# What do poles do for a filter?

What are the disadvantages of having too many poles?

Thanks.

$$y(k) = x(k) + \alpha y(k-1)$$
where $y(k)$ describes the output of the system, $x(k)$ the input and $y(k-1)$ the output of the system the sample before.
Now what the recursive part $y(k-1)$ does is that it feeds the system the last output, which can cause problems depending on the $\alpha$ you choose. If $\alpha \geq 1$, the system reacts to any given input with an ever increasing output, which makes the system unstable.