C++ 离散傅里叶逆变换

一、序言：

该教程承接上文的离散傅里叶变换，用于进行离散傅里叶逆变换。

二、设计目标

对复数数组进行离散傅里叶逆变换，并生成可供使用的图像类。

三、详细步骤

输入：经傅里叶变换后产生的复数数组

输出：MyImage图像

定义：

static MyImage* Idft2(ComplexNumber *Scr,int const width,int const height);

实现：

MyImage* MyCV::Idft2(ComplexNumber *Scr, int width, int height)
{
    int bytesPerLine = (width*8+31)/32*4;
    double* double_data = new double[width*height];
    memset(double_data,0,sizeof(double_data)*sizeof(double)); //全部赋值为0

    double fixed_factor_for_axisX = (2 * PI) / height;                  // evaluate i2π/N of i2πux/N, and store the value for computing efficiency

    double fixed_factor_for_axisY = (2 * PI) / width;                   // evaluate i2π/N of i2πux/N, and store the value for computing efficiency

    for (int x = 0; x<height; x++) {
        for (int y = 0; y<width; y++) {
            for (int u = 0; u<height; u++) {
                for (int v = 0; v<width; v++) {
                    double powerU = u * x * fixed_factor_for_axisX;         // evaluate i2πux/N
                    double powerV = v * y * fixed_factor_for_axisY;         // evaluate i2πux/N
                    ComplexNumber cplTemp;
                    cplTemp.SetValue(cos(powerU + powerV), sin(powerU + powerV));
                    double_data[y + x*width] = double_data[y + x*width] +
                            ((Scr[v + u*width] * cplTemp).m_rl
                            /(height*width));
                }
            }
        }
    }

    unsigned char *idft2_data = new unsigned char[bytesPerLine*height];//存储处理后的数据

    for(int i=0;i<height;i++)
        for(int j=0;j<width;j++)
        {
            idft2_data[i*bytesPerLine+j] = (unsigned char)double_data[i*width+j];
        }

    return new MyImage(idft2_data,width,height,MyImage::format::GRAY8);
}

至此，离散傅里叶逆变换的方法实现完成，效果图如下：