scfftm1du,dzfftm1du(3F) scfftm1du,dzfftm1du(3F)NAME
scfftm1du, dzfftm1du - Multiple 1D, Real to Complex, Direct Fast Fourier
Transforms.
SYNOPSYS
Fortran :
subroutine scfftm1du( sign, n, p, array, inc, lda, coef )
integer sign, n, p, inc, lda
real array(lda,p), coef(n+15)
subroutine dzfftm1du( 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 scfftm1du ( int sign, int n, int p, float *array,
int inc, int lda, float *coef);
int dzfftm1du ( int sign, int n, int p, double *array,
int inc, int lda, double *coef);
DESCRIPTION
scfftm1du and dzfftm1du compute the complex Fourier transform of P real
sequences of N samples each. The k-th index F(k) of the Transform of an N
sample sequence f(i) is equal to:
F(k) = Sum ( W^(i*k) * f(i) ), for i =0, ..., (N-1)
W = exp( (Sign*2*sqrt(-1)*PI) / N )
The Fourier transforms are computed in-place so the input sequence is
overwritten by the Fourier transform output. As the input sequences have
real values, only half of the results are computed since 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 input sequence,
the complex output of the 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 input.
PARAMETERS
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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scfftm1du,dzfftm1du(3F) scfftm1du,dzfftm1du(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
1D FFTs computed on 64 sequences of 1024 real values each. The 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.
Note : 1026 >= 1024+2 .
Fortran
real array(0:1026-1,0:64-1), coeff(1024+15)
call scfftm1dui( 1024, coeff)
call scfftm1du( -1, 1024, 64, array, 1, 1026, coeff)
C
#include <fft.h>
float array[64*1026], *coeff;
coeff = scfftm1dui( 1024, NULL);
scfftm1du( -1, 1024, 64, array, 1, 1026, coeff);
SEE ALSO
fft, scfftm1dui, dzfftm1dui, scfft1du, dzfft1du, csfftm1du, zdfftm1du
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