = AH <<16 + AL<<1. AH and AL are 16 bit signed integers. | | Since the LSB's also contain a sign bit, this format does not | | correspond to standard 32 bit integers. We use this format since | | it allows fast execution of multiplications and divisions. | | | | "DPF" will refer to this special format in the following text. | | See oper_32b.c | | | | The R[i] were normalized in routine AUTO (hence, R[i] < 1.0). | | The K[i] and Alpha are theoretically < 1.0. | | The A[i], for a sampling frequency of 8 kHz, are in practice | | always inferior to 16.0. | | | | These characteristics allow straigthforward fixed-point | | implementation. We choose to represent the parameters as | | follows : | | | | R[i] Q31 +- .99.. | | K[i] Q31 +- .99.. | | Alpha Normalized -> mantissa in Q31 plus exponent | | A[i] Q27 +- 15.999.. | | | | The additions are performed in 32 bit. For the summation used | | to calculate the K[i], we multiply numbers in Q31 by numbers | | in Q27, with the result of the multiplications in Q27, | | resulting in a dynamic of +- 16. This is sufficient to avoid | | overflow, since the final result of the summation is | | necessarily < 1.0 as both the K[i] and Alpha are | | theoretically < 1.0. | |___________________________________________________________________________| */ /* Last A(z) for case of unstable filter */ void Levinson (CodState *coder, Word16 Rh[], /* (i) : Rh[M+1] Vector of autocorrelations (msb) */ Word16 Rl[], /* (i) : Rl[M+1] Vector of autocorrelations (lsb) */ Word16 A[], /* (o) Q12 : A[M] LPC coefficients (m = 10) */ Word16 rc[] /* (o) Q15 : rc[M] Reflection coefficients. */ ) { Word16 i, j; Word16 hi, lo; Word16 Kh, Kl; /* reflection coefficient; hi and lo */ Word16 alp_h, alp_l, alp_exp; /* Prediction gain; hi lo and exponent */ Word16 Ah[M10 + 1], Al[M10 + 1]; /* LPC coef. in double prec. */ Word16 Anh[M10 + 1], Anl[M10 + 1]; /* LPC coef.for next iteration in double prec. */ Word32 t0, t1, t2; /* temporary variable */ /* K = A[1] = -R[1] / R[0] */ t1 = L_Comp (Rh[1], Rl[1]); /* R[1] in Q31 */ t2 = L_abs (t1); /* abs R[1] */ t0 = Div_32 (t2, Rh[0], Rl[0]); /* R[1]/R[0] in Q31 */ if (t1 > 0) t0 = L_negate (t0); /* -R[1]/R[0] */ L_Extract (t0, &Kh, &Kl); /* K in DPF */ rc[0] = Kh; t0 = L_shr (t0, 4); /* A[1] in Q27 */ L_Extract (t0, &Ah[1], &Al[1]); /* A[1] in DPF */ /* Alpha = R[0] * (1-K**2) */ t0 = Mpy_32 (Kh, Kl, Kh, Kl); /* K*K in Q31 */ t0 = L_abs (t0); /* Some case <0 !! */ t0 = L_sub ((Word32) 0x7fffffffL, t0); /* 1 - K*K in Q31 */ L_Extract (t0, &hi, &lo); /* DPF format */ t0 = Mpy_32 (Rh[0], Rl[0], hi, lo); /* Alpha in Q31 */ /* Normalize Alpha */ alp_exp = norm_l (t0); t0 = L_shl (t0, alp_exp); L_Extract (t0, &alp_h, &alp_l); /* DPF format */ /*--------------------------------------* * ITERATIONS I=2 to M * *--------------------------------------*/ for (i = 2; i <= M10; i++) { /* t0 = SUM ( R[j]*A[i-j] ,j=1,i-1 ) + R[i] */ t0 = 0; for (j = 1; j < i; j++) t0 = L_add (t0, Mpy_32 (Rh[j], Rl[j], Ah[i - j], Al[i - j])); t0 = L_shl (t0, 4); /* result in Q27 -> convert to Q31 */ /* No overflow possible */ t1 = L_Comp (Rh[i], Rl[i]); t0 = L_add (t0, t1); /* add R[i] in Q31 */ /* K = -t0 / Alpha */ t1 = L_abs (t0); t2 = Div_32 (t1, alp_h, alp_l); /* abs(t0)/Alpha */ if (t0 > 0) t2 = L_negate (t2); /* K =-t0/Alpha */ t2 = L_shl (t2, alp_exp); /* denormalize; compare to Alpha */ L_Extract (t2, &Kh, &Kl); /* K in DPF */ rc[i - 1] = Kh; /* Test for unstable filter. If unstable keep old A(z) */ if (sub (abs_s (Kh), 32750) > 0) { for (j = 0; j <= M10; j++) { A[j] = coder->old_A[j]; } rc[0] = coder->old_rc[0]; /* only two rc coefficients are needed */ rc[1] = coder->old_rc[1]; return; } /*------------------------------------------* * Compute new LPC coeff. -> An[i] * * An[j]= A[j] + K*A[i-j] , j=1 to i-1 * * An[i]= K * *------------------------------------------*/ for (j = 1; j < i; j++) { t0 = Mpy_32 (Kh, Kl, Ah[i - j], Al[i - j]); t0 = L_add (t0, L_Comp (Ah[j], Al[j])); L_Extract (t0, &Anh[j], &Anl[j]); } t2 = L_shr (t2, 4); /* t2 = K in Q31 ->convert to Q27 */ L_Extract (t2, &Anh[i], &Anl[i]); /* An[i] in Q27 */ /* Alpha = Alpha * (1-K**2) */ t0 = Mpy_32 (Kh, Kl, Kh, Kl); /* K*K in Q31 */ t0 = L_abs (t0); /* Some case <0 !! */ t0 = L_sub ((Word32) 0x7fffffffL, t0); /* 1 - K*K in Q31 */ L_Extract (t0, &hi, &lo); /* DPF format */ t0 = Mpy_32 (alp_h, alp_l, hi, lo); /* Alpha in Q31 */ /* Normalize Alpha */ j = norm_l (t0); t0 = L_shl (t0, j); L_Extract (t0, &alp_h, &alp_l); /* DPF format */ alp_exp = add (alp_exp, j); /* Add normalization to alp_exp */ /* A[j] = An[j] */ for (j = 1; j <= i; j++) { Ah[j] = Anh[j]; Al[j] = Anl[j]; } } /* Truncate A[i] in Q27 to Q12 with rounding */ A[0] = 4096; for (i = 1; i <= M10; i++) { t0 = L_Comp (Ah[i], Al[i]); coder->old_A[i] = A[i] = wround (L_shl (t0, 1)); } coder->old_rc[0] = rc[0]; coder->old_rc[1] = rc[1]; return; } /*-------------------------------------------------------------* * procedure Az_lsp: * * ~~~~~~ * * Compute the LSPs from the LPC coefficients (order=10) * *-------------------------------------------------------------*/ Word16 Chebps_11 (Word16 x, Word16 f[], Word16 n); Word16 Chebps_10 (Word16 x, Word16 f[], Word16 n); void Az_lsp (Word16 a[], /* (i) Q12 : predictor coefficients */ Word16 lsp[], /* (o) Q15 : line spectral pairs */ Word16 old_lsp[] /* (i) : old lsp[] (in case not found 10 roots) */ ) { Flag Overflow; Word16 i, j, nf, ip; Word16 xlow, ylow, xhigh, yhigh, xmid, ymid, xint; Word16 x, y, sign, exp; Word16 *coef; Word16 f1[M10 / 2 + 1], f2[M10 / 2 + 1]; Word32 t0, L_temp; Flag ovf_coef; Word16 (*pChebps) (Word16 x, Word16 f[], Word16 n); /*-------------------------------------------------------------* * find the sum and diff. pol. F1(z) and F2(z) * * F1(z) <--- F1(z)/(1+z**-1) & F2(z) <--- F2(z)/(1-z**-1) * * * * f1[0] = 1.0; * * f2[0] = 1.0; * * * * for (i = 0; i< NC; i++) * * { * * f1[i+1] = a[i+1] + a[M-i] - f1[i] ; * * f2[i+1] = a[i+1] - a[M-i] + f2[i] ; * * } * *-------------------------------------------------------------*/ ovf_coef = 0; pChebps = Chebps_11; f1[0] = 2048; /* f1[0] = 1.0 is in Q11 */ f2[0] = 2048; /* f2[0] = 1.0 is in Q11 */ for (i = 0; i < NC; i++) { Overflow = 0; t0 = L_mult_o (a[i + 1], 16384, &Overflow); /* x = (a[i+1] + a[M-i]) >> 1 */ t0 = L_mac_o (t0, a[M10 - i], 16384, &Overflow); /* -> From Q12 to Q11 */ x = extract_h (t0); if (Overflow) { ovf_coef = 1; } Overflow = 0; f1[i + 1] = sub_o (x, f1[i], &Overflow); /* f1[i+1] = a[i+1] + a[M-i] - f1[i] */ if (Overflow) { ovf_coef = 1; } Overflow = 0; t0 = L_mult_o (a[i + 1], 16384, &Overflow); /* x = (a[i+1] - a[M-i]) >> 1 */ t0 = L_msu_o (t0, a[M10 - i], 16384, &Overflow); /* -> From Q12 to Q11 */ x = extract_h (t0); if (Overflow) { ovf_coef = 1; } Overflow = 0; f2[i + 1] = add_o (x, f2[i], &Overflow); /* f2[i+1] = a[i+1] - a[M-i] + f2[i] */ if (Overflow) { ovf_coef = 1; } } if (ovf_coef) { /*printf("===== OVF ovf_coef =====\n"); */ pChebps = Chebps_10; f1[0] = 1024; /* f1[0] = 1.0 is in Q10 */ f2[0] = 1024; /* f2[0] = 1.0 is in Q10 */ for (i = 0; i < NC; i++) { t0 = L_mult (a[i + 1], 8192); /* x = (a[i+1] + a[M-i]) >> 1 */ t0 = L_mac (t0, a[M10 - i], 8192); /* -> From Q11 to Q10 */ x = extract_h (t0); f1[i + 1] = sub (x, f1[i]); /* f1[i+1] = a[i+1] + a[M-i] - f1[i] */ t0 = L_mult (a[i + 1], 8192); /* x = (a[i+1] - a[M-i]) >> 1 */ t0 = L_msu (t0, a[M10 - i], 8192); /* -> From Q11 to Q10 */ x = extract_h (t0); f2[i + 1] = add (x, f2[i]); /* f2[i+1] = a[i+1] - a[M-i] + f2[i] */ } } /*-------------------------------------------------------------* * find the LSPs using the Chebichev pol. evaluation * *-------------------------------------------------------------*/ nf = 0; /* number of found frequencies */ ip = 0; /* indicator for f1 or f2 */ coef = f1; xlow = grid[0]; ylow = (*pChebps) (xlow, coef, NC); j = 0; while ((nf < M10) && (j < GRID_POINTS)) { j = add (j, 1); xhigh = xlow; yhigh = ylow; xlow = grid[j]; ylow = (*pChebps) (xlow, coef, NC); L_temp = L_mult (ylow, yhigh); if (L_temp <= (Word32) 0) { /* divide 2 times the interval */ for (i = 0; i < 2; i++) { xmid = add (shr (xlow, 1), shr (xhigh, 1)); /* xmid = (xlow + xhigh)/2 */ ymid = (*pChebps) (xmid, coef, NC); L_temp = L_mult (ylow, ymid); if (L_temp <= (Word32) 0) { yhigh = ymid; xhigh = xmid; } else { ylow = ymid; xlow = xmid; } } /*-------------------------------------------------------------* * Linear interpolation * * xint = xlow - ylow*(xhigh-xlow)/(yhigh-ylow); * *-------------------------------------------------------------*/ x = sub (xhigh, xlow); y = sub (yhigh, ylow); if (y == 0) { xint = xlow; } else { sign = y; y = abs_s (y); exp = norm_s (y); y = shl (y, exp); y = div_s ((Word16) 16383, y); t0 = L_mult (x, y); t0 = L_shr (t0, sub (20, exp)); y = extract_l (t0); /* y= (xhigh-xlow)/(yhigh-ylow) in Q11 */ if (sign < 0) y = negate (y); t0 = L_mult (ylow, y); /* result in Q26 */ t0 = L_shr (t0, 11); /* result in Q15 */ xint = sub (xlow, extract_l (t0)); /* xint = xlow - ylow*y */ } lsp[nf] = xint; xlow = xint; nf = add (nf, 1); if (ip == 0) { ip = 1; coef = f2; } else { ip = 0; coef = f1; } ylow = (*pChebps) (xlow, coef, NC); } } /* Check if M roots found */ if (sub (nf, M10) < 0) { for (i = 0; i < M10; i++) { lsp[i] = old_lsp[i]; } /* printf("\n !!Not 10 roots found in Az_lsp()!!!