cprodm1d(3F)

NAME
     cprodm1d, zprodm1d - Compute the product of Multiple 1D Fourier
     transforms with Multiple 1D filters.

SYNOPSYS
     Fortran :
     subroutine cprodm1d( n,p,array,inca,lda,filter,incf,ldf)
          integer   n, p, inca, lda, incf, ldf
          complex   array(lda,p), filter(ldf,p)

     subroutine zprodm1d( n,p,array,inca,lda,filter,incf,ldf)
          integer   n, p, inca, lda, incf, ldf
          double complex      array(lda,p), filter(ldf,p)


     C :
     #include <fft.h>
     int cprodm1d(int n, int p, complex *array, int inc,int lda,
                    complex *filter, int incf, int ldf);
     int zprodm1d(int n, int p, zomplex *array,int inc,int lda,
                    zomplex *filter, int incf, int ldf);


DESCRIPTION
     cprodm1d and zprodm1d compute the product of the Fourier transforms of P
     complex sequences of N samples with the Fourier transforms of P complex
     filters.  Note, the product of the Fourier transforms of two sequences is
     equal to the Fourier transform of their convolution.


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


Example of Calling Sequence
     Working on 64 sequences of 1024 complex values each.  We successively
     apply a Direct Fourier Transform, the product with a SINGLE filter
     transform, then an Inverse Fourier Transform-
     Elements of each sequence are stored with increment (stride)1, and the
     offset between the first element of two succesive sequences (leading
     dimension) is 2049.
     Fortran
          complex array(0:2049-1,0:64-1),
                  filter(0:2049-1,0:64-1), coeff(1024+15)
          call cfftm1di( 1024, coeff)
          call cfftm1d( -1, 1024, 64, array, 1, 2049, coeff)
          call cprodm1d( 1024, 64, array, 1, 2049, filter, 1, 0)
          call cfftm1d(  1, 1024, 64, array, 1, 2049, coeff)

     C
          #include <fft.h>
          complex array[64*2049], filter[2049], *coeff;
          coeff = cfftm1di( 1024, NULL);
          cfftm1d( -1, 1024, 64, array, 1, 2049, coeff);
          cprodm1d( 1024, 64, array, 1, 2049, filter, 1, 0);
          cfftm1d( -1, 1024, 64, array, 1, 2049, 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 cscalm1d or zscalm1d to scale back the result, this
     scaling factor could be directly applied to the filter transform, thus
     saving some extra work.

SEE ALSO
     fft, cfftm1di, zfftm1di, cfftm1d, zfftm1d, cscalm1d, zscalm1d