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Let's say I have the given unit step response function $s$ defined as: $$s[n] = x[n]*a^{|n|} \text{ where } x[n] = u[n]$$ In this equation, I assumed that this system was causal since there was no dependence on future inputs. However, it is actually not causal for the following reason:

Since $h[n] \neq 0$ for $n < 0$, the system is not causal.

I don't understand the logic behind this. Mathematically, I can't see how this makes sense. Because, $x[n]$ only depends on the current value of $n$. Can someone reconcile this?

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    But $s$ depends on past and future values of $x$. – 2017-02-16
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    But, if $n \geq 0$, then $s[n]$ is just $a^n$ and if $n < 0$, then $s[n] = 0$. So how exactly does it depend on past and future values? – 2017-02-16
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    $*$ denotes a convolution operation. – 2017-02-16

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