The ideal FDDF may be defined by reference to analog time-delay
filters as described in diagram 1
[3]. From a time sequence 
we rebuild the original analog signal
, then we delay it and finally we
re-sample it in order to get 
.
This definition is no longer consistent if there is
some residual energy at the Nyquist frequency. For instance the
sequence 
may be the sampled
version of any of the 
functions. Furthermore a shifted cardinal sine isn't absolutely
summable which means that FDDFs aren't BIBO. For these reasons, we
shall limit the study of FDDFs only for input sequences
with no component at the Nyquist frequency. In this
subspace, FDDFs are consistent and BIBO.
