函数说明:更改主函数体中的N和length（=log2(N)）既可以实现任意点数(2的幂次)的FFT/ IFFT的实现，fft函数中flag标志位控制是正变换还是逆变换。

1.复数操作类

     定义复数类，重载复数四则运算符号，重载输出运算符，重载赋值运算符。

/**********预编译文件头文件complex.h********/#include"iostream"using namespace std;class complex{	double real,image;public:	complex(){real=0;image=0;}	complex(float i,float j){real=i;image=j;}	double getr(){return real;}	double geti(){return image;}	void show()	{		if(image>=0)			cout<
    
     <<"+"<
     <<"j"<<"   ";		else			cout<
     
      <
      <<"j"<<"   ";	}	void setvalue(double i=0,double j=0)	{		real=abs(i)<0.0001?0:i;		image=abs(j)<0.0001?0:j;	}	complex operator +(complex&);	complex operator-(complex&);	complex operator*(complex&);	complex operator /(int n);	void operator+=(complex&);	void operator =(complex&);	friend complex W(int m,int n, int flag);};complex complex::operator +(complex& c)	{		complex t;		t.real=real+c.real;		t.image=image+c.image;		return t;	}complex complex::operator*(complex& c)	{		complex t;		t.real=real*c.real-image*c.image ;		t.image=real*c.image+image*c.real;		return t;	}complex complex::operator/ (int n)	{		complex temp;		temp.real=real/n;		temp.image=image/n;		return temp;	 }complex complex::operator -(complex& c)	{		complex t;		t.real=real-c.real;		t.image=image-c.image;		return t;	}void complex::operator+=(complex&c)	{		real=real+c.real;		image=image+c.image;	}void complex::operator =(complex&c)	{		real=abs(c.real)<0.00001?0:(c.real);		image=abs(c.image)<0.00001?0:(c.image);	}
     
    

2.主函数

/*******************主函数体***********************/#include "stdafx.h"#include"iostream"#include"cmath"#include"complex.h"#define pi 3.141592657#define N 16//需要运算的fft的点数#define length 4//存储需要的二进制位,即length=log2(N)using namespace std;/*********************重新排列输入序列函数****************************/void bit_reversal(complex a[],int n){	int bitdesicion(unsigned);//用来重现排序原来的输入信号序列应该对应变换的信号的序号	complex temp;	int j;	for(int i=0;i
    
        void getW(complex w[],int len,int flag);//获得正变换(flag=1)或者逆变换系数(flag=0)   void fft_temporal(complex input[],int len,int flag);//基时间的fft,flag控制为正变换或者逆变换   void fft_frequency(complex input[],int len,int flag);//基频率的fft/************************************************************/   complex input[N];
    

complex output[N];   for(int i=0;i

output[j]=input[j];   fft_temporal(output,N,0);//"0"控制为逆变换   cout<<"基2时域IFFT输出信号为:"<