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Example

For the example of Eq.$ \,$(6.12), we obtain

\begin{eqnarray*} r_{11} &=& \left.\left(1-\frac{1}{2}z^{-1}\right)^3H(z)\right\... ...}{dz^{-1}} (-5 + 2z^{-1})\right\vert _{z^{-1}=2} = 2\cdot 2 = 4. \end{eqnarray*}

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Impulse Response of Repeated Poles
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Dealing with Repeated Poles Analytically