Question

This problem involves the statistical analysis of roundoff errors for an IIR second order section. Fig. 6.5 gives a block diagram for a second order FIR filter that has been implemented as two FIR lattice sections. Fig. 6.6 gives a block diagram for the same filter showing the input errors $\left(e_0(n)\right.$ to $\left.e_3(n)\right)$ associated with roundoff errors. The outputs from the adders are rounded from 32 bits by multiplying the adder output by $2^{-16}$ and truncating toward zero. The scaled coefficients are given by $$ \begin{aligned} & K_1=22921, \\ & K_2=-7504 . \end{aligned} $$ Compute the average power in the error free output from part 2 as $$ P Y=\frac{1}{N} \sum_{k=0}^{N-1} y^2(n) $$ where $y(n)$ is the error free output.

   This problem involves the statistical analysis of roundoff errors for an IIR second order section. Fig. 6.5 gives a block diagram for a second order FIR filter that has been implemented as two FIR lattice sections. Fig. 6.6 gives a block diagram for the same filter showing the input errors $\left(e_0(n)\right.$ to $\left.e_3(n)\right)$ associated with roundoff errors. The outputs from the adders are rounded from 32 bits by multiplying the adder output by $2^{-16}$ and truncating toward zero. The scaled coefficients are given by
$$
\begin{aligned}
& K_1=22921, \\
& K_2=-7504 .
\end{aligned}
$$

Compute the average power in the error free output from part 2 as $$
P Y=\frac{1}{N} \sum_{k=0}^{N-1} y^2(n)
$$
where $y(n)$ is the error free output.
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Digital Signal Processing. Principles, Algorithms and System Design
Digital Signal Processing. Principles, Algorithms and System Design
Winser Alexander and… 1st Edition
Chapter 6, Problem 4 ↓

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We are given the scaled coefficients $K_1$ and $K_2$ as $22921$ and $-7504$ respectively.  Show more…

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This problem involves the statistical analysis of roundoff errors for an IIR second order section. Fig. 6.5 gives a block diagram for a second order FIR filter that has been implemented as two FIR lattice sections. Fig. 6.6 gives a block diagram for the same filter showing the input errors $\left(e_0(n)\right.$ to $\left.e_3(n)\right)$ associated with roundoff errors. The outputs from the adders are rounded from 32 bits by multiplying the adder output by $2^{-16}$ and truncating toward zero. The scaled coefficients are given by $$ \begin{aligned} & K_1=22921, \\ & K_2=-7504 . \end{aligned} $$ Compute the average power in the error free output from part 2 as $$ P Y=\frac{1}{N} \sum_{k=0}^{N-1} y^2(n) $$ where $y(n)$ is the error free output.
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