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