GSL Fast Fourier Transform - Challenging Conclusion

Question

The Gaussian Fourier Transform is Gaussian, but for some reason, the fast Fourier Transform Library from the GNL Science Library (GNU) does not give this at all. I included the code that I used to generate (try) the Fourier transform, and two corresponding graphs immediately after it. Can it help me determine what I messed up?

#include <gsl/gsl_fft_complex.h> #include <fstream> #define REAL(z,i) ((z)[2*(i)]) //complex arrays stored as #define IMAG(z,i) ((z)[2*(i)+1]) using namespace std; int main(){ double N = pow(2,9); //power of 2 for Cooley-Tukey algorithm int n = (int) N; double f[2*n]; double dx = 10./N; double x = -5.; ofstream fileo("out.txt"); for (int i=0; i<n; ++i){ //initialize gaussian REAL(f,i)=exp(-0.5*x*x); IMAG(f,i)=0.; x+=dx; } gsl_fft_complex_radix2_forward(f, 1, n); //Fourier transform for (int i=0; i<n; ++i){ fileo<<i<<" "<<REAL(f,i)<<'\n'; //plot frequency distribution } fileo.close(); } 

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EDIT: Resolved!

As @ roadrunner66 said in the answer, the width of the original Gaussian was very wide, which led to a ridiculously narrow Gaussian in Fourier space. Moreover, my plot looked funny because, as suggested in the @nm comment (now deleted), the Fourier transform returns a DFT with projections onto k-values ​​indexed as k = 0,1, ..., N / 2, -N / 2, ...- 2, -1.

Answer 1

It looks good to me. Move the output vector to N / 2 and draw the absolute value of the output, not the real part.

Also note that your Gaussian input is quite wide, which makes it very narrow. For comparison, analyze the analytical solution for this case.