线性预测中的自相关系数.doc

线性预测中的自相关系数1原理线性预测是语音编码中的基本算法，其基本原理如下：设语音信号的样值序列，第k时刻的取样值xk可以用之前的P个样值的线性组合来预测。实际样值与预测值之间的误差为：因此预测系统的传递函数为：其中H(Z)是一个全极点滤波器，称为综合滤波器。A(Z)是H(Z)的逆滤波器，称为分析滤波器。在语音线性预测编码中，A(Z)的系数反映了声道特性。为了使预测误差最小，采用最小均方误差准则，即使误差的均方值最小。在预测阶数P给定后，就是所有预测系数的函数，因此：可见，要使的预测误差最小，则必须与所有数据正交，称为正交性原理。将上式展开，可得：其中，即信号的自相关系数。对平稳信号（语音信号一般不是平稳信号，但对单独处理的每帧来说，可以近似认为是短时平稳信号）来说，因此，可以得到：解此线性方程组，即可得到各预测系数。一般采用Levison-Durbin算法递推求解。在已知输入信号的情况下，必须先求各阶自相关系数。2G.729中的线性预测ITU-T G.729语音编码标准采用CS-ACELP混合编码方法，输出码率为8kbps，每帧语音长度10ms，在8kHz采样条件下，具有80个样点。在线性预测时一般采用连续3帧进行加窗处理后进行，因此计算自相关系数的数组具有240个样点值。下面是G.729参考代码中的相关程序部分，并附加说明。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 yL_WINDOW; Word32 sum; extern Flag Overflow; /* Windowing of signal */ for(i=0; iL_WINDOW; i+) yi = mult_r(xi, hamwindowi); /* Compute r0 and test for overflow */ do Overflow = 0; sum = 1; /* Avoid case of all zeros */ for(i=0; iL_WINDOW; i+) sum = L_mac(sum, yi, yi); /* If overflow divide y by 4 */ if(Overflow != 0) for(i=0; iL_WINDOW; i+) yi = shr(yi, 2); while (Overflow != 0); /* Normalization of r0 */ norm = norm_l(sum); sum = L_shl(sum, norm); L_Extract(sum, &r_h0, &r_l0); /* Put in DPF format (see oper_32b) */ /* r1 to rm */ for (i = 1; i = m; i+) sum = 0; for(j=0; jL_WINDOW-i; j+) sum = L_mac(sum, yj, yj+i); sum = L_shl(sum, norm); L_Extract(sum, &r_hi, &r_li); return;/*_ | | | Function Name : mult_r | | | | Purpose : | | | | Same as mult with rounding, i.e.: | | mult_r(var1,var2) = shr(var1*var2) + 16384),15) and | | mult_r(-32768,-32768) = 32767. | | | | Complexity weight : 2 | | | | Inputs : | | | | var1 | | 16 bit short signed integer (Word16) whose value falls in the | | range : 0xffff 8000 = var1 = 0x0000 7fff. | | | | var2 | | 16 bit short signed integer (Word16) whose value falls in the | | range : 0xffff 8000 = var1 = 0x0000 7fff. | | | | Outputs : | | | | none | | | | Return Value : | | | | var_out | | 16 bit short signed integer (Word16) whose value falls in the | | range : 0xffff 8000 = var_out = 15; /* shift */ if (L_produit_arr & (Word32) 0x00010000L) /* sign extend when necessary */ L_produit_arr |= (Word32) 0xffff0000L; var_out = sature(L_produit_arr); return(var_out);/*_ | | | Function Name : norm_l | | | | Purpose : | | | | Produces the number of left shift needed to normalize the 32 bit varia- | | ble l_var1 for positive values on the interval with minimum of | | 1073741824 and maximum of 2147483647, and for negative values on the in-| | terval with minimum of -2147483648 and maximum of -1073741824; in order | | to normalize the result, the following operation must be done : | | norm_L_var1 = L_shl(L_var1,norm_l(L_var1). | | | | Complexity weight : 30 | | | | Inputs : | | | | L_var1 | | 32 bit long signed integer (Word32) whose value falls in the | | range : 0x8000 0000 = var1 = 0x7fff ffff. | | | | Outputs : | | | | none | | | | Return Value : | | | | var_out | | 16 bit short signed integer (Word16) whose value falls in the | | range : 0x0000 0000 = var_out = 0x0000 001f. | |_|*/Word16 norm_l(Word32 L_var1) Word16 var_out; if (L_var1 = 0) var_out = 0; else if (L_var1 = (Word32)0xffffffffL) var_out = 31; else if (L_var1 0) L_var1 = L_var1; for(var_out = 0;L_var1 (Word32)0x40000000L;var_out+) L_var1 = 1; return(var_out); /*_ | | | Function Name : L_mac | | | | Purpose : | | | | Multiply var1 by var2 and shift the result left by 1. Add the 32 bit | | result to L_var3 with saturation, return a 32 bit result: | | L_mac(L_var3,var1,var2) = L_add(L_var3,(L_mult(var1,var2). | | | | Complexity weight : 1 | | | | Inputs : | | | | L_var3 32 bit long signed integer (Word32) whose value falls in the | | range : 0x8000 0000 = L_var3 = 0x7fff ffff. | | | | var1 | | 16 bit short signed integer (Word16) whose value falls in the | | range : 0xffff 8000 = var1 = 0x0000 7fff. | | | | var2 | | 16 bit short signed integer (Word16) whose value falls in the | | range : 0xffff 8000 = var1 = 0x0000 7fff. | | | | Outputs : | | | | none | | | | Return Value : | | | | L_var_out | | 32 bit long signed integer (Word32) whose value falls in the | | range : 0x8000 0000 = L_var_out = 0x7fff ffff. | |_|*/Word32 L_mac(Word32 L_var3, Word16 var1, Word16 var2) Word32 L_var_out; Word32 L_produit; L_produit = L_mult(var1,var2); L_var_out = L_add(L_var3,L_produit); return(L_var_out); /* Hamming_cos window for LPC analysis. */* Create with function ham_cos(window,200,40) */Word16 hamwindowL_WINDOW = 2621, 2623, 2629, 2638, 2651, 2668, 2689, 2713, 2741, 2772, 2808, 2847, 2890, 2936, 2986, 3040, 3097, 3158, 3223, 3291, 3363, 3438, 3517, 3599, 3685, 3774, 3867, 3963, 4063, 4166, 4272, 4382, 4495, 4611, 4731, 4853, 4979, 5108, 5240, 5376, 5514, 5655, 5800, 5947, 6097, 6250, 6406, 6565, 6726, 6890, 7057, 7227, 7399, 7573, 7750, 7930, 8112, 8296, 8483, 8672, 8863, 9057, 9252, 9450, 9650, 9852, 10055, 10261, 10468, 10677, 10888, 11101, 11315, 11531, 11748, 11967, 12187, 12409, 12632, 12856, 13082, 13308, 13536, 13764, 13994, 14225, 14456, 14688, 14921, 15155, 15389, 15624, 15859, 16095, 16331, 16568, 16805, 17042, 17279, 17516, 17754, 17991, 18228, 18465, 18702, 18939, 19175, 19411, 19647, 19882, 20117, 20350, 20584, 20816, 21048, 21279, 21509, 21738, 21967, 22194, 22420, 22644, 22868, 23090, 23311, 23531, 23749, 23965, 24181, 24394, 24606, 24816, 25024, 25231, 25435, 25638, 25839, 26037, 26234, 26428, 26621, 26811, 26999, 27184, 27368, 27548, 27727, 27903, 28076, 28247, 28415, 28581, 28743, 28903, 29061, 29215, 29367, 29515, 29661, 29804, 29944, 30081, 30214, 30345, 30472, 30597, 30718, 30836, 30950, 31062, 31170,