此FFT 是用VC6.0编写，由FFT.CPP；STDAFX.H和STDAFX.CPP三个文件组成，编译成功。程序可以用文件输入和输出为文件。文件格式为TXT文件。测试结果如下：悄晌模
输入文件：8.TXT 或手动输入
8 //N
1
2
3
4
5
6
7
8
输出结果谨戚为：或保存为TXT文件。（8OUT.TXT）
8
(36,0)
(-4,9.65685)
(-4,4)
(-4,1.65685)
(-4,0)
(-4,-1.65685)
(-4,-4)
(-4,-9.65685)
下面为FFT.CPP文件：
/启缓/ FFT.cpp : 定义控制台应用程序的入口点。
#include "stdafx.h"
#include <iostream>
#include <complex>
#include <bitset>
#include <vector>
#include <conio.h>
#include <string>
#include <fstream>
using namespace std
bool inputData(unsigned long &, vector<complex<double>>&) //手工输入数据
void FFT(unsigned long &, vector<complex<double>>&) //FFT变换
void display(unsigned long &, vector<complex<double>>&) //显示结果
bool readDataFromFile(unsigned long &, vector<complex<double>>&) //从文件中读取数据
bool saveResultToFile(unsigned long &, vector<complex<double>>&) //保存结果至文件中
const double PI = 3.1415926
int _tmain(int argc, _TCHAR* argv[])
{
vector<complex<double>>vecList //有限长序列
unsigned long ulN = 0 //N
char chChoose = ' ' //功能选择
//功能循环
while(chChoose != 'Q' &&chChoose != 'q')
{
//显示选择项
cout <<"\nPlease chose a function" <<endl
cout <<"\t1.Input data manually, press 'M':" <<endl
cout <<"\t2.Read data from file, press 'F':" <<endl
cout <<"\t3.Quit, press 'Q'" <<endl
cout <<"Please chose:"
//输入选择
chChoose = getch()
//判断
switch(chChoose)
{
case 'm': //手工输入数据
case 'M':
if(inputData(ulN, vecList))
{
FFT(ulN, vecList)
display(ulN, vecList)
saveResultToFile(ulN, vecList)
}
break
case 'f'://从文档读取数据
case 'F':
if(readDataFromFile(ulN, vecList))
{
FFT(ulN, vecList)
display(ulN, vecList)
saveResultToFile(ulN, vecList)
}
break
}
}
return 0
}
bool Is2Power(unsigned long ul) //判断是否是2的整数次幂
{
if(ul <2)
return false
while( ul >1 )
{
if( ul % 2 )
return false
ul /= 2
}
return true
}
bool inputData(unsigned long &ulN, vector<complex<double>>&vecList)
{
//题目
cout<<"\n\n\n==============================Input Data===============================" <<endl
//输入N
cout<<"\nInput N:"
cin>>ulN
if(!Is2Power(ulN)) //验证N的有效性
{
cout<<"N is invalid (N must like 2, 4, 8, .....), please retry." <<endl
return false
}
//输入各元素
vecList.clear() //清空原有序列
complex<double>c
for(unsigned long i = 0i <ulNi++)
{
cout <<"Input x(" <<i <<"):"
cin >> c
vecList.push_back(c)
}
return true
}
bool readDataFromFile(unsigned long &ulN, vector<complex<double>>&vecList) //从文件中读取数据
{
//题目
cout<<"\n\n\n===============Read Data From File==============" <<endl
//输入文件名
string strfilename
cout <<"Input filename:"
cin >>strfilename
//打开文件
cout <<"open file " <<strfilename <<"......." <<endl
ifstream loadfile
loadfile.open(strfilename.c_str())
if(!loadfile)
{
cout <<"\tfailed" <<endl
return false
}
else
{
cout <<"\tsucceed" <<endl
}
vecList.clear()
//读取N
loadfile >>ulN
if(!loadfile)
{
cout <<"can't get N" <<endl
return false
}
else
{
cout <<"N = " <<ulN <<endl
}
//读取元素
complex<double>c
for(unsigned long i = 0i <ulNi++)
{
loadfile >>c
if(!loadfile)
{
cout <<"can't get enough infomation" <<endl
return false
}
else
cout <<"x(" <<i <<") = " <<c <<endl
vecList.push_back(c)
}
//关闭文件
