Method

The FIR part is first extracted, and the (strictly proper) remainder is passed to residuez for expansion of the IIR part (into a sum of complex resonators). One must remember that, in this case, the impulse-response of the IIR part $R(z)$ begins after the impulse-response of the FIR part $F(z)$ has finished, i.e.,

$$H(z) = F(z) + z^{-{N_f}}R(z)$$

where $N_f$ is the length of the FIR part (order of $F(z)$ plus 1).

See §6.8.8 for an example usage of residued (with a comparison to residuez).