Shifted spectrum

I have omitted a bit of theory here that is found in PVI.

For an FT matrix of arbitrary size N, the desired shift is N/2, so values at alternate points in the time axis are multiplied by -1. A subroutine for that purpose is fth(). 

# FT a vector in a matrix, with first omega = - pi
#
subroutine  fth( adj,sign, m1, n12, cx)
integer i,       adj,      m1, n12
real sign
complex cx(m1,n12)
temporary complex temp(n12)
do i= 1, n12
        temp(i) = cx(1,i)
if( adj == 0)   { do i= 2, n12, 2
                        temp(i) =  -temp(i)
                  call ftu(  sign, n12, temp)
                }
else            { call ftu( -sign, n12, temp)
                  do i= 2, n12, 2
                        temp(i) =  -temp(i)
                }
do i= 1, n12
        cx(1,i) = temp(i)
return; end

To Fourier transform a 1024-point complex vector cx(1024) and then inverse transform it, you would

call fth( 0, 1., 1, 1024, cx)
 call fth( 1, 1., 1, 1024, cx)

You might wonder about the apparent redundancy of using both the argument conj and the argument sign. Having two arguments instead of one allows us to define the forward transform for a time axis with the opposite sign as the forward transform for a space axis.

The subroutine fth() is somewhat cluttered by the inclusion of a frequently needed practical feature--namely, the facility to extract vectors from a matrix, transform the vectors, and then restore them into the matrix.