loadfile.close()
return true
}
bool saveResultToFile(unsigned long &ulN, vector<complex<double>>&vecList) //保存结果至文件中
{
//询问是否需要将结果保存至文件
char chChoose = ' '
cout <<"Do you want to save the result to file? (y/n):"
chChoose = _getch()
if(chChoose != 'y' &&chChoose != 'Y')
{
return true
}
//输入文件名
string strfilename
cout <<"\nInput file name:"
cin >>strfilename
cout <<"Save result to file " <<strfilename <<"......" <<endl
//打开文件
ofstream savefile(strfilename.c_str())
if(!savefile)
{
cout <<"can't open file" <<endl
return false
}
//写入N
savefile <<ulN <<endl
//写入元素
for(vector<complex<double>>::iterator i = vecList.begin()i <vecList.end()i++)
{
savefile <<*i <<endl
}
//写入完毕
cout <<"save succeed." <<endl
//关闭文件
savefile.close()
return true
}
void FFT(unsigned long &ulN, vector<complex<double>>&vecList)
{
//得到幂数
unsigned long ulPower = 0 //幂数
unsigned long ulN1 = ulN - 1
while(ulN1 >0)
{
ulPower++
ulN1 /= 2
}
//反序
bitset<sizeof(unsigned long) * 8>bsIndex //二进制容器
unsigned long ulIndex//反转后的序号
unsigned long ulK
for(unsigned long p = 0p <ulNp++)
{
ulIndex = 0
ulK = 1
bsIndex = bitset<sizeof(unsigned long) * 8>(p)
for(unsigned long j = 0j <ulPowerj++)
{
ulIndex += bsIndex.test(ulPower - j - 1) ? ulK : 0
ulK *= 2
}
if(ulIndex >p)
{
complex<double>c = vecList[p]
vecList[p] = vecList[ulIndex]
vecList[ulIndex] = c
}
}
//计算旋转因子
vector<complex<double>>vecW
for(unsigned long i = 0i <ulN / 2i++)
{
vecW.push_back(complex<double>(cos(2 * i * PI / ulN) , -1 * sin(2 * i * PI / ulN)))
}
for(unsigned long m = 0m <ulN / 2m++)
{
cout<<"\nvW[" <<m <<"]=" <<vecW[m]
}
//计算FFT
unsigned long ulGroupLength = 1 //段的长度
unsigned long ulHalfLength = 0 //段长度的一半
unsigned long ulGroupCount = 0//段的数量
complex<double>cw //WH(x)
complex<double>c1 //G(x) + WH(x)
complex<double>c2 //G(x) - WH(x)
for(unsigned long b = 0b <ulPowerb++)
{
ulHalfLength = ulGroupLength
ulGroupLength *= 2
for(unsigned long j = 0j <ulNj += ulGroupLength)
{
for(unsigned long k = 0k <ulHalfLengthk++)
{
cw = vecW[k * ulN / ulGroupLength] * vecList[j + k + ulHalfLength]
c1 = vecList[j + k] + cw
c2 = vecList[j + k] - cw
vecList[j + k] = c1
vecList[j + k + ulHalfLength] = c2
}
}
}
}
void display(unsigned long &ulN, vector<complex<double>>&vecList)
{
cout <<"\n\n===========================Display The Result=========================" <<endl
for(unsigned long d = 0d <ulNd++)
{
cout <<"X(" <<d <<")\t\t\t = " <<vecList[d] <<endl
}
}
下面为STDAFX.H文件：
// stdafx.h : 标准系统包含文件的包含文件，
// 或是常用但不常更改的项目特定的包含文件
#pragma once
#include <iostream>
#include <tchar.h>
// TODO: 在此处引用程序要求的附加头文件
下面为STDAFX.CPP文件：
// stdafx.cpp : 只包括标准包含文件的源文件
// FFT.pch 将成为预编译头
// stdafx.obj 将包含预编译类型信息
#include "stdafx.h"
// TODO: 在 STDAFX.H 中
//引用任何所需的附加头文件，而不是在此文件中引用
C语言程序代码如下：
#include <stdio.h>
main()
{
long int f1,f2
int i
f1=1
f2=1
for (i=1i<=9i++)
{
printf("%ld %ld ",f1,f2)
if (i%3==0) printf("\n")
f1=f1+f2
f2=f2+f1
}
return 0
}
if语句是使输出6个数后换行。因为i是循环变量，当i为偶数时换行，因此斗早i每姿岩隔空册雀2换一次行相当于每输出6个数后换行。
输出结果如下
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