求基2、基4、基8FFT（快速傅里叶变换）的c语言程序，要能运行得出来的 求个快速傅里叶变换的C语言程序
\u6c42\u57fa4fft\u7684C\u8bed\u8a00\u7a0b\u5e8f\u55ef\uff1f\u662fmatlab\u8bed\u8a00\u5427
void fft(){ int nn,n1,n2,i,j,k,l,m,s,l1; float ar[1024],ai[1024]; // \u5b9e\u90e8 \u865a\u90e8 float a[2050]; float t1,t2,x,y; float w1,w2,u1,u2,z; float fsin[10]={0.000000,1.000000,0.707107,0.3826834,0.1950903,0.09801713,0.04906767,0.02454123,0.01227154,0.00613588,};// \u4f18\u5316 float fcos[10]={-1.000000,0.000000,0.7071068,0.9238796,0.9807853,0.99518472,0.99879545,0.9996988,0.9999247,0.9999812,}; nn=1024; s=10; n1=nn/2; n2=nn-1; j=1; for(i=1;i>1; w1=fcos[i-1]; w2=-fsin[i-1]; for(j=1;j<=k;j++) { for(l=j;l<nn;l=l+m) { l1=l+k; t1=a[2*l1]*u1-a[2*l1+1]*u2; t2=a[2*l1]*u2+a[2*l1+1]*u1; a[2*l1]=a[2*l]-t1; a[2*l1+1]=a[2*l+1]-t2; a[2*l]=a[2*l]+t1; a[2*l+1]=a[2*l+1]+t2; } z=u1*w1-u2*w2; u2=u1*w2+u2*w1; u1=z; } } for(i=1;i<=nn/2;i++) { ar[i]=a[2*i+2]/nn; ai[i]=-a[2*i+3]/nn; a[i]=4*sqrt(ar[i]*ar[i]+ai[i]*ai[i]); // \u5e45\u503c }}
1.FFT：
// data为输入和输出的数据，N为长度
bool CFFT::Forward(complex *const Data, const unsigned int N)
{
if (!Data || N < 1 || N & (N - 1))
return false;
// 排序
Rearrange(Data, N);
// FFT计算：const bool Inverse = false
Perform(Data, N);
return true;
}
2.IFFT：
// Scale 为是否缩放
bool CFFT::Inverse(complex *const Data, const unsigned int N,
const bool Scale /* = true */)
{
if (!Data || N < 1 || N & (N - 1))
return false;
// 排序
Rearrange(Data, N);
// FFT计算，ture表示是逆运算
Perform(Data, N, true);
// 对结果进行缩放
if (Scale)
CFFT::Scale(Data, N);
return true;
}
3.排序：
void CFFT::Rearrange(complex *const Data, const unsigned int N)
{
// Swap position
unsigned int Target = 0;
// Process all positions of input signal
for (unsigned int Position = 0; Position < N; ++Position)
{
// Only for not yet swapped entries
if (Target > Position)
{
// Swap entries
const complex Temp(Data[Target]);
Data[Target] = Data[Position];
Data[Position] = Temp;
}
// Bit mask
unsigned int Mask = N;
// While bit is set
while (Target & (Mask >>= 1))
// Drop bit
Target &= ~Mask;
// The current bit is 0 - set it
Target |= Mask;
}
}
4.FFT计算：
void CFFT::Perform(complex *const Data, const unsigned int N,
const bool Inverse /* = false */)
{
const double pi = Inverse ? 3.14159265358979323846 : -3.14159265358979323846;
// Iteration through dyads, quadruples, octads and so on...
