Even thought the transfer function 
corresponding to the ideal
FDDF of delay d does not exist, the Fourier transform
of the ideal impulse response exists
and is equal to 
. The
analytic extention 
of 
plays the
same role as the usual transfer function. The holomorphic function
is defined on the whole 
plane, except for the
negative real semi-axis which is an area of discontinuity. We
note
this function 
.