File:Sinftes04t300.jpg

Explicit plot of the simplest self-SinFT function

$y=F(x)=2x \exp(-x^2/2)~$, thin smooth curve,

its discrete representation at the mesh with 4 nodes (thick colored segmented line),

and its SFT (black segmented line). Even with so view nodes, visually, the two segmented curves practically coincide; the array is reproduced with at least 3 decimal digits.

C++ generator of lines
// Files ado.cin and scft.cin should be loaded in order of compile the code below int main{ int i; double a[NP],b[NP]; double d=sqrt(M_PI/NP); double x,y; FILE *o; for(i=0;i<NP;i++){ x=i*d; a[i]=b[i]=2.*x*exp(-.5*x*x); } sinft(b-1,NP); for(i=0;i<NP;i++) { b[i]*=sqrt(2./NP); printf("%2d %19.14lf %19.14lf %19.14lf\n",i,a[i],b[i], b[i]-a[i]);} //o=fopen("34.eps","w"); ado(o,470,140); o=fopen("sinftes04.eps","w"); ado(o,570,140); fprintf(o,"10 10 translate 100 100 scale 2 setlinecap 1 setlinejoin\n"); for(i=0;i<12;i++){M(.5*i,0)L(.5*i,1)} for(i=0;i<3;i++){M(0,.5*i)L(5.5,.5*i)} fprintf(o,".007 W S\n"); M(0,0); for(i=1;i<110;i++) { x=.05*i; y=2.*x*exp(-.5*x*x); L(x,y);} fprintf(o,".009 W 0 0 0 RGB S\n"); M(0,0); for(i=1;i
 * 2) include 
 * 3) include
 * 4) include "scft.cin"
 * 5) include "ado.cin"
 * 6) define NP 4
 * 1) define M(x,y) fprintf(o,"%9.4lf %9.4lf M\n",x+0.,y+0.);
 * 2) define L(x,y) fprintf(o,"%9.4lf %9.4lf L\n",x+0.,y+0.);

fprintf(o,"showpage\n%c%cTrailer\n",'%','%'); fclose(o); system("epstopdf sinftes04.eps"); system(   "open sinftes04.pdf"); }