File:Fafo2test1.png

Modullus of the Fourier-2 transform of the bi–dimiensional real array.

The density of rectangles represents $|A(x,y)|$ of $|B(x,y)|$ in the $x,y$ plane.

The discrete implementation of the Fourier–2 transform approximates the integral transform $B$ of the function $A$ in the following form:
 * $\displaystyle B(p,q)=\frac{1}{2\pi} \int \int \mathrm d x \mathrm d y  \exp(-ipx-iqy) A(x,y)$

The spots, that determine the structure of the "face" shown, are barely seen around the central spot; their intensity is only few percents of the intensity at the central spot.

C++ generator
// Files ado.cin and fafo.cin should be loaded in the working directory in order to compile the code below:

using namespace std;
 * 1) include
 * 2) include
 * 3) include 
 * 4) include
 * 1) define z_type complex
 * 2) define DB double
 * 3) define DO(x,y) for(x=0;x= N dx=sqrt(2.*M_PI/M); dy=sqrt(2.*M_PI/N); DO(m,M){ x=dx*(m-M/2.); DO(n,N){ y=dy*(n-N/2.); if(.3*x*x+.2*y*y >2.1) A[n*M+m]=0.; else A[n*M+m]=1.; if(fabs(x)<.8 && fabs(y+1.7)<.3 )  A[n*M+m]-=1.; if( (fabs(x-1.)<.3 || fabs(x+1.)<.3 ) && fabs(y-.8)<.2 )  A[n*M+m]-=1.; }} DO(m,M){ DO(n,N) b[n]=A[n*M+m]; fafo(b,N,1); DO(n,N) A[n*M+m]=b[n]; } DO(n,N){ DO(m,M) b[m]=A[n*M+m]; fafo(b,M,1); DO(m,M) A[n*M+m]=b[m]; } fprintf(o,"gsave\n"); fprintf(o,"%2d %2d scale\n",M,N); fprintf(o,"%2d %2d 4 [%2d 0 0 %2d 0 %2d]\n<", M,N,M,-N,N); s=0; DO(m,M) DO(n,N){ t=abs(A[n*M+m]); if(t>s) s=t; } s=15./s; for(n=N-1;n>=0;n--) { fprintf(o,"\n"); DO(m,M){ fprintf(o,"%1x",int(s*abs(A[n*M+m])+.6) ); }} fprintf(o,"\n>\n"); fprintf(o,"image\n"); free(A); fprintf(o,"grestore\n"); M(M/2.+.5,-1); L(M/2+.5,N+1); M(-1,N/2.+.5); L(M+1,N/2.+.5); fprintf(o,"1 0 0 RGB .1 W S\n"); fprintf(o,"showpage\n%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf fafo2test1.eps"); system( "convert fafo2test1.eps fafo2test1.png "); system(  "open fafo2test1.png"); } // Copyleft 2011 by Dmitrii Kouznetsov
 * 1) define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);

EPS version
%!PS-Adobe-2.0 EPSF-2.0

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Keywords
Foutier-transform, Image gsave grestore