快速傅里叶变化C++实现

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#include <stdio.h>

#include <math.h>

#include <stdlib.h>

#include <iostream>

#include <fstream>

#include <vector>

#include  <ctime>

#include <iomanip>

usingnamespace std;

 

#define PI 3.14159265 

#define N  4095       //采样256次

 

typedefstruct              //定义结构体

{

    doublereal;/*实部*/

    doubleimg;/*虚部*/

}complex;

 

complex x[N * 2], *W;                       /*输出序列的值*/                     //序列长度 全局变量

 

voidadd(complex a, complex b, complex *c)      //  复数加运算

{

    c->real = a.real + b.real;

    c->img = a.img + b.img;

}

voidsub(complex a, complex b, complex *c)      //  复数减运算

{

    c->real = a.real - b.real;

    c->img = a.img - b.img;

}

voidmul(complex a, complex b, complex *c)      //复数乘运算

{

    c->real = a.real*b.real - a.img*b.img;

    c->img = a.real*b.img + a.img*b.real;

}

voiddivi(complex a, complex b, complex *c)      //  复数除运算

{

    c->real = (a.real*b.real + a.img*b.img) / (b.real*b.real + b.img*b.img);

    c->img = (a.img*b.real - a.real*b.img) / (b.real*b.real + b.img*b.img);

}

 

voidinitW(intsize)                                //欧拉公式运算  

{

    inti;

    W = (complex*)malloc(sizeof(complex)* size);    //分配内存空间

    for(i = 0; i<size; i++)

    {

        W[i].real = cos(2 * PI / size*i);

        W[i].img = -1 * sin(2 * PI / size*i);

    }

    /*for (i = 0; i < size; i++)

    {

    cout << endl;

    cout << endl;

    cout << endl;

    cout << W[i].real << " ";

    cout << W[i].img <<"j" << " ";

    }*/

}

 

voidchangex(intsize)                      //变址运算 

{

    complex temp;

    unsignedinti = 0, j = 0, k = 0;

    doublet;

    for(i = 0; i<size; i++)

    {

        k = i; j = 0;

        t = (log(size) / log(2));

        while((t--)>0)

        {

            j = j << 1;

            j |= (k & 1);

            k = k >> 1;

        }

        if(j>i)

        {

            temp = x[i];

            x[i] = x[j];

            x[j] = temp;

        }

    }

}

 

 

voidfftx()                             //快速傅里叶函数

{

    long   int i = 0, j = 0, k = 0, l = 0;

    complex up, down, product;

    changex(N);

    for(i = 0; i<log(N) / log(2); i++) /*一级蝶形运算*/

    {

        l = 1 << i;

        for(j = 0; j<N; j += 2 * l) /*一组蝶形运算*/

        {

            for(k = 0; k<l; k++) /*一个蝶形运算*/

            {

                mul(x[j + k + l], W[N*k / 2 / l], &product);

                add(x[j + k], product, &up);

                sub(x[j + k], product, &down);

                x[j + k] = up;

                x[j + k + l] = down;

            }

        }

    }

}

 

 

voidoutput()   /*输出x结果*/

{

    inti;

    printf("\nx傅里叶变换结果\n");

    for(i = 0; i<N; i++)

    {

        if(i % 4 == 0 && i != 0) printf("\n");

        printf("  %.2f", x[i].real);

        if(x[i].img >= 0.0001)

            printf("+%.2fj  ", x[i].img);

        elseif (fabs(x[i].img)<0.0001)

            printf("+0.0000j  ");

        else

            printf("%.2fj  ", x[i].img);

    }

    printf("\n");

}

 

/*void save()           //保存x傅里叶变换结果

{

    int i;

    ofstream outfile("D:\\result1.txt", ios::out);

    if (!outfile)

    {

        cerr << "open result1.txt erro!" << endl;

        exit(1);

    }

    outfile << "x傅里叶变换结果:" << endl;

    for (i = 0; i<N; i++)

    {

        outfile << x[i].real;

        if (x[i].img >= 0.0001)

            outfile << "+" << x[i].img << "j" << " ";

        else   if (fabs(x[i].img)<0.0001)

            outfile << "+" << "0.00" << "j" << " ";

        else

            outfile << x[i].img << "j" << " ";

    }

    printf("\n");

    outfile.close();

}*/

 

intmain()

{

    clock_tstart = clock();

    doubleduration;

    /*对x进行傅里叶变换*/

    inti, j = 0, t = 0;

    doubledata[N * 2] = { 0 };

    doubleresult[N * 2] = { 0 };

    floattx = 0;

    //ofstream outfile1("D:\\result.txt", ios::out);

    for(t = 0; t < N; t++)

    {

        data[t] = 5 + 7 * cos(30 * PI / 128 * t - 30 * PI / 180) + 3 * cos(80 * PI / 128 * t - 90 * PI / 180);

    }

    for(i = 0; i<N; i++)            //求出x的256个采样点的值 下一步傅里叶变化

    {

        x[i].real = data[i];

        x[i].img = 0;

        //printf("%.4f ", x[i].real);

        //printf("%.4f ", x[i].img);

    }

    initW(N);

    fftx();

    //output();

    cout << "输出信号的模";

    cout << endl;

    for(i = 0; i < N; i++)

    {

        result[i] = sqrt(x[i].real*x[i].real + x[i].img*x[i].img);

        if(i % 4 == 0)

            cout << endl;

        cout << setprecision(2) << result[i]/N*2 << " ";

        //outfile1 << result[i] / N * 2 << endl;

}

    //save();

    clock_tend = clock();

    cout << "所用的时间： ";

    duration = (double)(end - start) / CLOCKS_PER_SEC;

    cout << duration << "ms";

    cout << endl;

    return0;

}