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Multi-Dimensional Forward Transform of Real Data

This code illustrates how to find the different momentum components in the output of fftrn. The initial array of size ($N1$,$N2$) is generated with only two sinusoidal modes excited, the real part of $\vec{k}=(3,1)$ and the imaginary part of $\vec{k}=(2,0)$. The loop at the end shows how to find the different momenta. The excitation $(3,1)$ only shows up once but the mode $(2,0)$ and its complex conjugate $(-2,0)$ are redundantly included in the output. Note that no matter what you put in as input the output components $F_{0,0}$, $F_{0,N2/2}$, $F_{N1/2,0}$ and $F_{N1/2,N2/2}$ will be real.

#define N1 8 // Number of real points in the data - first dimension
#define N2 4 // Second dimension
void main()
  int a,b,ka,kb;
  float f[N1][N2]; // An array of real numbers
  float fnyquist[2*N1]; // For storing k_2 = N2/2 frequencies
  int size[2]={N1,N2}; // Size of data in all dimensions
  float pi=2.*asin(1.),x1=2.*pi/(float)N1,x2=2.*pi/(float)N2;

      f[a][b]=5.*cos(3.*x1*(float)a + x2*(float)b)+sin(2.*x1*(float)a);

  fftrn((float *)f,(float *)fnyquist,2,size,1);

    ka = (a<=N1/2 ? a : a-N1); // ka is the frequency stored at position a
      kb = b; // kb is the frequency stored at position b
      printf("Frequency={%d,%d}, Transform value={%f + i %f}\n",ka,kb,f[a][2*b],f[a][2*b+1]);
    printf("Frequency={%d,%d}, Transform value={%f + i %f}\n",ka,N2/2,fnyquist[2*a],fnyquist[2*a+1]);


Frequency={0,0}, Transform value={-0.000002 + i 0.000000}
Frequency={0,1}, Transform value={0.000000 + i 0.000003}
Frequency={2,0}, Transform value={0.000002 + i 15.999999}
Frequency={3,1}, Transform value={79.999992 + i -0.000023}
Frequency={-2,0}, Transform value={0.000002 + i -15.999999}
Frequency={-1,1}, Transform value={0.000004 + i 0.000004}
Frequency={-1,2}, Transform value={-0.000000 + i 0.000001}

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This documentation was generated on 2003-09-30