Calculate impulse response for given system

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i am given an exercise in which i need to find the impulse response for this given system:

$$y(n) = 2x(n-2) + x(n) -2x(n+2)$$

This is the only information i have. I don't even understand which formula should be applied to get the result.

May any merciful soul help me on my way to find the solution? :)

Thanks!

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1 Answer

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You only need to apply an impulse input (i.e. $x(n) = \delta (n)$), and see what is the response $y(n)$ (It is usually called $h(n)$). In this case, as the output does not depend on its self, you simply obtain: $$h(n) = \delta (n) + 2 \delta (n-2) - 2 \delta (n+2) $$ From this impulse response you can obtain the response for any input.

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