Plotting frequency spectrum with c++

Question

Please see the Edits in the answer below this question.

I have written a script to plot the frequency spectrum of a sinusoidal signal with c++. Here are the steps

1. Applying Hanning window
2. Apply FFT using fftw3 library

I have three graphs: Signal, Signal when is multiplied to Hanning function, and the frequency spectrum. The frequency spectrum looks wrong. It should have a peak at 50 Hz. Any suggestion would be appreciated. Here is the code:

#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;
  }

I have to add that I have plotted the graphs using gnuplot after inserting the results into example2.txt. So ff[i] vs v[i] should give me the frequency spectrum.

Here are the plots: Frequency Spectrum and Sinusoidal time Window respectively:

Answer 1

My Frequency intervals were completely wrong. According to http://www.ni.com/white-paper/3995/en/#toc1; the frequency range and resolution on the x-axis depend on sampling rate and N. The last point on the frequency axis should be Fs/2-Fs/N and the resolution dF=FS/N.So I have changed my script to: (since frequency resolution is Fs/N as you increase the number of smaples N (or decrease sampling frequency Fs) you get smaller frequency resolution and better results.)

#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

I think you may not have enough samples, particularly, reference this Electronics.StackExhcange post: https://electronics.stackexchange.com/q/12407/84272.

You're sampling for 50 samples, so 25 FFT bins. You're sampling at 1000 Hz, so 1000 / 2 / 25 == 250 Hz per FFT bins. Your bin resolution is too low.

I think you need to lower the sampling frequency or increase the number of samples.

Answer 3

Since your question in on SO, your code could use some indentation and style improvement to make it easier to read.

#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;
    }

Your code can use more comments, especially before loops or function calls to specify their input value (purpose) and/or returning value (result).