imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user-pd
| | Importing file |
| |description = Application of the [[Discrete Fourier operator]] at the sample of 4 nodes.
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2011
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| |pub-country = Japan
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| |notes = The [[Gaussian function]] <math>f(x)=\exp(−x^2/2)</math> is shown with dashed curve.
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| The discrete analogy <math>A</math> is shown with blue segmented line.
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| The [[Discrete Fourier transform]] <math>B</math> is shown with red segmented line.
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| |versions = http://tori.ils.uec.ac.jp/TORI/index.php/File:FourierExampleGauss04Ta.png
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| }}
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| == Licensing ==
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| {{CC|zero|1.0}}
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| ==[[C++]] generator of curves==
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| // FIles [[fafo.cin]] and [[ado.cin]] should be in the working directory for the compilation of the code below.
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| #include<math.h>
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| #include<stdio.h>
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| #include <stdlib.h>
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| #include <complex>
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| using namespace std;
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| #define z_type complex<double>
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| #define Re(x) x.real()
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| #define Im(x) x.imag()
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| #define RI(x) x.real(),x.imag()
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| #define DB double
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| #define DO(x,y) for(x=0;x<y;x++)
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| #include "ado.cin"
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| #include"fafo.cin"
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| // DB F(DB x){DB u=x*x; return u*(-3.+u)*exp(-x*x/2.);} //Another self-Fourier function
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| DB F(DB x){return exp(-x*x/2.);}
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| main(){ z_type * a, *b, c; int j,m,n, N=4; FILE *o;
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| double step=sqrt(2*M_PI/N),x,y,u;
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| a=(z_type *) malloc((size_t)((N+1)*sizeof(z_type)));
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| b=(z_type *) malloc((size_t)((N+1)*sizeof(z_type)));
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| for(j=0;j<N;j++) { x=step*(j-N/2); u=x*x; a[j]=b[j]=F(x); }
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| fafo(b,N,1);
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| for(j=0;j<N;j++) printf("%2d %18.15f %18.15f %18.15f %18.15f\n", j, RI(a[j]), RI(b[j]) );
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| o=fopen("FourierExampleGauss04a.eps","w"); ado(o,624,124);
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| #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
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| #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
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| fprintf(o,"322 22 translate 100 100 scale\n");
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| M(-3,0) L(3,0) M(0,0) L(0,1) fprintf(o,".01 W S\n");
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| M(-3,1) L(3,1)
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| for(m=-3;m<4;m++) {M(m,0) L(m,1)} fprintf(o,".004 W S\n");
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| DO(m,121){x=-3.+.05*m; y=F(x); if(m/2*2==m)M(x,y)else L(x,y);} fprintf(o,".008 W 0 0 0 RGB S\n");
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| DB *X; X=(DB *) malloc((size_t)((N+1)*sizeof(DB))); DO(j,N){ x=step*(j-N/2); X[j]=x; }
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| DO(j,N){x=X[j];y=Re(a[j]); if(j==0)M(x,y)else L(x,y);} fprintf(o,".01 W 0 0 1 RGB S\n");
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| DO(j,N){x=X[j];y=Re(b[j]); if(j==0)M(x,y)else L(x,y);} fprintf(o,"0.01 W 1 0 0 RGB S\n");
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| // DO(j,N){x=X[j];y=100.*(Re(b[j])-F(x)); if(j==0)M(x,y)else L(x,y);} fprintf(o,"0.007 W 0 0 .3 RGB S\n");
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| printf("X[0]=%9.5f\n",X[0]);
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| fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
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| system("epstopdf FourierExampleGauss04a.eps");
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| system( "open FourierExampleGauss04a.pdf"); //these 2 commands may be specific for macintosh
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| getchar(); system("killall Preview");// if run at another operational system, may need to modify
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| free(a);
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| free(b);
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| free(X);
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| }
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| /*Copyeft 2011 by Dmitrii Kouznetsov */
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