基于c++实现离散余弦变换（DCT）

最近研究jpeg图像的编码解码，涉及到DCT即离散余弦变换，参考CSDN上一位calcular博客的文章，进行简易修改。

#include<iostream>
#include<math.h>
using namespace std;
#define PI 3.14159265354

#define DCT_SIZE 8

float DCT_Mat[DCT_SIZE][DCT_SIZE];

  float DctMap[DCT_SIZE][DCT_SIZE]=
{
    1,2,3,4,5,6,7,8,
    9,10,11,12,13,14,15,16,
    17,18,19,20,21,22,23,24,
    25,26,27,28,29,30,31,32,
    33,34,35,36,37,38,39,40,
    41,42,43,44,45,56,47,48,
    49,50,51,52,53,54,55,56,
    57,58,59,60,61,62,63,64

};
float DCT_COS[DCT_SIZE][DCT_SIZE] = {
                    0.35355338f, 0.35355338f, 0.35355338f, 0.35355338f, 0.35355338f, 0.35355338f, 0.35355338f, 0.35355338f,
                    0.49039263f, 0.41573480f, 0.27778509f, 0.09754512f, -0.09754516f, -0.27778518f, -0.41573483f, -0.49039266f,
                    0.46193978f, 0.19134171f, -0.19134176f, -0.46193978f, -0.46193978f, -0.19134156f, 0.19134180f, 0.46193978f,
                    0.41573480f, -0.09754516f, -0.49039266f, -0.27778500f, 0.27778521f, 0.49039263f, 0.09754504f, -0.41573489f,
                    0.35355338f, -0.35355338f, -0.35355332f, 0.35355350f, 0.35355338f, -0.35355362f, -0.35355327f, 0.35355341f,
                    0.27778509f, -0.49039266f, 0.09754521f, 0.41573468f, -0.41573489f, -0.09754511f, 0.49039266f, -0.27778542f,
                    0.19134171f, -0.46193978f, 0.46193978f, -0.19134195f, -0.19134149f, 0.46193966f, -0.46193987f, 0.19134195f,
                    0.09754512f, -0.27778500f, 0.41573468f, -0.49039260f, 0.49039271f, -0.41573480f, 0.27778557f, -0.09754577f
                 };
float IDCT_COS[DCT_SIZE][DCT_SIZE] = {
                    0.35355338f, 0.49039263f, 0.46193978f, 0.41573480f, 0.35355338f, 0.27778509f, 0.19134171f, 0.09754512f,
                    0.35355338f, 0.41573480f, 0.19134171f, -0.09754516f, -0.35355338f, -0.49039266f, -0.46193978f, -0.27778500f,
                    0.35355338f, 0.27778509f, -0.19134176f, -0.49039266f, -0.35355332f, 0.09754521f, 0.46193978f, 0.41573468f,
                    0.35355338f, 0.09754512f, -0.46193978f, -0.27778500f, 0.35355350f, 0.41573468f, -0.19134195f, -0.49039260f,
                    0.35355338f, -0.09754516f, -0.46193978f, 0.27778521f, 0.35355338f, -0.41573489f, -0.19134149f, 0.49039271f,
                    0.35355338f, -0.27778518f, -0.19134156f, 0.49039263f, -0.35355362f, -0.09754511f, 0.46193966f, -0.41573480f,
                    0.35355338f, -0.41573483f, 0.19134180f, 0.09754504f, -0.35355327f, 0.49039266f, -0.46193987f, 0.27778557f,
                    0.35355338f, -0.49039266f, 0.46193978f, -0.41573489f, 0.35355341f, -0.27778542f, 0.19134195f, -0.09754577f
                 };
float DctMapTmp[DCT_SIZE][DCT_SIZE];

void InitDctMat()
{
    int i,j,t;
    for(i=0;i<DCT_SIZE;i++) DCT_Mat[0][i]=sqrt(2.0/DCT_SIZE)*sqrt(1.0/2);
    for(i=1;i<DCT_SIZE;i++)
    {
        t=0;
        for(j=0;j<DCT_SIZE;j++)
        {
            DCT_Mat[i][j]=sqrt(2.0/DCT_SIZE)*cos(PI/(2.0*DCT_SIZE)*(i+t));t+=2*i;
        }
    }
    cout<<"=========initDctMat========"<<endl;
    for(int i=0;i<DCT_SIZE;i++)
    {
        for(int j=0;j<DCT_SIZE;j++)
        {
            cout<<DCT_Mat[i][j]<<"  ";
        }
        cout<<endl;
    }
    cout<<"=========initDctMat========"<<endl;
}

void DCT()
{
    float t=0;
    int i,j,k;
    for(i=0;i<DCT_SIZE;i++){
        for(j=0;j<DCT_SIZE;j++){
            t=0;
            for(k=0;k<DCT_SIZE;k++)
                //t+=DCT_Mat[i][k]*DctMap[k][j];
                t+=DCT_COS[i][k]*DctMap[k][j];
            DctMapTmp[i][j]=t;
        }
    }
    for(i=0;i<DCT_SIZE;i++){
        for(j=0;j<DCT_SIZE;j++){
            t=0;
            for(k=0;k<DCT_SIZE;k++)
                //t+=DctMapTmp[i][k]*DCT_Mat[j][k];
                t+=DctMapTmp[i][k]*DCT_COS[j][k];
            DctMap[i][j]=t;
        }
    }

    cout<<"=========DCT========"<<endl;
    for(int i=0;i<DCT_SIZE;i++)
    {
        for(int j=0;j<DCT_SIZE;j++)
        {
            cout<<DctMap[i][j]<<"  ";
        }
        cout<<endl;
    }
    cout<<"=========DCT========"<<endl;
}

void IDCT()
{
    float t=0;
    int i,j,k;
    for(i=0;i<DCT_SIZE;i++){
        for(j=0;j<DCT_SIZE;j++){
            t=0;
            for(k=0;k<DCT_SIZE;k++)
                //t+=DCT_Mat[k][i]*DctMap[k][j];
                t+=IDCT_COS[i][k]*DctMap[k][j];
            DctMapTmp[i][j]=t;
        }
    }
    for(i=0;i<DCT_SIZE;i++){
        for(j=0;j<DCT_SIZE;j++){
            t=0;
            for(k=0;k<DCT_SIZE;k++)
                //t+=DctMapTmp[i][k]*DCT_Mat[k][j]
                t+=DctMapTmp[i][k]*IDCT_COS[j][k];
            DctMap[i][j]=(int)(t);
        }
    }
     cout<<"=========IDCT========"<<endl;
    for(int i=0;i<DCT_SIZE;i++)
    {
        for(int j=0;j<DCT_SIZE;j++)
        {
            cout<<DctMap[i][j]<<"  ";
        }
        cout<<endl;
    }
    cout<<"=========IDCT========"<<endl;
}

int main()
{
    //InitDctMat();
    DCT();
    IDCT();

}