（十三）用JAVA编写MP3解码器——IMDCT快速算法
解码一帧Layer3第7步：IMDCT和子带混合 -- class Layer3内的hybrid方法
这一步可细分为3个步骤：
1.初始化加窗系数floatWinIMDCT[][] 初始化floatWinIMDCT[][]时直接代入相关公式，我这事先另外编程用公式把加窗系数计算出来，供程序中直接查表使用，而不是运行时进行初始化。初始化floatWinIMDCT[][]的代码正好还留着，就顺便贴出来：
public class InitIMDCT {
public static void main(String args[]) {
int i, j;
final double PI12 = 0.26179938779914943653855361527329;
final double PI36 = 0.087266462599716478846184538424431;
final double PI72 = 0.043633231299858239423092269212215;
double[][] doubleWinIMDCT = new double[4][36];
// type 0
for (i = 0; i < 36; i++)
doubleWinIMDCT[0][i] = Math.sin(PI36 * (i + 0.5));
// type 1
for (i = 0; i < 18; i++)
doubleWinIMDCT[1][i] = Math.sin(PI36 * (i + 0.5));
for (i = 18; i < 24; i++)
doubleWinIMDCT[1][i] = 1.0;
for (i = 24; i < 30; i++)
doubleWinIMDCT[1][i] = Math.sin(PI12 * (i + 0.5 - 18));
for (i = 30; i < 36; i++)
doubleWinIMDCT[1][i] = 0.0;
// type 2 (not needed...)
// type 3
for (i = 0; i < 6; i++)
doubleWinIMDCT[3][i] = 0.0;
for (i = 6; i < 12; i++)
doubleWinIMDCT[3][i] = Math.sin(PI12 * (i + 0.5 - 6.0));
for (i = 12; i < 18; i++)
doubleWinIMDCT[3][i] = 1.0;
for (i = 18; i < 36; i++)
doubleWinIMDCT[3][i] = Math.sin(PI36 * (i + 0.5));
for (i = 0; i < 4; i++) {
doubleWinIMDCT[i][0] /= 2 * Math.cos(19 * PI72);
doubleWinIMDCT[i][1] /= 2 * Math.cos(21 * PI72);
doubleWinIMDCT[i][2] /= 2 * Math.cos(23 * PI72);
doubleWinIMDCT[i][3] /= 2 * Math.cos(25 * PI72);
doubleWinIMDCT[i][4] /= 2 * Math.cos(27 * PI72);
doubleWinIMDCT[i][5] /= 2 * Math.cos(29 * PI72);
doubleWinIMDCT[i][6] /= 2 * Math.cos(31 * PI72);
doubleWinIMDCT[i][7] /= 2 * Math.cos(33 * PI72);
doubleWinIMDCT[i][8] /= 2 * Math.cos(35 * PI72);
doubleWinIMDCT[i][9] /= 2 * Math.cos(37 * PI72);
doubleWinIMDCT[i][10] /= 2 * Math.cos(39 * PI72);
doubleWinIMDCT[i][11] /= 2 * Math.cos(41 * PI72);
doubleWinIMDCT[i][12] /= 2 * Math.cos(43 * PI72);
doubleWinIMDCT[i][13] /= 2 * Math.cos(45 * PI72);
doubleWinIMDCT[i][14] /= 2 * Math.cos(47 * PI72);
doubleWinIMDCT[i][15] /= 2 * Math.cos(49 * PI72);
doubleWinIMDCT[i][16] /= 2 * Math.cos(51 * PI72);
doubleWinIMDCT[i][17] /= 2 * Math.cos(53 * PI72);
