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 is the order of the quotient polynomial in , and is the

In the discrete-time case, we have the -plane transfer function

For compatibility with Matlab's

where .

We see that the -plane case formally does what we desire if we
treat -plane polynomials as polynomials in instead of
. From Eq. (H.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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