离散余弦变换DCT代码C++

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