简单就地离散傅立叶变换（DFT） [英] Simple in-place discrete fourier transform ( DFT )

问题描述

我在写一个非常简单的就地DFT。我现在用的公式如下所示：
http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Definition < /一>使用欧拉公式沿着以避免使用复杂的数类只是这个。到目前为止，我有这样的：

I'm writing a very simple in-place DFT. I am using the formula shown here: http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Definition along with Euler's formula to avoid having to use a complex number class just for this. So far I have this:

private void fft(double[] data)
        {
            double[] real = new double[256];
            double[] imag = new double[256];
            double pi_div_128 = -1 * Math.PI / 128;
            for (int k = 0; k < 256; k++)
            {
                for (int n = 0; n < 256; n++)
                {
                    real[k] += data[k] * Math.Cos(pi_div_128 * k * n);
                    imag[k] += data[k] * Math.Sin(pi_div_128 * k * n);
                }
                data[k] = Math.Sqrt(real[k] * real[k] + imag[k] * imag[k]);
            }
        }

但Math.Cos和Math.Sin最终条款去正面和负面的，这样我加入乘以数据[K]这些条款，它们抵消，而我只是得到了一些肮脏的小值。我看到它是如何发生的，但我不能让我的代码怎么可能是误代表的数学意义。任何帮助表示赞赏。仅供参考，我必须写我自己，我知道我可以得到现成的FFT的。

But the Math.Cos and Math.Sin terms eventually go both positive and negative, so as I'm adding those terms multiplied with data[k], they cancel out and I just get some obscenely small value. I see how it is happening, but I can't make sense of how my code is perhaps mis-representing the mathematics. Any help is appreciated. FYI, I do have to write my own, I realize I can get off-the shelf FFT's.

推荐答案

我相信你（; N< 256; N + INT N = 0）
{$ b在本节

I believe You have an error in this section

for (int n = 0; n < 256; n++)
{
    real[k] += data[k] * Math.Cos(pi_div_128 * k * n);
    imag[k] += data[k] * Math.Sin(pi_div_128 * k * n);
}

您应该替换数据[K]数据[N]

You should replace data[k] with data[n]

编辑：

您也破坏了行，您的数据：

You are also destroying Your data in the line:

data[k] = Math.Sqrt(real[k] * real[k] + imag[k] * imag[k]);

您必须存储您的复数或其他地方以后的模量。如果模是你想要的，你想将其存储在数据[]你有计算变换后的代码中的另一个循环，整个数据[]是必要的计算每一个真正的[k]和IMAG [K]。

You have to store the moduli of your complex numbers somewhere else or later. If the modulus is all you want, and You want to store it in data[] You have to code another loop after computing the transform., The whole data[] is necessary for computing every real[k] and imag [k].

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