I have a FIR filter $L(z)$ and an IIR filter $H(z) = \frac{B(z)}{A(z)}$ which are cascaded together as $L(z)H(z) = L(z)\frac{B(z)}{A(z)}$.
For specific reasons I want to calculate a parallel topology that is equivalent to the original $L(z)H(z)$. I can achieve this using long division to divide $L(z)B(z)$ by $A(z)$ to obtain:
$L(z)H(z) = \frac{L(z)B(z)}{A(z)} = Q(z) + \frac{R(z)}{A(z)}$
Where $Q(z)$ is the quotient and $R(z)$ is the remainder of the long division of $L(z)B(z)$ by $A(z)$.
However, the resulting IIR, $\frac{R(z)}{A(z)}$, has a delay equal to the number of taps of the original FIR $L(z)$
Is it possible to do some clever re-arranging before the division so that the resulting IIR part of the long division is not delayed?
Of course one approach is to flip the filters so the magnitude of the poles are greater than one and perform long division using an unstable filter and flip back (which is a simple change of variable $z \to \frac{1}{z}$ and back again), but this isn't a useful solution.