Question

The system transfer function for an FIR digital filter is given by $$ \begin{aligned} H(z)= & -0.0087-0.1448 z^{-1}+0.0663 z^{-2}+0.6962 z^{-3} \\ & +0.0663 z^{-4}-0.1448 z^{-5}-0.0087 z^{-6} \end{aligned} $$ Assume that you want to implement this filter using 14 bit fixed point arithmetic. Determine the coefficients for the implementation of the filter using fixed point arithmetic. Represent the numbers in the form $$ \widehat{b(k)}=M \times 2^{-13} $$ where $M$ is an integer in the range $-2^{13} \leq M \leq 2^{13}-1$.

   The system transfer function for an FIR digital filter is given by
$$
\begin{aligned}
H(z)= & -0.0087-0.1448 z^{-1}+0.0663 z^{-2}+0.6962 z^{-3} \\
& +0.0663 z^{-4}-0.1448 z^{-5}-0.0087 z^{-6}
\end{aligned}
$$
Assume that you want to implement this filter using 14 bit fixed point arithmetic.

Determine the coefficients for the implementation of the filter using fixed point arithmetic. Represent the numbers in the form
$$
\widehat{b(k)}=M \times 2^{-13}
$$
where $M$ is an integer in the range $-2^{13} \leq M \leq 2^{13}-1$.

Digital Signal Processing. Principles, Algorithms and System Design

Winser Alexander and… 1st Edition

Chapter 6, Problem 1

Instant Answer

Step 1

To convert the coefficients to fixed point representation, we need to multiply them by $2^{13}$ and round to the nearest integer. For the first coefficient, $-0.0087$, we have: $$ \widehat{b(0)} = -0.0087 \times 2^{13} = -113.28 \approx -113 $$ For the second Show more…

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The system transfer function for an FIR digital filter is given by $$ \begin{aligned} H(z)= & -0.0087-0.1448 z^{-1}+0.0663 z^{-2}+0.6962 z^{-3} \\ & +0.0663 z^{-4}-0.1448 z^{-5}-0.0087 z^{-6} \end{aligned} $$ Assume that you want to implement this filter using 14 bit fixed point arithmetic. Determine the coefficients for the implementation of the filter using fixed point arithmetic. Represent the numbers in the form $$ \widehat{b(k)}=M \times 2^{-13} $$ where $M$ is an integer in the range $-2^{13} \leq M \leq 2^{13}-1$.

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