csfft1du,zdfft1du(3F) csfft1du,zdfft1du(3F)
csfft1du, zdfft1du - 1D, Complex to Real, Inverse Fast Fourier
Transforms.
Fortran :
subroutine csfft1du( sign, n, array, inc, coeff )
integer sign, n, inc
real array(0:(2*((N+2)/2)-1)*inc), coeff(n+15)
subroutine zdfft1du( sign, n, array, inc, coeff )
integer sign, n, inc
real*8 array(0:(2*((N+2)/2)-1)*inc), coeff(n+15)
C :
#include <fft.h>
int csfft1du ( int sign, int n, float *array,
int inc, float *coeff);
int zdfft1du ( int sign, int n, double *array,
int inc, double *coeff);
csfft1du and zdfft1du compute the real sequence of N samples, from its
Fourier transform. The i-th index f(i) of a sequence with Fourier
transform F(k) is equal to:
f(i) = Sum ( W^(i*k) * F(k) ), for k =0, ..., (N-1)
W = exp( (Sign*2*sqrt(-1)*PI) / N )
The Inverse Fourier transform is performed in-place, so the input Fourier
transform is overwritten by the final sequence output. As the output
sequence has real values, only the first half of the transform is needed.
The (N-k)-th sample of the transform would be the conjugate of the k-th
sample.
However, some extra space is necessary. For an N sample output sequence,
the input complex transform takes ((N+2)/2) complex values. This
represents either N+1(odd case) or N+2(even case) real values, that's one
or two more real values than the output real sequence.
SIGN Integer specifying which sign to be used for the expression of W
(see above) - must be either +1 or -1.
Unchanged on exit.
N Integer, the number of samples in each sequence.
Unchanged on exit.
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csfft1du,zdfft1du(3F) csfft1du,zdfft1du(3F)
ARRAY Array containing the Fourier Transform.
On output, the element "i" of the real sequence is stored as A(i*inc) in
Fortran , and A[i*inc] in C.
On exit, the array is overwritten by its transform.
INC Integer, increment between two consecutive elements of a sequence.
Unchanged on exit.
COEFF Array of at least ( N + 15 ) elements. On entry it contains the
Sines/Cosines and factorization of N. COEFF needs to be initialized with
a call to scfft1dui or dzfft1dui.
Unchanged on exit.
Example of Calling Sequence
Working on a sequences of 1024 real values. We successively apply a
Direct Fourier Transform, an Inverse Fourier Transform and finally scale
back the result by a factor 1/N (1/1024.)-
This sequence DirectFFT-InverseFFT-Scaling is equivalent to the identity
operator and the final sequence should be equal (with round-off
precision) to the initial sequence.
Elements of each sequence are stored with increment (stride) 1, and the
offset between the first element of two succesive sequence (leading
dimension) is 1026 (1026 >= 1024+2).
Fortran
real array(0:1026-1), coeff(1024+15)
call scfft1dui( 1024, coeff)
call csfft1du( -1, 1024, array, 1, coeff)
call scfft1du( 1, 1024, array, 1, coeff)
call sscal1d( 1024, (1./real(1024)), array, 1)
C
#include <fft.h>
float array[1026], *coeff;
coeff = scfft1dui( 1024, NULL);
csfft1du( -1, 1024, array, 1, coeff);
scfft1du( 1, 1024, array, 1, coeff);
sscal1d( 1024, 1./(float)1024, array, 1);
NOTE_1 : The Direct and Inverse transforms should use opposite signs -
Which one is used (+1 or -1) for Direct transform is just a matter of
convention
NOTE_2 : The Fourier Transforms are not normalized so the succession
Direct-Inverse transform scales the input data by a factor equal to the
size of the transform.
fft, scfft1dui, dzfft1dui, scfft1du, dzfft1du, sscal1d, dscal1d
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