# Tag Info

That purple array is giving the impulse response over time. You can get it directly from the difference equation. Assume initial rest, $y[-1]=0$, then write out the impulse response for $n=0, 1, 2, ...$. If you do that you will get: \begin{align} h[0]&=1+0 \\ h[1] &= 0 + 0.5 \\ h[2] &= 0 + 0.25 \\ h[3] &= 0 + 0.125 \\ ... \end{align}