doubleWinIMDCT[i][18] /= 2 * Math.cos(55 * PI72);
doubleWinIMDCT[i][19] /= 2 * Math.cos(57 * PI72);
doubleWinIMDCT[i][20] /= 2 * Math.cos(59 * PI72);
doubleWinIMDCT[i][21] /= 2 * Math.cos(61 * PI72);
doubleWinIMDCT[i][22] /= 2 * Math.cos(63 * PI72);
doubleWinIMDCT[i][23] /= 2 * Math.cos(65 * PI72);
doubleWinIMDCT[i][24] /= 2 * Math.cos(67 * PI72);
doubleWinIMDCT[i][25] /= 2 * Math.cos(69 * PI72);
doubleWinIMDCT[i][26] /= 2 * Math.cos(71 * PI72);
doubleWinIMDCT[i][27] /= 2 * Math.cos(71 * PI72);
doubleWinIMDCT[i][28] /= 2 * Math.cos(69 * PI72);
doubleWinIMDCT[i][29] /= 2 * Math.cos(67 * PI72);
doubleWinIMDCT[i][30] /= 2 * Math.cos(65 * PI72);
doubleWinIMDCT[i][31] /= 2 * Math.cos(63 * PI72);
doubleWinIMDCT[i][32] /= 2 * Math.cos(61 * PI72);
doubleWinIMDCT[i][33] /= 2 * Math.cos(59 * PI72);
doubleWinIMDCT[i][34] /= 2 * Math.cos(57 * PI72);
doubleWinIMDCT[i][35] /= 2 * Math.cos(55 * PI72);
}
System.out.println("private static float[][] doubleWinIMDCT = {");
for(i = 0; i < 4; i++) {
System.out.printf("{");
for(j = 0; j < 35; j++) {
System.out.printf("%gf,", doubleWinIMDCT[i][j]);
if(j % 6 == 5)
System.out.printf("\n");
}
System.out.printf("%gf},\n", doubleWinIMDCT[i][j]);
}
System.out.println("};");
}
}
运行程序将输出COPY到源代码的“private static final float[][] floatWinIMDCT = ”那就行了。
2.IMDCT 这里用到两种反向改进型离散余弦变换（IMDCT）：短块用12点的IMDCT；长块用36点IMDCT。在解码端应用IMDCT完成频域到时域的转换，IMDCT计算的公式是：
从公式可以看出，如果长块n=36，直接计算需要18*36=648次浮点乘法；如果是短块，则n=12，直接运算需要6*12=72次浮点乘法。解码一帧采用标准立体声编码的MP3需要调用4次，运算量很大，所以必须采用快速算法。程序中用到的快速算法的作者是Mikko Tommila（copyright 1997，现已应用于公共领域），后来由Jeff改进。出于改进程序运行速度的考虑，这里采用了快速算法的展开式。快速算法的推算时把公式展开为具有递推特性的表达式，利用递推式一直递推到2点和3点的IDCT。推导过程可以参考我以前的一篇贴子《MP3解码之DCT(32→64)快速算法的展开》，需要说明的是DCT与IDCT由于公式不同所以推算过程是完全不同的，但从这篇贴子可以看到利用“递推”特性逐步缩小乘法运算规模，就明白各点快速算法的函数了，即使明白了各点快速算法的函数，还是不建议你看展开式，看展开式是理不清头绪的，尽管源码中作了比较详细的说明。如果你想深入了解编解码知识的话，建议你亲自动手推导一下，我这里就省略掉IMDCT快速算法的推导过程，后文直接给快速算法的展开式。
3.混合滤波带（hybrid filterbank） 先定义一个先进先出的队列floatPrevBlck[][][]，经IMDCT后产生的36个输出中的前18个值和这个队列中的18个值相加输出到xr[]，再将IMDCT产生的36个输出值中的后18个写入队列；每解码完一个粒度组内的一个声道后要将当前的最大子带之后对应的队列数据清零。
【提示】以下代码是Layer3.java的一部分，应遵守《（一）用JAVA编写MP3解码器——前言》中的许可协议。
class Layer3内的hybrid方法的源码如下：
//7.
//>>>>HYBRID(synthesize via iMDCT)=========================================
private static final float[][] floatWinIMDCT = {
{0.0322824f,0.1072064f,0.2014143f,0.3256164f,0.5f,0.7677747f,
1.2412229f,2.3319514f,7.7441506f,-8.4512568f,-3.0390580f,-1.9483297f,
-1.4748814f,-1.2071068f,-1.0327232f,-0.9085211f,-0.8143131f,-0.7393892f,
-0.6775254f,-0.6248445f,-0.5787917f,-0.5376016f,-0.5f,-0.4650284f,
-0.4319343f,-0.4000996f,-0.3689899f,-0.3381170f,-0.3070072f,-0.2751725f,
-0.2420785f,-0.2071068f,-0.1695052f,-0.1283151f,-0.0822624f,-0.0295815f},
{0.0322824f,0.1072064f,0.2014143f,0.3256164f,0.5f,0.7677747f,
1.2412229f,2.3319514f,7.7441506f,-8.4512568f,-3.0390580f,-1.9483297f,
-1.4748814f,-1.2071068f,-1.0327232f,-0.9085211f,-0.8143131f,-0.7393892f,
-0.6781709f,-0.6302362f,-0.5928445f,-0.5636910f,-0.5411961f,-0.5242646f,
-0.5077583f,-0.4659258f,-0.3970546f,-0.3046707f,-0.1929928f,-0.0668476f,
-0.0f,-0.0f,-0.0f,-0.0f,-0.0f,-0.0f},
{/* block_type = 2 */},
{0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,
0.3015303f,1.4659259f,6.9781060f,-9.0940447f,-3.5390582f,-2.2903500f,
-1.6627548f,-1.3065630f,-1.0828403f,-0.9305795f,-0.8213398f,-0.7400936f,
-0.6775254f,-0.6248445f,-0.5787917f,-0.5376016f,-0.5f,-0.4650284f,
-0.4319343f,-0.4000996f,-0.3689899f,-0.3381170f,-0.3070072f,-0.2751725f,
-0.2420785f,-0.2071068f,-0.1695052f,-0.1283151f,-0.0822624f,-0.0295815f} };
/*
* inv_mdct -- 12点和36点IMDCT快速算法(展开式)
*/
private void inv_mdct(final float[] in, final float[] out, final int block_type) {
int i, idx6 = 0;
float in0,in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17;
float out0,out1,out2,out3,out4,out5,out6,out7,out8,out9,
out10,out11,out12,out13,out14,out15,out16,out17, tmp;
if(block_type == 2) {
out[0]=out[1]=out[2]=out[3]=out[4]=out[5]=out[6]=out[7]
=out[8]=out[9]=out[10]=out[11]=out[12]=out[13]=out[14]
=out[15]=out[16]=out[17]=out[18]=out[19]=out[20]=out[21]
=out[22]=out[23]=out[24]=out[25]=out[26]=out[27]=out[28]
=out[29]=out[30]=out[31]=out[32]=out[33]=out[34]=out[35]=0.0f;
for (i = 0; i < 3; i++) {
//>>>>>>>>>>>> 12-point IMDCT
//>>>>>> 6-point IDCT
in[15 + i] += (in[12 + i] += in[9 + i]) + in[6 + i];
in[9 + i] += (in[6 + i] += in[3 + i]) + in[i];
in[3 + i] += in[i];
//>>> 3-point IDCT on even
out1 = (in1 = in[i]) - (in2 = in[12+i]);
in3 = in1 + in2 * 0.5f;
in4 = in[6+i] * 0.8660254f;
out0 = in3 + in4;
out2 = in3 - in4;
//<<< End 3-point IDCT on even
//>>> 3-point IDCT on odd (for 6-point IDCT)
out4 = ((in1 = in[3+i]) - (in2 = in[15+i])) * 0.7071068f;
in3 = in1 + in2 * 0.5f;
in4 = in[9+i] * 0.8660254f;
out5 = (in3 + in4) * 0.5176381f;
out3 = (in3 - in4) * 1.9318516f;
//<<< End 3-point IDCT on odd
// Output: butterflies on 2,3-point IDCT's (for 6-point IDCT)
tmp = out0; out0 += out5; out5 = tmp - out5;
tmp = out1; out1 += out4; out4 = tmp - out4;
tmp = out2; out2 += out3; out3 = tmp - out3;
//<<<<<< End 6-point IDCT
