The system transfer function for a digital filter is given by
$$
H(z)=\frac{B(z)}{A(z)}
$$
where
$$
\begin{aligned}
B(z)= & 0.2324+1.6073 z^{-1}+5.0891 z^{-2}+9.5962 z^{-3}+11.7644 z^{-4} \\
& +9.5962 z^{-5}+5.0891 z^{-6}+1.6073 z^{-7}+0.2324 z^{-8}
\end{aligned}
$$
and
$$
\begin{aligned}
A(z)= & 1.0+4.4704 z^{-1}+9.9870 z^{-2}+13.7949 z^{-3}+12.9880 z^{-4} \\
& +8.5743 z^{-5}+4.0521 z^{-6}+1.3003 z^{-7}+0.2508 z^{-8}
\end{aligned}
$$
You are required to scale the filter coefficients for fixed point implementation using an input sequence with words scaled to 14 bits and with a requirement that the output can be represented using 32 bit words. Show all computations.
Determine the scale factor for the numerator coefficients.