Does anyone know how we can determine input/state/output representation for a discrete - time system? For example we have the discrete-time system y(t) = u(t)u(t-1)u(t-2) how can we determine an i/s/o representation for it?
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Well first of all assuming that $u$ is the unit step function you may want to simplify this to $y(t) = u(t-2)$. – J P Oct 09 '19 at 18:40
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how do we simplify? I don't know the procedure and I was looking for it all day – Kate Jns Oct 09 '19 at 18:42
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Sorry, I had a typo on my last comment. Well the unit step function $u(t)$ is defined to be $0$ if $t < 0$ and $1$ if $t \geq 0$. So in your equation if $t < 2$, the third term will be $0$ so the product will be $0$. If $t \geq 2$, then all three terms will be $1$. In other words, it works the exact same as $u(t-2)$. – J P Oct 09 '19 at 18:47