FFT c代碼的收集

收集的一些FFT 的c實現代碼，進過整理改動能夠跑通，從測試的波函數採樣（採樣點的幅值）經過FFT計算得出頻率分佈結果（該採樣段的頻率成分（單頻波成分）以及對應頻率的幅值）。下一步工作（未開始）是大量的準確度測試，效率測試和優化。

1

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#include<unistd.h>
#include<string.h>

#define PI 3.1415926

double x1[100000],x2[100000],w1[100000],w2[100000];//角標1代表實數部分,2虛數部分
int visited[100000];
int s[1000];
void wnp(int M,int L,int N) //求(WN)^p
{
    int i,k;
    int t1=(int)(pow(2.0,M-L))-1;
    double t2=-2*PI/N;
    double a,b;
    memset(w1,0,sizeof(w1));
    memset(w2,0,sizeof(w2));
    k=(int)(pow(2.0,L-1));
    a=cos(t2*k);
    b=sin(t2*k);
    w1[0]=1; //當0的情況
    w2[0]=0;
    for(i=1;i<=t1;i++)
    {
        w1[i]=a*w1[i-1]-b*w2[i-1];
        w2[i]=a*w2[i-1]+b*w1[i-1];
    }
}
void FFT(int N,int M)
{
    int i,j,n=N;
    double a,b;
    for(i=1;i<=M;i++)  //從第1級到M級
    {
        n/=2;
        memset(visited,0,sizeof(visited));//標記數組清零
        wnp(M,i,N);  //調用wnp函數
        for(j=0;j<N;j++)   //分別求每一級的當前實數部分和虛數部分
        {
            if(!visited[j])
            {
                visited[j]=1;
                visited[j+n]=1;
                a=x1[j]-x1[j+n]; //此處曾出錯 應先計算出其值 因爲後面 x1[j]和x2[j]的值會改變
                b=x2[j]-x2[j+n];
                x1[j]=x1[j]+x1[j+n];
                x2[j]=x2[j]+x2[j+n];

                int t=j%(N/(int)(pow(2.0,i*1.0)));
                x1[j+n]=a*w1[t]-b*w2[t];
                x2[j+n]=a*w2[t]+b*w1[t];
            }
        }
    }
}
void solve(double *x,int N,int M) //數位倒讀
{
    int a,i,j,k;
    double t;
    for(k=0;k<N;k++)
    {
        i=k;
        a=0;
        memset(s,0,sizeof(s));
        for(j=0;j<M;j++)
        {
            s[j]=i%2;
            i/=2;
        }
        for(j=0;j<M;j++)
        {
            a=a+s[j]*(int)(pow(2.0,M-1-j));
        }
        if(a<k)
        {
            t=x[a];
            x[a]=x[k];
            x[k]=t;
        }
    }
}



int main()
{
    int N,i,M;
    printf("input N(N): ");
    scanf("%d",&N);
    if(N < 2)
    {
        printf("too small\n");
    }
    unsigned short amp[N];
    int fs = 44100;
    M=floor(log10(N*1.0)/log10(2.0)+0.5);
    for(i=0;i<N;i++)
    {
        x1[i] = 7000*cos(1000*2*(double)PI*((double)i/44100) + (double)3/5*PI)
                + 200*cos(600*2*(double)PI*((double)i/44100) + (double)1/2*PI);
        x2[i] = 0;
    }
    FFT(N,M);
    solve(x1,N,M);
    solve(x2,N,M);
    printf("得到的頻譜值爲:\n");
    for(i=0;i<N/2;i++)
    {
        double originamp = sqrt(x1[i]*x1[i] + x2[i]*x2[i]);
        if(i == 0)
        {
            amp[i] = originamp/N;
        }
        else
        {
            amp[i] = originamp/N*2;
        }
        if(amp[i] > 20)
        {
            printf("f:%.2lf amp:%d\n",(double)i*fs/N,amp[i]);
        }
    }
    return 0;
}

2

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
//精度0.0001弧度

typedef struct//複數類型
{
    float real;       //實部
    float imag;       //虛部
}complex;

