C/C++ 实现FFT

来源：互联网发布：猎虎88数据编辑：程序博客网时间：2024/06/16 05:52

说明：

1、默认FFT点数为2的整数次幂

2、把需要处理的数据放在Data[ ]数据中即可，DataReRank(int num)参数为FFT点数

3、编译工具：Visual Studio Professional 2013

#include<iostream>#include<list>#include<vector>using namespace std;float Data[] = {1,2,3,4,5,6,7,8};//进行FFT的数据struct Complex{  float imaginary;  float real; };Complex ComplexMulti( Complex One, Complex Two);   //复数乘法函数Complex StoreResult[sizeof(Data) / sizeof(float)];    //存储计算的结果void DataReRank(int num);void FFT();int DataLength = sizeof(Data) / sizeof(float);  //数据长度const int PI = 3.1415926;int main(){DataReRank(8);FFT();for (auto data : StoreResult) cout << sqrt(pow(data.imaginary, 2) + pow(data.real, 2))<<endl;return 0;}void DataReRank(int num){int BitNum = log2(num);int flag = 1, index = 0, flag2 = 0;list<int> Bit;   //存放二进制数，重复使用，每次用完需清零vector<float> DataTemp; //暂时存放重新排列过后的FFT数据for (int i = 0; i < num; i++){for (int j = 0; j < BitNum; j++){              //十进制转化为长度一致的二进制数int x = (i & flag)>0 ? 1 : 0;Bit.push_front(x);flag <<= 1;}for (auto it :Bit)  index += it*pow(2, flag2++); //将原数组的索引倒序DataTemp.push_back(Data[index]);Bit.clear();flag = 1; flag2 = 0; index = 0;}for (int i = 0; i < num; i++) Data[i]=DataTemp[i];  //将DataTemp中数据复制到Data}Complex ComplexMulti(Complex One, Complex Two){Complex Temp;Temp.imaginary = One.imaginary *Two.real + One.real*Two.imaginary;Temp.real = One.real*Two.real - One.imaginary*Two.imaginary;return Temp;}void FFT(){int Level = log2(DataLength);      //需要运算的级数Complex Temp,up;//先将数据转移到复数结构里for (int i = 0; i < DataLength; i++) StoreResult[i].real = Data[i];for (int i = 1; i <= Level; i++){Complex Factor;  //定义旋转因子int BowknotDis = 2 << (i - 1);     //没有交叉的蝶形结的距离int CalDis = BowknotDis / 2;   //同一蝶形计算中两个数字的距离for (int j = 0; j < CalDis; j++) {   //每一级蝶形运算中有CalDis个不同旋转因子Factor.real = cos(2 * PI /pow(2,i)*j);Factor.imaginary = -sin(2 * PI /pow(2,i)*j);for (int k = j; k < DataLength - 1; k += BowknotDis){Temp = ComplexMulti(Factor, StoreResult[k + CalDis]);up.imaginary = StoreResult[k].imaginary + Temp.imaginary;up.real = StoreResult[k].real + Temp.real;StoreResult[k + CalDis].imaginary = StoreResult[k].imaginary - Temp.imaginary;StoreResult[k + CalDis].real = StoreResult[k].real - Temp.real;StoreResult[k] = up;}}}}

对代码中的数据进行计算：

编译器：

Matlab：

代码的计算结果与matlab稍有偏差，不过可以看出代码的计算方法与结果是正确的

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