用c++绘制频谱图

Question

请看下面这个问题的答案的编辑。

我已经写了一个脚本，用c++绘制正弦信号的频谱。以下是步骤

1. 应用汉宁窗
2. 利用fftw3库实现快速傅立叶变换

我有三个图:信号，信号乘以汉宁函数，以及频谱。频谱看起来不对。它应该在50赫兹处有一个峰值。如有任何建议，将不胜感激。以下是代码：

#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <fftw3.h>
#include <iostream>
#include <cmath>
#include <fstream>
using namespace std;

int main()
{
int i;
double y;
int N=50;
double Fs=1000;//sampling frequency
double  T=1/Fs;//sample time 
double f=50;//frequency
double *in;
fftw_complex *out;
double t[N];//time vector 
double ff[N];
fftw_plan plan_forward;

in = (double*) fftw_malloc(sizeof(double) * N);
out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);

 for (int i=0; i< N;i++)
 {
    t[i]=i*T;
    ff[i]=1/t[i];
    in[i] =0.7 *sin(2*M_PI*f*t[i]);// generate sine waveform
    double multiplier = 0.5 * (1 - cos(2*M_PI*i/(N-1)));//Hanning Window
    in[i] = multiplier * in[i];
  }

  plan_forward = fftw_plan_dft_r2c_1d ( N, in, out, FFTW_ESTIMATE );

  fftw_execute ( plan_forward );

  double v[N];

  for (int i = 0; i < N; i++)
    {

    v[i]=20*log(sqrt(out[i][0]*out[i][0]+ out[i][1]*out[i][1])/N/2);//Here I have calculated the y axis of the spectrum in dB

    }

   fstream myfile;

   myfile.open("example2.txt",fstream::out);

   myfile << "plot '-' using 1:2" << std::endl;

   for(i = 0; i < N; ++i)

    { 

      myfile << ff[i]<< " " << v[i]<< std::endl;

    }

 myfile.close();

 fftw_destroy_plan ( plan_forward );
 fftw_free ( in );
 fftw_free ( out );
 return 0;
  }

我必须补充的是，在将结果插入example2.txt之后，我已经使用gnu图绘制了这些图表。所以ffi vs vi应该给我频谱。

以下是情节：

频谱和正弦时间窗分别：

​

Answer 1

​

我的频率间隔完全错了。根据http://www.ni.com/white-paper/3995/en/#toc1；x轴上的频率范围和分辨率取决于采样率和N。频率轴上的最后一点应该是Fs/2-Fs/N，分辨率dF= Fs/N，所以我已经将脚本更改为：(由于频率分辨率是Fs/N，因此增加smaples (或减少采样频率Fs)的次数，可以获得较小的频率分辨率和更好的结果。)

#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <fftw3.h>
#include <iostream>
#include <cmath>
#include <fstream>
using namespace std;

int main()
{
int i;
double y;
int N=550;//Number of points acquired inside the window
double Fs=200;//sampling frequency
double dF=Fs/N;
double  T=1/Fs;//sample time 
double f=50;//frequency
double *in;
fftw_complex *out;
double t[N];//time vector 
double ff[N];
fftw_plan plan_forward;

in = (double*) fftw_malloc(sizeof(double) * N);
out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);

 for (int i=0; i<= N;i++)
 {
 t[i]=i*T;

in[i] =0.7 *sin(2*M_PI*f*t[i]);// generate sine waveform
double multiplier = 0.5 * (1 - cos(2*M_PI*i/(N-1)));//Hanning Window
in[i] = multiplier * in[i];
 }

 for (int i=0; i<= ((N/2)-1);i++)
{ff[i]=Fs*i/N;
}
plan_forward = fftw_plan_dft_r2c_1d ( N, in, out, FFTW_ESTIMATE );

fftw_execute ( plan_forward );

double v[N];

for (int i = 0; i<= ((N/2)-1); i++)
{

v[i]=(20*log(sqrt(out[i][0]*out[i][0]+ out[i][1]*out[i][1])))/N;  //Here   I  have calculated the y axis of the spectrum in dB

   }

fstream myfile;

myfile.open("example2.txt",fstream::out);

myfile << "plot '-' using 1:2" << std::endl;

for(i = 0;i< ((N/2)-1); i++)

{ 

myfile << ff[i]<< " " << v[i]<< std::endl;

}

 myfile.close();

 fftw_destroy_plan ( plan_forward );
 fftw_free ( in );
 fftw_free ( out );
 return 0;
}

Answer 2

我认为您可能没有足够的示例，特别是参考以下Electronics.StackExhcange文章：https://electronics.stackexchange.com/q/12407/84272。

你在取样50个样本，所以25个FFT垃圾箱。你是在1000赫兹采样，所以1000 /2/ 25 == 250赫兹每个快速傅立叶变换桶。你的垃圾桶分辨率太低了。

我认为你需要降低采样频率或增加样本数量。

Answer 3

由于您的问题是这样，您的代码可以使用一些缩进和风格改进，以使它更容易阅读。

#include <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <fftw3.h>
#include <iostream>
#include <cmath>
#include <fstream>
using namespace std;

int main(){
    // use meaningful names for all the variables
    int i;  
    double y;
    int N = 550; // number of points acquired inside the window
    double Fs = 200; // sampling frequency
    double dF = Fs / N;
    double  T = 1 / Fs; // sample time 
    double f = 50; // frequency
    double *in;
    fftw_complex *out;
    double t[N]; // time vector 
    double ff[N];
    fftw_plan plan_forward;

    in = (double*) fftw_malloc(sizeof(double) * N);
    out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);

    for (int i = 0; i <= N; i++){
        t[i]=i*T;
        in[i] = 0.7 * sin(2 * M_PI * f * t[i]); // generate sine waveform
        double multiplier = 0.5 * (1 - cos(2 * M_PI * i / (N-1))); // Hanning Window
        in[i] = multiplier * in[i];
    }

    for(int i = 0; i <= ((N/2)-1); i++){
        ff[i] = (Fs * i) / N;
    }

    plan_forward = fftw_plan_dft_r2c_1d(N, in, out, FFTW_ESTIMATE);

    fftw_execute(plan_forward);

    double v[N];
    // Here I have calculated the y axis of the spectrum in dB
    for(int i = 0; i <= ((N/2)-1); i++){
        v[i] = (20 * log(sqrt(out[i][0] * out[i][0] + out[i][1] * out[i][1]))) / N;  
    }

    fstream myfile;
    myfile.open("example2.txt", fstream::out);
    myfile << "plot '-' using 1:2" << std::endl;

    for(i = 0; i < ((N/2)-1); i++){ 
        myfile << ff[i] << " " << v[i] << std::endl;
    }
    myfile.close();

    fftw_destroy_plan(plan_forward);
    fftw_free(in);
    fftw_free(out);

    return 0;
    }

您的代码可以使用更多的注释，特别是在循环或函数调用之前指定它们的输入值(目的)和/或返回值(结果)。