for (unsigned int Step = 1; Step < N; Step <<= 1)
{
// Jump to the next entry of the same transform factor
const unsigned int Jump = Step << 1;
// Angle increment
const double delta = pi / double(Step);
// Auxiliary sin(delta / 2)
const double Sine = sin(delta * .5);
// Multiplier for trigonometric recurrence
const complex Multiplier(-2. * Sine * Sine, sin(delta));
// Start value for transform factor, fi = 0
complex Factor(1.);
// Iteration through groups of different transform factor
for (unsigned int Group = 0; Group < Step; ++Group)
{
// Iteration within group
for (unsigned int Pair = Group; Pair < N; Pair += Jump)
{
// Match position
const unsigned int Match = Pair + Step;
// Second term of two-point transform
const complex Product(Factor * Data[Match]);
// Transform for fi + pi
Data[Match] = Data[Pair] - Product;
// Transform for fi
Data[Pair] += Product;
}
// Successive transform factor via trigonometric recurrence
Factor = Multiplier * Factor + Factor;
}
}
}
5.缩放：
void CFFT::Scale(complex *const Data, const unsigned int N)
{
const double Factor = 1. / double(N);
// Scale all data entries
for (unsigned int Position = 0; Position < N; ++Position)
Data[Position] *= Factor;
}
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
typedef struct{
double r;
double i;
}my_complex
;
//检查a是否为2的整数次方数
#define NOT2POW(a) (((a)-1)&(a)||(a)<=0)
//pi
#define MYPI 3.14159265358979323846
my_complex* fft(const my_complex* x, unsigned int len){
unsigned int ex=0,t=len;
unsigned int i,j,k;
my_complex *y;
double tr,ti,rr,ri,yr,yi;
if(NOT2POW(len)) return NULL; //如果失败，返回空指针
for(;!(t&1);t>>=1) ex++; //len应该等于2的ex次方
y=(my_complex*)malloc(len*sizeof(my_complex));
if(!y) return NULL;
//变址计算，库里-图基算法
for(i=0;i<len;i++){
k=i;
j=0;
t=ex;
while((t--)>0){
j<<=1;
j|=k&1;
k>>=1;
}
if(j>=i){
y[i]=x[j];
y[j]=x[i];
}
}
//用变址后的y向量进行计算
for(i=0;i<ex;i++){
t=1<<i;
for(j=0;j<len;j+=t<<1){
for(k=0;k<t;k++){
ti=-MYPI*k/t;
rr=cos(ti);
ri=sin(ti);
tr=y[j+k+t].r;
ti=y[j+k+t].i;
yr=rr*tr-ri*ti;
yi=rr*ti+ri*tr;
tr=y[j+k].r;
ti=y[j+k].i;
y[j+k].r=tr+yr;
y[j+k].i=ti+yi;
y[j+k+t].r=tr-yr;
y[j+k+t].i=ti-yi;
}
}
}
return y;
}
//以下为测试
int main()
{
int i,DATA_LEN;
my_complex *x,*y;
printf("基二FFT测试\n输入生成序列长度:");
scanf("%d",&DATA_LEN);
x=(my_complex*)malloc(DATA_LEN*sizeof(my_complex));
for(i=0;i<DATA_LEN;i++){
x[i].r=i;
x[i].i=i-1;
}
printf("处理前...\n实部\t\t虚部\n");
for(i=0;i<DATA_LEN;i++)
printf("%lf\t%lf\n",x[i].r,x[i].i);
y=fft(x,DATA_LEN);
if(!y){
printf("序列长度不为2的整数次方!\n");
return 0;
}
printf("处理后...\n实部\t\t虚部\n");
for(i=0;i<DATA_LEN;i++)
printf("%lf\t%lf\n",y[i].r,y[i].i);
free(y);
free(x);
return 0;
}
绛旓細1.FFT锛// data涓鸿緭鍏ュ拰杈撳嚭鐨勬暟鎹紝N涓洪暱搴ool CFFT::Forward(complex *const Data, const unsigned int N){ if (!Data || N < 1 || N & (N - 1)) return false; // 鎺掑簭 Rearrange(Data, N); // FFT璁＄畻锛歝onst bool Inverse = false Perform(Data, ...
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