\n"); */ } return; } /*--------------------------------------------------------------* * function Chebps_11, Chebps_10: * * ~~~~~~~~~~~~~~~~~~~~ * * Evaluates the Chebichev polynomial series * *--------------------------------------------------------------* * * * The polynomial order is * * n = M/2 (M is the prediction order) * * The polynomial is given by * * C(x) = 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(Chebps_11), in Q10(Chebps_10) * * n: order of the pol. * * * * The value of C(x) is returned. (Saturated to +-1.99 in Q14) * * * *--------------------------------------------------------------*/ Word16 Chebps_11 (Word16 x, Word16 f[], Word16 n) { Word16 i, cheb; Word16 b0_h, b0_l, b1_h, b1_l, b2_h, b2_l; Word32 t0; /* Note: All computation are done in Q24. */ b2_h = 256; /* b2 = 1.0 in Q24 DPF */ b2_l = 0; t0 = L_mult (x, 512); /* 2*x in Q24 */ t0 = L_mac (t0, f[1], 4096); /* + f[1] in Q24 */ L_Extract (t0, &b1_h, &b1_l); /* b1 = 2*x + f[1] */ for (i = 2; i < n; i++) { t0 = Mpy_32_16 (b1_h, b1_l, x); /* t0 = 2.0*x*b1 */ t0 = L_shl (t0, 1); t0 = L_mac (t0, b2_h, (Word16) - 32768L); /* t0 = 2.0*x*b1 - b2 */ t0 = L_msu (t0, b2_l, 1); t0 = L_mac (t0, f[i], 4096); /* t0 = 2.0*x*b1 - b2 + f[i]; */ L_Extract (t0, &b0_h, &b0_l); /* b0 = 2.0*x*b1 - b2 + f[i]; */ b2_l = b1_l; /* b2 = b1; */ b2_h = b1_h; b1_l = b0_l; /* b1 = b0; */ b1_h = b0_h; } t0 = Mpy_32_16 (b1_h, b1_l, x); /* t0 = x*b1; */ t0 = L_mac (t0, b2_h, (Word16) - 32768L); /* t0 = x*b1 - b2 */ t0 = L_msu (t0, b2_l, 1); t0 = L_mac (t0, f[i], 2048); /* t0 = x*b1 - b2 + f[i]/2 */ t0 = L_shl (t0, 6); /* Q24 to Q30 with saturation */ cheb = extract_h (t0); /* Result in Q14 */ return (cheb); } Word16 Chebps_10 (Word16 x, Word16 f[], Word16 n) { Word16 i, cheb; Word16 b0_h, b0_l, b1_h, b1_l, b2_h, b2_l; Word32 t0; /* Note: All computation are done in Q23. */ b2_h = 128; /* b2 = 1.0 in Q23 DPF */ b2_l = 0; t0 = L_mult (x, 256); /* 2*x in Q23 */ t0 = L_mac (t0, f[1], 4096); /* + f[1] in Q23 */ L_Extract (t0, &b1_h, &b1_l); /* b1 = 2*x + f[1] */ for (i = 2; i < n; i++) { t0 = Mpy_32_16 (b1_h, b1_l, x); /* t0 = 2.0*x*b1 */ t0 = L_shl (t0, 1); t0 = L_mac (t0, b2_h, (Word16) - 32768L); /* t0 = 2.0*x*b1 - b2 */ t0 = L_msu (t0, b2_l, 1); t0 = L_mac (t0, f[i], 4096); /* t0 = 2.0*x*b1 - b2 + f[i]; */ L_Extract (t0, &b0_h, &b0_l); /* b0 = 2.0*x*b1 - b2 + f[i]; */ b2_l = b1_l; /* b2 = b1; */ b2_h = b1_h; b1_l = b0_l; /* b1 = b0; */ b1_h = b0_h; } t0 = Mpy_32_16 (b1_h, b1_l, x); /* t0 = x*b1; */ t0 = L_mac (t0, b2_h, (Word16) - 32768L); /* t0 = x*b1 - b2 */ t0 = L_msu (t0, b2_l, 1); t0 = L_mac (t0, f[i], 2048); /* t0 = x*b1 - b2 + f[i]/2 */ t0 = L_shl (t0, 7); /* Q23 to Q30 with saturation */ cheb = extract_h (t0); /* Result in Q14 */ return (cheb); }