How to stabilize a filter
The magnitude of the frequency response will remain unchanged if you reflect any poles outside the unit circle - these are the ones causing instability - back inside the circle. I.e., a pole $p$ (with $|p|&gt;1$) is replaced by the new pole $\tilde{p}=1/p^*$, where $*$ denotes complex conjugation. This will not change the magnitude of the frequency response (up to a scaling factor), but it will change the phase response.

The correct scaling is obtained if each factor $(1-p_iz^{-1})$ with $|p_i|&gt;1$ of the denominator polynomial $A(z)$ is replaced by $|p_i|(1-z^{-1}/p_i^*)$.