void initDCTParam(int deg)
{
// deg 为DCT变换数据长度的幂
if(bHasInit)
{
return; //不用再计算查找表
}
int total, halftotal, i, group, endstart, factor;
total = 1 << deg;
if(C != NULL) delete []C;
C = (double *)new double[total];
halftotal = total >> 1;
for(i=0; i < halftotal; i++)
C[total-i-1]=(double)(2*i+1);
for(group=0; group < deg-1; group++)
{
endstart=1 << (deg-1-group);
int len = endstart >> 1;
factor=1 << (group+1);
for(int j = 0;j < len; j++)
C[endstart-j-1] = factor*C[total-j-1];
}
for(i=1; i < total; i++)
C[i] = 2.0*cos(C[i]*PI/(total << 1)); ///C[0]空着，没使用
bHasInit=true;
}
DCT变换过程可分为两部分：前向追底和后向回根
前向追底：
void dct_forward(double *f,int deg)
{
// f中存储DCT数据
int i_deg, i_halfwing, total, wing, wings, winglen, halfwing;
double temp1,temp2;
total = 1 << deg;
for(i_deg = 0; i_deg < deg; i_deg++)
{
wings = 1 << i_deg;
winglen = total >> i_deg;
halfwing = winglen >> 1;
for(wing = 0; wing < wings; wing++)
{
for(i_halfwing = 0; i_halfwing < halfwing; i_halfwing++)
{
temp1 = f[wing*winglen+i_halfwing];
temp2 = f[(wing+1)*winglen-1-i_halfwing];
if(wing%2)
swap(temp1,temp2); // 交换temp1与temp2的值
f[wing*winglen+i_halfwing] = temp1+temp2;
f[(wing+1)*winglen-1-i_halfwing] =
(temp1-temp2)*C[winglen-1-i_halfwing];
}
}
}
}
后向回根： void dct_backward(double *f,int deg)
{
// f中存储DCT数据
int total,i_deg,wing,wings,halfwing,winglen,i_halfwing,temp1,temp2;
total = 1 << deg;
for(i_deg = deg-1; i_deg >= 0; i_deg--)
{
wings = 1 << i_deg;
winglen = 1 << (deg-i_deg);
halfwing = winglen >> 1;
for(wing = 0; wing < wings; wing++)
{
for(i_halfwing = 0; i_halfwing < halfwing; i_halfwing++)
{
//f[i_halfwing+wing*winglen] = f[i_halfwing+wing*winglen];
if(i_halfwing == 0)
{
f[halfwing+wing*winglen+i_halfwing] =
0.5*f[halfwing+wing*winglen+i_halfwing];
}
else
{
temp1=bitrev(i_halfwing,deg-i_deg-1); // bitrev为位反序
temp2=bitrev(i_halfwing-1,deg-i_deg-1); // 第一参数为要变换的数
// 第二参数为二进制长度
f[halfwing+wing*winglen+temp1] =
f[halfwing+wing*winglen+temp1]-f[halfwing+wing*winglen+temp2];
}
}
}
}
}
位反序函数如下：int bitrev(int bi,int deg)
{
int j = 1, temp = 0, degnum, halfnum;
degnum = deg;
//if(deg<0) return 0;
if(deg == 0) return bi;
halfnum = 1 << (deg-1);
while(halfnum)
{
if(halfnum&bi)
temp += j;
j<<=1;
halfnum >>= 1;
}
return temp;
}
完整实现一维DCT变换：void fdct_1D_no_param(double *f,int deg)
{
initDCTParam(deg);
dct_forward(f,deg);
dct_backward(f,deg);
fbitrev(f,deg); // 实现位反序排列
f[0] = 1/(sqrt(2.0))*f[0];
}
void fdct_1D(double *f,int deg)
{
fdct_1D_no_param(f,deg);
int total = 1 << deg;
double param = sqrt(2.0/total);
for(int i = 0; i < total; i++)
f[i] = param*f[i];
}
利用一维DCT变换来实现二维DCT变换：void fdct_2D(double *f,int deg_row,int deg_col)
{
int rows,cols,i_row,i_col;
double two_div_sqrtcolrow;
rows=1 << deg_row;
cols=1 << deg_col;
init2D_Param(rows,cols);
two_div_sqrtcolrow = 2.0/(sqrt(double(rows*cols)));
for(i_row = 0; i_row < rows; i_row++)
{
fdct_1D_no_param(f+i_row*cols,deg_col);
}
for(i_col = 0; i_col < cols; i_col++)
{
for(i_row = 0; i_row < rows; i_row++)
{
temp_2D[i_row] = f[i_row*cols+i_col];
}
fdct_1D_no_param(temp_2D, deg_row);
for(i_row = 0; i_row < rows; i_row++)
{
f[i_row*cols+i_col] = temp_2D[i_row]*two_div_sqrtcolrow;
}
}
bHasInit = false;
}
IDCT快速变换
初始化查找表： void initIDCTParam(int deg)
{
if(bHasInit)
return; //不用再计算查找表
int total, halftotal, i, group, endstart, factor;
total = 1 << deg;
// if(C!=NULL) delete []C;
// C=(double *)new double[total];
// 由于正变换已经为C申请了空间，所以逆变换就需再申请空间了！
halftotal = total >> 1;
for(i = 0; i < halftotal; i++)
C[total-i-1] = (double)(2*i+1);
for(group = 0; group < deg-1; group++)
{
endstart = 1 << (deg-1-group);
int len = endstart>>1;
factor = 1 << (group+1);
for(int j = 0; j < len; j++)
C[endstart-j-1] = factor*C[total-j-1];
}
for(i = 1; i < total; i++)
C[i] = 1.0/(2.0*cos(C[i]*PI/(total << 1))); // C[0]空着没用
bHasInit=true;
}
IDCT变换过程也可分为两部分：前向追底和后向回根
前向追底 void idct_forward(double *F,int deg)
{
int total,i_deg,wing,wings,halfwing,winglen,i_halfwing,temp1,temp2;
total = 1 << deg;
for(i_deg = 0; i_deg < deg; i_deg++)
{
wings = 1 << i_deg;
winglen = 1 << (deg-i_deg);
halfwing = winglen >> 1;
for(wing = 0; wing < wings; wing++)
{
for(i_halfwing = halfwing-1; i_halfwing >= 0; i_halfwing--)
{
if(i_halfwing == 0)
{
F[halfwing+wing*winglen+i_halfwing] =
2.0*F[halfwing+wing*winglen+i_halfwing];
}
else
{
temp1 = bitrev(i_halfwing,deg-i_deg-1);
temp2 = bitrev(i_halfwing-1,deg-i_deg-1);
F[halfwing+wing*winglen+temp1] = F[halfwing+wing*winglen+temp1]
+F[halfwing+wing*winglen+temp2];
}
}
}
}
}
后向回根void idct_backward(double *F, int deg)
{
int i_deg,i_halfwing,total,wing,wings,winglen,halfwing;
double temp1, temp2;
total = 1 << deg;
for(i_deg = deg-1; i_deg >= 0; i_deg--)
{
wings = 1 << i_deg;
winglen = total >> i_deg;
halfwing = winglen >> 1;
for(wing = 0; wing < wings; wing++)
{
for(i_halfwing = 0; i_halfwing < halfwing; i_halfwing++)
{
temp1 = F[wing*winglen+i_halfwing];
temp2 = F[(wing+1)*winglen-1-i_halfwing]*C[winglen-1-i_half
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