Impulse Response DT Convolution CT Convolution Properties of LTI Systems
Memoryless Causality Stability Invertibility
\begin{align} y[n]=\sum_{k=-\infty}^{\infty}h[k]x[n-k] \nonumber \end{align}

Namely $y[n]$ does not depend on $x[n+k] \hspace{0.2cm}\forall k>0$ and $x[n-k] \hspace{0.2cm}\forall k<0$.Clearly, $h[k]$ must be zero $\forall k<0$ as shown in figure.


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