Consider two filters:

H$($z$)=0\mathrm{.}5/(0\mathrm{.}8+0\mathrm{.}1$z$+0\mathrm{.}1$z$^2)$

H$($z$)=0\mathrm{.}5/(0\mathrm{.}9-0\mathrm{.}59$z$+0\mathrm{.}1$z$^2)$

Questions

$1.$ Quantize the coefficients for both filters $(4$ bits, $2\text{'}$s complement$)$

$2.$ Calculate the quantization error for each of the poles

$3.$ Compare $-$ which filter has more pole quantization error and why?

$4.$ Is stability preserved after quantization for these two filters? $($Both are BIBO$-$stable in infinite precision.$)$ Why or why not?