This problem involves the statistical analysis of roundoff...

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 $$ \begin{aligned} & K_1=22921, \\ & K_2=-7504 . \end{aligned} $$ Write a Matlab script to compute the contributions to the error due to rounding from each of the error sources. Use the Matlab rand script to generate appropriate random sequences to model each of the roundoff error inputs. Compute the average power for each error output. For example, if the output due to $e_0(n)$ is $d_0(n)$, then the average power for $d_0(n)$ can be computed as $$ P_0=\frac{1}{N} \sum_{k=0}^{N-1} d_0^2(n) $$

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
$$
\begin{aligned}
& K_1=22921, \\
& K_2=-7504 .
\end{aligned}
$$

Write a Matlab script to compute the contributions to the error due to rounding from each of the error sources. Use the Matlab rand script to generate appropriate random sequences to model each of the roundoff error inputs. Compute the average power for each error output. For example, if the output due to $e_0(n)$ is $d_0(n)$, then the average power for $d_0(n)$ can be computed as $$
P_0=\frac{1}{N} \sum_{k=0}^{N-1} d_0^2(n)
$$

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