note

若要求矩阵的傅里叶变换，则对每个行或列向量求对应的傅里叶变换。

比如matlab中对矩阵求fft傅里叶变换就是对每个列向量分别求傅里叶变换。

 code

/*
 \brief:离散傅里叶变换
 \param dir:变换方向，-1为傅里叶正变换，+1为傅里叶反变换
 \param m:个数(向量的维数)
 \param real:向量的实部
 \param image:向量的虚部
*/
int DFT(int dir, int m, double *real, double *image)
{
	if (dir != -1 && dir != 1)
	{
		return 0;
	}
	if (m < 1)
	{
		return 0;
	}
	if (real == NULL || image == NULL)
	{
		return 0;
	}
    long i,k;
    double arg;
    double cosarg,sinarg;
    double *x2 = NULL, *y2 = NULL;

    x2 = (double*)malloc(m * sizeof(double));	// 临时数据
    y2 = (double*)malloc(m * sizeof(double));
    if(x2 == NULL || y2 == NULL)
	{
		if (x2 != NULL)
		{
			free(x2);
		}
		if (y2 != NULL)
		{
			free(y2);
		}
		return(0);
	}
		
    for(i = 0; i < m; i++)
    {
        x2[i] = 0;
        y2[i] = 0;
        arg = dir * 2.0 * 3.141592654 * (double)i / (double)m;
        for(k= 0; k < m; k++)
        {
            cosarg = cos(k * arg);
            sinarg = sin(k * arg);
            x2[i] += (real[k] * cosarg - image[k] * sinarg);
            y2[i] += (real[k] * sinarg + image[k] * cosarg);
        }
    }

	for (i = 0; i < m; i++)
	{
		if(dir == 1)	// 傅里叶逆变换
		{
			real[i] = x2[i] / (double)m;
            image[i] = y2[i] / (double)m;
		}
		else if (dir == -1)	// 傅里叶正变换
		{
			real[i] = x2[i];
            image[i] = y2[i];
		}
	}
	
    free(x2);
    free(y2);
    return(1);
}