#define PI 3.1415926


///////////////////////////////////////////
void conjugate_complex(int n,complex in[],complex out[]);
void c_plus(complex a,complex b,complex *c);//複數加
void c_mul(complex a,complex b,complex *c) ;//複數乘
void c_sub(complex a,complex b,complex *c); //複數減法
void c_div(complex a,complex b,complex *c); //複數除法
void fft(int N,complex f[]);//傅立葉變換 輸出也存在數組f中
void c_abs(complex f[],float out[],int n);//複數數組取模

void conjugate_complex(int n,complex in[],complex out[])
{
    int i = 0;
    for(i=0;i<n;i++)
    {
        out[i].imag = -in[i].imag;
        out[i].real = in[i].real;
    }
}

void c_abs(complex f[],float out[],int n)
{
    int i = 0;
    float t;
    for(i=0;i<n;i++)
    {
        t = f[i].real * f[i].real + f[i].imag * f[i].imag;
        out[i] = sqrt(t);
    }
}


void c_plus(complex a,complex b,complex *c)
{
    c->real = a.real + b.real;
    c->imag = a.imag + b.imag;
}

void c_sub(complex a,complex b,complex *c)
{
    c->real = a.real - b.real;
    c->imag = a.imag - b.imag;
}

void c_mul(complex a,complex b,complex *c)
{
    c->real = a.real * b.real - a.imag * b.imag;
    c->imag = a.real * b.imag + a.imag * b.real;
}

void c_div(complex a,complex b,complex *c)
{
    c->real = (a.real * b.real + a.imag * b.imag)/(b.real * b.real +b.imag * b.imag);
    c->imag = (a.imag * b.real - a.real * b.imag)/(b.real * b.real +b.imag * b.imag);
}

#define SWAP(a,b)  tempr=(a);(a)=(b);(b)=tempr

void Wn_i(int n,int i,complex *Wn,char flag)
{
    Wn->real = cos(2*PI*i/n);
    if(flag == 1)
        Wn->imag = -sin(2*PI*i/n);
    else if(flag == 0)
        Wn->imag = -sin(2*PI*i/n);
}

//傅里葉變化
void fft(int N,complex f[])
{
    complex t,wn;//中間變量
    int i,j,k,m,n,l,r,M;
    int la,lb,lc;
    /*----計算分解的級數M=log2(N)----*/
    for(i=N,M=1;(i=i/2)!=1;M++);
    /*----按照倒位序重新排列原信號----*/
    for(i=1,j=N/2;i<=N-2;i++)
    {
        if(i<j)
        {
            t=f[j];
            f[j]=f[i];
            f[i]=t;
        }
        k=N/2;
        while(k<=j)
        {
            j=j-k;
            k=k/2;
        }
        j=j+k;
    }

    /*----FFT算法----*/
    for(m=1;m<=M;m++)
    {
        la=pow(2,m); //la=2^m代表第m級每個分組所含節點數
        lb=la/2;    //lb代表第m級每個分組所含碟形單元數
        //同時它也表示每個碟形單元上下節點之間的距離
        /*----碟形運算----*/
        for(l=1;l<=lb;l++)
        {
            r=(l-1)*pow(2,M-m);
            for(n=l-1;n<N-1;n=n+la) //遍歷每個分組，分組總數爲N/la
            {
                lc=n+lb;  //n,lc分別代表一個碟形單元的上、下節點編號
                Wn_i(N,r,&wn,1);//wn=Wnr
                c_mul(f[lc],wn,&t);//t = f[lc] * wn複數運算
                c_sub(f[n],t,&(f[lc]));//f[lc] = f[n] - f[lc] * Wnr
                c_plus(f[n],t,&(f[n]));//f[n] = f[n] + f[lc] * Wnr
            }
        }
    }
}


int main()
{
    int N,i,M;
    printf("input N(N): ");
    scanf("%d",&N);
    if(N < 2)
    {
        printf("too small\n");
        return 0;
    }
    unsigned short amp[N];
    int fs = 44100;

    complex input[N];
    for(i=0;i<N;i++)
    {
        input[i].real = 7000*cos(1000*2*(double)PI*((double)i/44100) + (double)3/5*PI)
                + 200*cos(600*2*(double)PI*((double)i/44100) + (double)1/2*PI);
        input[i].imag = 0;
    }

    fft(N,input);

    printf("得到的頻譜值爲:\n");
    for(i=0;i<N/2;i++)
    {
        double originamp = sqrt(input[i].real*input[i].real + input[i].imag*input[i].imag);
        if(i == 0)
        {
            amp[i] = originamp/N;
        }
        else
        {
            amp[i] = originamp/N*2;
        }
        if(amp[i] > 20)
        {
            printf("f:%.2lf amp:%d\n",(double)i*fs/N,amp[i]);
        }
    }
    return 0;
}