scfft1du,dzfft1du(3F)					 scfft1du,dzfft1du(3F)

NAME    [Toc]    [Back]

     scfft1du, dzfft1du	- 1D, Real to Complex, Direct Fast Fourier Transforms.

SYNOPSYS    [Toc]    [Back]

     Fortran :
     subroutine	scfft1du( sign,	n, array, inc, coeff )
	  integer sign,	n, inc
	  real array(0:(2*((N+2)/2)-1)*inc), coeff(n+15)
     subroutine	dzfft1du( 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 scfft1du ( int	sign, int n, float *array,
	       int inc,	float *coeff);
     int dzfft1du ( int	sign, int n, double *array,
	       int inc,	double *coeff);

DESCRIPTION    [Toc]    [Back]

     scfft1du and dzfft1du compute the Fourier transform of a real sequence.
     The k-th index F(k) of the	Fourier	transform of a real 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 Direct	Fourier	transform is performed in-place, so the	input sequence
     is	overwritten by its Fourier transform. As the input 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 sequence, the
     output 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 input real sequence.

PARAMETERS    [Toc]    [Back]

     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.

     ARRAY Array containing the	samples	of the sequence	to be transformed.
     On	input, the element "i" of the sequence is stored as A(i*inc) in
     Fortran , and A[i*inc] in C.
     On	exit, the array	is overwritten by its transform.




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scfft1du,dzfft1du(3F)					 scfft1du,dzfft1du(3F)



     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
     Direct Fourier Transform of a sequence of 1024 real values.  Elements of
     sequence are stored with increment	(stride) 1.
     Fortran
	  real array(0:1026-1),	coeff(1024+15)
	  call scfft1dui( 1024,	coeff)
	  call scfft1du( -1, 1024, array, 1, coeff)

     C
	  #include <fft.h>
	  float	array[1026], *coeff;
	  coeff	= scfft1dui( 1024, NULL);
	  scfft1du( -1,	1024, array, 1,	coeff);

SEE ALSO    [Toc]    [Back]

     fft, scfft1dui, dzfft1dui,	csfft1du, zdfft1du


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