I am trying to find the minimum-phase system of the transfer function $H(z) = \frac{2 + 3.125z^{-2}}{1-0.9z^{-1}+0.81z^{-2}}$.
I know I need to find and remove the allpass (basically reflect the two zeroes on the imaginary axis inside the unit circle?), and I've gotten so far as this: $H(z) = 2\frac{1 + \frac{3.125}{2}z^{-2}}{1-0.9z^{-1}+0.81z^{-2}} = 2\frac{1 + \frac{3.125}{2}z^{-2}}{1-0.9z^{-1}+0.81z^{-2}} \frac{\frac{3.125}{2} + z^{-2}}{1 + \frac{3.125}{2}z^{-2}}=,$
and then I'm not really sure where to go next. Is my thinking correct thus far? What step should I do next?
Thank you.
Edit:
This is the kind of thing I'm trying to do, as per the example in my book: