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/* fft1.c: fast Fourier transform base on 2 for one dimensional
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complex array, direct and inverse,
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This program is contributed by Jiang Yong, 2003. 1. */
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include "fft.h"
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static int ifirst=0, sign=-1;
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static unsigned M, jup[64], kup[64];
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static float pi, wr[N], wi[N];
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/********* initial **************/
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void initial(void)
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{
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unsigned long int i, j, ni;
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float unit, tt;
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ni = N;
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M = 0;
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while (ni > 1) { ni=ni/2; M=M+1; }
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ni = 1;
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for(j=0; j<M; j++) ni = ni * 2;
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if ((ni-N) != 0)
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{
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printf("N isn't compatible! (N => %i, ni -> %lu)\n", N, ni);
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exit(1);
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}
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kup[0] = N/2; /* kup[l] = 2 ^ (M - l - 1) */
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jup[0] =1;
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for (j=1;j<M;j++)
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{
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kup[j]=kup[j-1]/2;
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jup[j]=jup[j-1]*2;
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}
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pi=4.0*atan((float)1.0);
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unit=2.0*pi/((float)N);
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tt=0.0;
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for(i=0;i<N;i++)
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{
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wr[i] = cos(tt);
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wi[i] = sign * sin(tt);
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tt = tt + unit;
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}
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}
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/** ifft=1<-->FFT ** ifft=-1<-->IFFT **/
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void fft1(float A[2][N], int ifft)
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{
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unsigned long int l, k, i, j, jl0, jl0k, jl1k, reseq, ij;
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float wrc, wis, ar, ai, x[2][N];
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if (ifirst == 0) { initial(), ifirst=1; }
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if (ifft == -1)
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for(i=0;i<N;i++) A[1][i] = -A[1][i];
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for (l=0; l<M; l++)
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{
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for (j=0; j<jup[l]; j++)
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{
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reseq=inverseq(j, l);
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ij=kup[l]*reseq;
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jl0=2*kup[l]*j;
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wrc = wr[ij];
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wis = wi[ij];
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for (k=0; k<kup[l]; k++)
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{
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jl0k = jl0 + k;
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jl1k = jl0 + kup[l] + k;
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ar = A[0][jl1k] * wrc - A[1][jl1k] * wis;
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ai = A[0][jl1k] * wis + A[1][jl1k] * wrc;
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A[0][jl1k] = A[0][jl0k] - ar;
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A[1][jl1k] = A[1][jl0k] - ai;
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A[0][jl0k] = A[0][jl0k] + ar;
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A[1][jl0k] = A[1][jl0k] + ai;
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}
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}
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}
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for (i=0; i<N; i++)
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{
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j=inverseq(i, M);
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x[0][i] = A[0][j];
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x[1][i] = A[1][j];
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}
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for (i=0; i<N; i++)
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{
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A[0][i] = x[0][i];
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A[1][i] = x[1][i];
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}
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if (ifft == -1)
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for (i=0; i<N; i++)
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{
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A[0][i] = A[0][i]/((float)N);
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A[1][i] = -A[1][i]/((float)N);
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}
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}
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/*********************************/
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unsigned long int inverseq(unsigned long int i1,
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unsigned long int imax)
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{
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unsigned long int j, ii, i0, inv;
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i0 = i1;
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inv = 0;
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for (j=0; j < imax; j++)
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{
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ii=i0%2;
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inv=2*inv+ii;
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i0=(i0-ii)/2;
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}
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return (inv);
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}
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/* ifft=1 <--> FFT ** ifft=-1 <--> IFFT */
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void fft1r2(float A[2][N], float B[2][N], int ifft)
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{
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unsigned long int k, j;
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float norm, c[2][N];
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if (ifft != -1)
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{
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for (k=0; k<N; k++)
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{
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c[0][k]=A[0][k];
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c[1][k]=B[0][k];
