快速傅立叶变换（FFT）的C#代码

这个代码是从《 快速傅立叶变换（FFT）的C++实现与Matlab实验 》这篇文章里的源代码转换而来，请注意查看原文。

在这里自己转换成了C#代码，并作了一些改动，主要是对N值的确定，原文的N值为常量1024，自己通过对输入的数组的长度来确定N值，N值的确定符合2的n次方，函数返回N值。通过作者提供的测试变量进行测试，能得到相应的结果。代码如下：

FFT代码：

using System;
using System.Collections.Generic;
using System.Text;

namespace ConsoleApplication1
{
    ///

    /// 快速傅立叶变换(Fast Fourier Transform)。 
    ///

    public class TWFFT
    {
        private TWFFT()
        {
        }

        private static void bitrp(float[] xreal, float[] ximag, int n)
        {
            // 位反转置换 Bit-reversal Permutation
            int i, j, a, b, p;

            for (i = 1, p = 0; i < n; i *= 2)
            {
                p++;
            }
            for (i = 0; i < n; i++)
            {
                a = i;
                b = 0;
                for (j = 0; j < p; j++)
                {
                    b = b * 2 + a % 2;
                    a = a / 2;
                }
                if (b > i)
                {
                    float t = xreal[i];
                    xreal[i] = xreal[b];
                    xreal[b] = t;

                    t = ximag[i];
                    ximag[i] = ximag[b];
                    ximag[b] = t;
                }
            }
        }

        public static int FFT(float[] xreal, float[] ximag)
        {
            //n值为2的N次方
            int n = 2;
            while (n <= xreal.Length)
            {
                n *= 2;
            }
            n /= 2;

            // 快速傅立叶变换，将复数 x 变换后仍保存在 x 中，xreal, ximag 分别是 x 的实部和虚部
            float[] wreal = new float[n / 2];
            float[] wimag = new float[n / 2];
            float treal, timag, ureal, uimag, arg;
            int m, k, j, t, index1, index2;

            bitrp(xreal, ximag, n);

            // 计算 1 的前 n / 2 个 n 次方根的共轭复数 W'j = wreal [j] + i * wimag [j] , j = 0, 1, ... , n / 2 - 1
            arg = (float)(-2 * Math.PI / n);
            treal = (float)Math.Cos(arg);
            timag = (float)Math.Sin(arg);
            wreal[0] = 1.0f;
            wimag[0] = 0.0f;
            for (j = 1; j < n / 2; j++)
            {
                wreal[j] = wreal[j - 1] * treal - wimag[j - 1] * timag;
                wimag[j] = wreal[j - 1] * timag + wimag[j - 1] * treal;
            }

            for (m = 2; m <= n; m *= 2)
            {
                for (k = 0; k < n; k += m)
                {
                    for (j = 0; j < m / 2; j++)
                    {
                        index1 = k + j;
                        index2 = index1 + m / 2;
                        t = n * j / m;    // 旋转因子 w 的实部在 wreal [] 中的下标为 t
                        treal = wreal[t] * xreal[index2] - wimag[t] * ximag[index2];
                        timag = wreal[t] * ximag[index2] + wimag[t] * xreal[index2];
                        ureal = xreal[index1];
                        uimag = ximag[index1];
                        xreal[index1] = ureal + treal;
                        ximag[index1] = uimag + timag;
                        xreal[index2] = ureal - treal;
                        ximag[index2] = uimag - timag;
                    }
                }
            }

            return n;
        }

        public static int IFFT(float[] xreal, float[] ximag)
        {
            //n值为2的N次方
            int n = 2;
            while (n <= xreal.Length)
            {
                n *= 2;
            }
            n /= 2;

            // 快速傅立叶逆变换
            float[] wreal = new float[n / 2];
            float[] wimag = new float[n / 2];
            float treal, timag, ureal, uimag, arg;
            int m, k, j, t, index1, index2;

            bitrp(xreal, ximag, n);

            // 计算 1 的前 n / 2 个 n 次方根 Wj = wreal [j] + i * wimag [j] , j = 0, 1, ... , n / 2 - 1
            arg = (float)(2 * Math.PI / n);
            treal = (float)(Math.Cos(arg));
            timag = (float)(Math.Sin(arg));
            wreal[0] = 1.0f;
            wimag[0] = 0.0f;
            for (j = 1; j < n / 2; j++)
            {
                wreal[j] = wreal[j - 1] * treal - wimag[j - 1] * timag;
                wimag[j] = wreal[j - 1] * timag + wimag[j - 1] * treal;
            }

            for (m = 2; m <= n; m *= 2)
            {
                for (k = 0; k < n; k += m)
                {
                    for (j = 0; j < m / 2; j++)
                    {
                        index1 = k + j;
                        index2 = index1 + m / 2;
                        t = n * j / m;    // 旋转因子 w 的实部在 wreal [] 中的下标为 t
                        treal = wreal[t] * xreal[index2] - wimag[t] * ximag[index2];
                        timag = wreal[t] * ximag[index2] + wimag[t] * xreal[index2];
                        ureal = xreal[index1];
                        uimag = ximag[index1];
                        xreal[index1] = ureal + treal;
                        ximag[index1] = uimag + timag;
                        xreal[index2] = ureal - treal;
                        ximag[index2] = uimag - timag;
                    }
                }
            }

            for (j = 0; j < n; j++)
            {
                xreal[j] /= n;
                ximag[j] /= n;
            }

            return n;
        }
    }
}

这里只给出了函数FFT()的，函数IFFT()可以进行相应测试。测试代码：

using System;
using System.Collections.Generic;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            float[] a = {
                0.5751f,0.4514f,0.0439f,0.0272f,0.3127f,0.0129f,0.3840f,0.6831f,
                0.0928f,0.0353f,0.6124f ,0.6085f,0.0158f,0.0164f,0.1901f,0.5869f};

            float[] b = {
                0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,
                0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f};

            int n = TWFFT.FFT(a,b);

            Console.WriteLine("FFT:");

            Console.WriteLine("FFT的返回值N = {0}",n);
            Console.WriteLine();

            Console.WriteLine("i\ta\tb");

            Console.WriteLine();
            for (int i = 0; i < n; i++)
            {
                Console.WriteLine("{0}\t{1}\t{2}",i,a[i],b[i]);
            }

            Console.ReadLine();
        }
    }
}