//<<<<<<<<<<<< End 12-point IDCT
// Shift
in1 = out3 * 0.1072064f;
out[6 + idx6] += in1;
out[7 + idx6] += out4 * 0.5f;
out[8 + idx6] += out5 * 2.3319512f;
out[9 + idx6] -= out5 * 3.0390580f;
out[10 + idx6] -= out4 * 1.2071068f;
out[11 + idx6] -= in1 * 7.5957541f;
out[12 + idx6] -= out2 * 0.6248445f;
out[13 + idx6] -= out1 * 0.5f;
out[14 + idx6] -= out0 * 0.4000996f;
out[15 + idx6] -= out0 * 0.3070072f;
out[16 + idx6] -= out1 * 0.2071068f;
out[17 + idx6] -= out2 * 0.0822623f;
idx6 += 6;
}
} else {
//>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 36-point IDCT
//>>>>>>>>>>>>>>>>>> 18-point IDCT for odd
in[17] += (in[16] += in[15]) + in[14];
in[15] += (in[14] += in[13]) + in[12];
in[13] += (in[12] += in[11]) + in[10];
in[11] += (in[10] += in[9]) + in[8];
in[9] += (in[8] += in[7]) + in[6];
in[7] += (in[6] += in[5]) + in[4];
in[5] += (in[4] += in[3]) + in[2];
in[3] += (in[2] += in[1]) + in[0];
in[1] += in[0];
//>>>>>>>>> 9-point IDCT on even
/*
* for(i = 0; i < 9; i++) {
* sum = 0;
* for(j = 0; j < 18; j += 2)
* sum += in[j] * cos(PI36 * (2 * i + 1) * j);
* out18[i] = sum;
* }
*/
in0 = in[0] + in[12] * 0.5f;
in1 = in[0] - in[12];
in2 = in[8] + in[16] - in[4];
out4 = in1 + in2;
in3 = in1 - in2 * 0.5f;
in4 = (in[10] + in[14] - in[2]) * 0.8660254f; // cos(PI/6)
out1 = in3 - in4;
out7 = in3 + in4;
in5 = (in[4] + in[8]) * 0.9396926f; //cos( PI/9)
in6 = (in[16] - in[8]) * 0.1736482f; //cos(4PI/9)
in7 = -(in[4] + in[16]) * 0.7660444f; //cos(2PI/9)
in17 = in0 - in5 - in7;
in8 = in5 + in0 + in6;
in9 = in0 + in7 - in6;
in12 = in[6] * 0.8660254f; //cos(PI/6)
in10 = (in[2] + in[10]) * 0.9848078f; //cos(PI/18)
in11 = (in[14] - in[10]) * 0.3420201f; //cos(7PI/18)
in13 = in10 + in11 + in12;
out0 = in8 + in13;
out8 = in8 - in13;
in14 = -(in[2] + in[14]) * 0.6427876f; //cos(5PI/18)
in15 = in10 + in14 - in12;
in16 = in11 - in14 - in12;
out3 = in9 + in15;
out5 = in9 - in15;
out2 = in17 + in16;
out6 = in17 - in16;
//<<<<<<<<< End 9-point IDCT on even
//>>>>>>>>> 9-point IDCT on odd
/*
* for(i = 0; i < 9; i++) {
* sum = 0;
* for(j = 0;j < 18; j += 2)
* sum += in[j + 1] * cos(PI36 * (2 * i + 1) * j);
* out18[17-i] = sum;
* }
*/
in0 = in[1] + in[13] * 0.5f; //cos(PI/3)
in1 = in[1] - in[13];
in2 = in[9] + in[17] - in[5];
out13 = (in1 + in2) * 0.7071068f; //cos(PI/4)
in3 = in1 - in2 * 0.5f;
in4 = (in[11] + in[15] - in[3]) * 0.8660254f; //cos(PI/6)
out16 = (in3 - in4) * 0.5176381f; // 0.5/cos( PI/12)
out10 = (in3 + in4) * 1.9318517f; // 0.5/cos(5PI/12)
in5 = (in[5] + in[9]) * 0.9396926f; // cos( PI/9)
in6 = (in[17] - in[9])* 0.1736482f; // cos(4PI/9)
in7 = -(in[5] + in[17])*0.7660444f; // cos(2PI/9)
in17 = in0 - in5 - in7;
in8 = in5 + in0 + in6;
in9 = in0 + in7 - in6;
in12 = in[7] * 0.8660254f; // cos(PI/6)
in10 = (in[3] + in[11]) * 0.9848078f; // cos(PI/18)
in11 = (in[15] - in[11])* 0.3420201f; // cos(7PI/18)
in13 = in10 + in11 + in12;
