Method
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:
where








In the discrete-time case, we have the -plane transfer function
For compatibility with Matlab's residuez, we need a PFE of the form


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









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Example with Repeated Poles
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The Padé-Prony Method