csfftm1du,zdfftm1du(3F) csfftm1du,zdfftm1du(3F)
csfftm1du, zdfftm1du - Multiple 1D, Complex to Real, Inverse Fast Fourier
Transforms.
Fortran :
subroutine csfftm1du( sign, n, p, array, inc, lda, coef )
integer sign, n, p, inc, lda
real array(lda,p), coef(n+15)
subroutine zdfftm1du( sign, n, p, array, inc, lda, coef )
integer sign, n, p, inc, lda
real*8 array(lda,p), coef(n+15)
C :
#include <fft.h>
int csfftm1du ( int sign, int n, int p, float *array,
int inc, int lda, float *coef);
int zdfftm1du ( int sign, int n, int p, double *array,
int inc, int lda, double *coef);
csfftm1du and zdfftm1du compute the P real sequences of N samples each,
from their Fourier transform. The i-th index f(i) of a sequence of N
samples, 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 transforms are performed in-place, so the input
Fourier transform is overwritten by the final sequence output. As the
output sequences have 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.
P Integer, the number of sequences. Unchanged on exit.
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csfftm1du,zdfftm1du(3F) csfftm1du,zdfftm1du(3F)
ARRAY Array containing the samples of the sequence to be transformed.
On input, the element "i" of the sequence "j" is stored as A(i*inc,j) in
Fortran , and A[i*inc+j*lda] in C.
On exit, the array is overwritten by its transform.
INC Integer, increment between two consecutive elements of a sequence.
Unchanged on exit.
LDA Integer, leading dimension: increment between the first samples of
two consecutive sequences. 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 scfftm1dui or dzfftm1dui. Unchanged on exit.
Example of Calling Sequence
Working on 64 sequences of 1024 real values each. We successively apply
a Direct Fourier Transform, an Inverse Fourier Trasnform 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(0:1026-1,0:64-1), coeff(1024+15)
call scfftm1dui( 1024, coeff)
call csfftm1du( -1, 1024, 64, array, 1, 1026, coeff)
call scfftm1du( 1, 1024, 64, array, 1, 1026, coeff)
call sscalm1d( 1024,64,(1./real(1024)),array,1,1026)
C
#include <fft.h>
float array[64*1026], *coeff;
coeff = scfftm1dui( 1024, NULL);
csfftm1du( -1, 1024, 64, array, 1, 1026, coeff);
scfftm1du( 1, 1024, 64, array, 1, 1026, coeff);
sscalm1d( 1024, 64, 1./(float)1024, array, 1, 1026);
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.
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csfftm1du,zdfftm1du(3F) csfftm1du,zdfftm1du(3F)
SEE ALSO
fft, scfftm1dui, dzfftm1dui, scfftm1du, dzfftm1du, sscalm1d, dscalm1d
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