As can be seen from the code listing, this implementation of
residuez simply calls residue, which was written to
carry out the partial fraction expansions of
-plane
(continuous-time) transfer functions
:
where
is the ``quotient'' and
is the ``remainder'' in the PFE:
In the discrete-time case, we have the
-plane transfer function
where
.
We see that the
-plane case formally does what we desire if we
treat
-plane polynomials as polynomials in
instead of
. From Eq.(J.2), we see that this requires reversing the
coefficient-order of B and A in the call to
residue. In the returned result, we obtain terms such as
where the second form is simply the desired canonical form for
and the
Finally, the returned quotient polynomial must be flipped for the same reason that the input polynomials needed to be flipped (to convert from left-to-right descending powers of