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I've been asked to find the poles, impulse response of a system (in digital signal processing).
The transfer function was,
$$H(z) = \frac{z^2+z}{z^2-z+0.5}$$
I solved it by the partial fractions method as follows.
$$\color{blue}{H(z) = \frac{z(z+1)}{z^2-z+0.5}}$$
$$\begin{align} &\Rightarrow \fra...