out17 = (in8 + in13) * 0.5019099f; // 0.5/cos(PI/36)
out9 = (in8 - in13) * 5.7368566f; // 0.5/cos(17PI/36)
in14 = -(in[3] + in[15]) * 0.6427876f; // cos(5PI/18)
in15 = in10 + in14 - in12;
in16 = in11 - in14 - in12;
out14 = (in9 + in15) * 0.6103873f; // 0.5/cos(7PI/36)
out12 = (in9 - in15) * 0.8717234f; // 0.5/cos(11PI/36)
out15 = (in17 + in16) * 0.5516890f; // 0.5/cos(5PI/36)
out11 = (in17 - in16) * 1.1831008f; // 0.5/cos(13PI/36)
//<<<<<<<<< End 9-point IDCT on odd
// Butterflies on 9-point IDCT's
tmp = out0; out0 += out17; out17 = tmp - out17;
tmp = out1; out1 += out16; out16 = tmp - out16;
tmp = out2; out2 += out15; out15 = tmp - out15;
tmp = out3; out3 += out14; out14 = tmp - out14;
tmp = out4; out4 += out13; out13 = tmp - out13;
tmp = out5; out5 += out12; out12 = tmp - out12;
tmp = out6; out6 += out11; out11 = tmp - out11;
tmp = out7; out7 += out10; out10 = tmp - out10;
tmp = out8; out8 += out9; out9 = tmp - out9;
//<<<<<<<<<<<<<<<<<< End 18-point IDCT
//<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< End 36-point IDCT
// Shift
final float[] winp = floatWinIMDCT[block_type];
out[0] = out9 * winp[0];
out[1] = out10 * winp[1];
out[2] = out11 * winp[2];
out[3] = out12 * winp[3];
out[4] = out13 * winp[4];
out[5] = out14 * winp[5];
out[6] = out15 * winp[6];
out[7] = out16 * winp[7];
out[8] = out17 * winp[8];
out[9] = out17 * winp[9];
out[10] = out16 * winp[10];
out[11] = out15 * winp[11];
out[12] = out14 * winp[12];
out[13] = out13 * winp[13];
out[14] = out12 * winp[14];
out[15] = out11 * winp[15];
out[16] = out10 * winp[16];
out[17] = out9 * winp[17];
out[18] = out8 * winp[18];
out[19] = out7 * winp[19];
out[20] = out6 * winp[20];
out[21] = out5 * winp[21];
out[22] = out4 * winp[22];
out[23] = out3 * winp[23];
out[24] = out2 * winp[24];
out[25] = out1 * winp[25];
out[26] = out0 * winp[26];
out[27] = out0 * winp[27];
out[28] = out1 * winp[28];
out[29] = out2 * winp[29];
out[30] = out3 * winp[30];
out[31] = out4 * winp[31];
out[32] = out5 * winp[32];
out[33] = out6 * winp[33];
out[34] = out7 * winp[34];
out[35] = out8 * winp[35];
}
}
private static float[] floatRawOut; // [36];
private static float[][][] floatPrevBlck; // [2][32][18];
private void hybrid(final int ch, final int gr) {
GRInfo gr_info = (objSI.ch[ch].gr[gr]);
int sb, ss, bt;
int max_sb = (17 + rzero_index[ch]) / 18;
for (sb = 0; sb < max_sb; sb++) {
bt = ((gr_info.window_switching_flag != 0)
&& (gr_info.mixed_block_flag != 0) && (sb < 2)) ? 0
: gr_info.block_type;
inv_mdct(xr[ch][sb], floatRawOut, bt);
for(ss = 0; ss < 18; ss++) {
xr[ch][sb][ss] = floatRawOut[ss] + floatPrevBlck[ch][sb][ss];
floatPrevBlck[ch][sb][ss] = floatRawOut[18 + ss];
}
}
for (; sb < 32; sb++)
for(ss = 0; ss < 18; ss++) {
xr[ch][sb][ss] = floatPrevBlck[ch][sb][ss];
floatPrevBlck[ch][sb][ss] = 0;
}
}
//<<<<HYBRID(synthesize via iMDCT)=========================================