The system transfer function for a discrete time system is...

The system transfer function for a discrete time system is given by $$ \begin{aligned} H(z)= & \frac{B(z)}{A(z)}, \\ B(z)= & 0.3428+2.1417 z^{-1}+5.9713 z^{-2}+9.6003 z^{-3} \\ & +9.6003 z^{-4}+5.9713 z^{-5}+2.1417 z^{-6}+0.3428 z^{-7}, \\ A(z)= & 1.0+4.3846 z^{-1}+8.9602 z^{-2}+10.5621 z^{-3} \\ & +7.5750 z^{-4}+3.1003 z^{-5}+0.5560 z^{-6}-0.0261 z^{-7} . \end{aligned} $$ Determine the scale factor for the denominator coefficients to scale the coefficients to 13 bit fixed point numbers with 1 bit representing the sign bit, 5 bits representing the whole number part, and 7 bits representing the fractional part. The scale factor for the coefficients is restricted to be a power of $2\left(s_2=2^m\right)$. This is equivalent to the fixed point format $Q 5.7$.

The system transfer function for a discrete time system is given by
$$
\begin{aligned}
H(z)= & \frac{B(z)}{A(z)}, \\
B(z)= & 0.3428+2.1417 z^{-1}+5.9713 z^{-2}+9.6003 z^{-3} \\
& +9.6003 z^{-4}+5.9713 z^{-5}+2.1417 z^{-6}+0.3428 z^{-7}, \\
A(z)= & 1.0+4.3846 z^{-1}+8.9602 z^{-2}+10.5621 z^{-3} \\
& +7.5750 z^{-4}+3.1003 z^{-5}+0.5560 z^{-6}-0.0261 z^{-7} .
\end{aligned}
$$
Determine the scale factor for the denominator coefficients to scale the coefficients to 13 bit fixed point numbers with 1 bit representing the sign bit, 5 bits representing the whole number part, and 7 bits representing the fractional part. The scale factor for the coefficients is restricted to be a power of $2\left(s_2=2^m\right)$. This is equivalent to the fixed point format $Q 5.7$.

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