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}
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fft1(c, 1);
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A[0][0] = c[0][0];
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A[1][0] = 0.0;
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B[0][0] = c[1][0];
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B[1][0] = 0.0;
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for (j=1; j<N; j++)
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{
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A[0][j] = 0.5 * (c[0][j] + c[0][N-j]);
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A[1][j] = 0.5 * (c[1][j] - c[1][N-j]);
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B[0][j] = 0.5 * (c[1][j] + c[1][N-j]);
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B[1][j] = -0.5 * (c[0][j] - c[0][N-j]);
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}
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} /* end if*/
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else
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{
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for (j=0; j<N/2; j++)
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/* check {xj}, {yj} is to real {Ak}, {Bk} */
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{
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if (j == 0) norm = 2.0 * fabs(A[1][0])
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+ 2.0 * fabs(B[1][0]);
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else norm = fabs(A[1][j]+A[1][N-j])
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+ fabs(A[0][j]-A[0][N-j])
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+ fabs(B[1][j]+B[1][N-j])
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+ fabs(B[0][j]-B[0][N-j]);
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if (norm > eps)
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{
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printf("The IDFT of the series isn't real!\n");
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exit(0);
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}
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}
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for (j=0; j<N; j++)
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{
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c[0][j]=A[0][j] -B[1][j];
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c[1][j]=A[1][j] +B[0][j];
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}
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fft1(c, -1);
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for (k=0; k<N; k++)
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{
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A[0][k] = c[0][k];
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B[0][k] = c[1][k];
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A[1][k] = 0.0;
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B[1][k] = 0.0;
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}
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} /* end else */
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}
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/* ifft = 1 <--> FFT ** ifft = -1 <--> IFFT */
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void fft1r1(float A[2][DN], int ifft)
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{
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unsigned long int j, k, dk;
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float norm, c[2][N], d[2][N], tt, hunit, cosj, sinj;
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hunit = 4.0 * atan(1.0) / (float)N;
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if ( ifft != -1)
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{
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for (k=0; k<N; k++)
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{
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dk = k + k;
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c[0][k] = A[0][dk];
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d[0][k] = A[0][dk+1];
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c[1][k] = 0.0;
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d[1][k] = 0.0;
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}
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fft1r2(c, d, 1);
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for (j = 0; j < N; j++)
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{
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tt = (float)j * hunit;
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cosj = cos(tt);
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sinj = sign * sin(tt);
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A[0][j] = c[0][j] + cosj * d[0][j] - sinj * d[1][j];
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A[1][j] = c[1][j] + cosj * d[1][j] + sinj * d[0][j];
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}
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A[0][N] = c[0][0] - d[0][0];
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A[1][N] = c[1][0] - d[1][0];
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for(j=1; j<N; j++)
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{
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A[0][DN-j] = A[0][j];
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A[1][DN-j] = -A[1][j];
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}
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} // end if
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else
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{
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for (j = 0; j <N; j++) // check {xj} is to real {Ak}
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{
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if (j ==0) norm = 2.0 * fabs(A[1][0]);
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else norm = fabs(A[1][j]+A[1][DN-j])+
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fabs(A[0][j]-A[0][DN-j]);
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if (norm > eps)
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{
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printf("The IDFT of the series {xj} isn't real!\n");
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exit(0);
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}
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}
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for (j = 0; j <N; j++)
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{
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c[0][j]= 0.5 * (A[0][j]+A[0][N+j]);
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c[1][j]= 0.5 * (A[1][j]+A[1][N+j]);
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tt = (float) j * hunit;
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cosj = cos(tt);
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sinj = -sign*sin(tt);
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d[0][j]= 0.5 * (cosj * (A[0][j]-A[0][N+j])
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-sinj*(A[1][j] - A[1][N+j]));
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}
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fft1r2(c, d, -1);
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for (k=0; k<N; k++)
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{
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dk = k+k;
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A[0][dk]=c[0][k];
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A[0][dk+1]=d[0][k];
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A[1][dk]=0.0;
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A[1][dk+1]=0.0;
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}
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} // end else
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}
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