sprodm1du,dprodm1du(3F)				       sprodm1du,dprodm1du(3F)

NAME    [Toc]    [Back]

     sprodm1du,	dprodm1du - Compute the	product	of Multiple 1D Fourier
     transforms	with Multiple 1D filters.

SYNOPSYS    [Toc]    [Back]

     Fortran :
     subroutine	sprodm1du( n,p,array,inca,lda,filter,incf,ldf)
	  integer   n, p, inca,	lda, incf, ldf
	  real	    array(lda,p), filter(ldf,p)

     subroutine	dprodm1du( n,p,array,inca,lda,filter,incf,ldf)
	  integer   n, p, inca,	lda, incf, ldf
	  real*8    array(lda,p), filter(ldf,p)


     C :
     #include <fft.h>
     int sprodm1du(int n, int p, float *array, int inc,int lda,
		    float *filter, int incf, int ldf);
     int dprodm1du(int n, int p, double	*array,int inc,int lda,
		    double *filter, int	incf, int ldf);

DESCRIPTION    [Toc]    [Back]

     sprodm1du and dprodm1du compute the product of the	Fourier	transforms of
     P real sequences of N samples with	the Fourier transforms of P real
     filters. Note, the	product	of the Fourier transforms of two sequences is
     equal to the Fourier transform of their convolution.

PARAMETERS    [Toc]    [Back]

     N Integer,	the number of samples in each sequence.	 Unchanged on exit.

     P Integer,	the number of sequences.  Unchanged on exit.

     ARRAY Array containing the	Fourier	Transform.  On exit, the array is
     overwritten by the	product.

     INCA Integer, increment between two consecutive elements of the sequence.
     Unchanged on exit.

     LDA Integer, leading dimension: increment between the first samples of
     two consecutive sequences.	 Unchanged on exit.

     FILTER Array containing the Fourier Transform of the filter(s).
     Unchanged on exit.

     INCF Integer, increment between two consecutive elements of the filter.
     Unchanged on exit.






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sprodm1du,dprodm1du(3F)				       sprodm1du,dprodm1du(3F)



     LDF Integer, leading dimension: increment between the first samples of
     two consecutive filter.  Unchanged	on exit.


Example	of Calling Sequence
     Working on	64 sequences of	1024 real values each.	We successively	apply
     a Direct Fourier Transform, the product with a SINGLE filter transform,
     then an Inverse Fourier TransformElements
 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), filter(0:1026-1,0:64-1),
	       coeff(1024+15)
	  call scfftm1dui( 1024, coeff)
	  call scfftm1du( -1, 1024, 64,	array, 1, 1026,	coeff)
	  call sprodm1du( 1024,	64, array, 1, 1026, filter, 1, 0)
	  call csfftm1du(  1, 1024, 64,	array, 1, 1026,	coeff)

     C
	  #include <fft.h>
	  float	array[64*1026],	filter[1026], *coeff;
	  coeff	= scfftm1dui( 1024, NULL);
	  scfftm1du( -1, 1024, 64, array, 1, 1026, coeff);
	  sprodm1du( 1024, 64, array, 1, 1026, filter, 1, 0);
	  csfftm1du( -1, 1024, 64, array, 1, 1026, coeff);

     NOTE_1 : Using a 0	leading	dimension for the filter is equivalent to
     applying the same filter to all the input sequences.

     NOTE_2 : As the FFTs are not normalized, a	successive direct, then
     inverse transform,	scales the original input by the size of the sequence.
     Rather than calling sscalm1d or dscalm1d to scale back the	result,	this
     scaling factor could be directly applied to the filter transform, thus
     saving some extra work.

SEE ALSO    [Toc]    [Back]

     fft, scfftm1dui, dzfftm1dui, scfftm1du, dzfftm1du,	sscalm1d, dscalm1d


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