Question

The system transfer function for a discrete time system is given by$$\begin{aligned} H(z)= & \frac{B(z)}{A(z)}, \\ B(z)= & 0.1296-0.5471 z^{-1}+1.1387 z^{-2}-1.4293 z^{-3}+1.1387 z^{-4} \\ & -0.5471 z^{-5}+0.1296 z^{-6}, \\ A(z)= & 1.0-1.0584 z^{-1}+2.0396 z^{-2}-0.8474 z^{-3}+1.0440 z^{-4} \\ & -0.1153 z^{-5}+0.2654 z^{-6} . \end{aligned}$$ Determine the scale factor for the numerator coefficients to scale the coefficients to 14 bit fixed point numbers using the format Q5.8.

   The system transfer function for a discrete time system is given by$$\begin{aligned}
H(z)= & \frac{B(z)}{A(z)}, \\
B(z)= & 0.1296-0.5471 z^{-1}+1.1387 z^{-2}-1.4293 z^{-3}+1.1387 z^{-4} \\
& -0.5471 z^{-5}+0.1296 z^{-6}, \\
A(z)= & 1.0-1.0584 z^{-1}+2.0396 z^{-2}-0.8474 z^{-3}+1.0440 z^{-4} \\
& -0.1153 z^{-5}+0.2654 z^{-6} .
\end{aligned}$$
Determine the scale factor for the numerator coefficients to scale the coefficients to 14 bit fixed point numbers using the format Q5.8.

Digital Signal Processing. Principles, Algorithms and System Design

Winser Alexander and… 1st Edition

Chapter 6, Problem 1

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In this case, the maximum absolute value of the numerator coefficients is 1.4293. Show more…

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The system transfer function for a discrete time system is given by$$\begin{aligned} H(z)= & \frac{B(z)}{A(z)}, \\ B(z)= & 0.1296-0.5471 z^{-1}+1.1387 z^{-2}-1.4293 z^{-3}+1.1387 z^{-4} \\ & -0.5471 z^{-5}+0.1296 z^{-6}, \\ A(z)= & 1.0-1.0584 z^{-1}+2.0396 z^{-2}-0.8474 z^{-3}+1.0440 z^{-4} \\ & -0.1153 z^{-5}+0.2654 z^{-6} . \end{aligned}$$ Determine the scale factor for the numerator coefficients to scale the coefficients to 14 bit fixed point numbers using the format Q5.8.

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