# Causality on an accumulator system

Can anybody explain why is this system not causal.

$$T[x[n]] = \sum_{k=n_0}^{n} x[k]$$

How does it depend from future inputs when $$n < n_0$$.

If $$n < n_0$$ then $$T[x[n]]$$ is zero because of summation properties.

• You are correct about the convention for the sum. Maybe your instructor is using a different definition?
– MBaz
Oct 28 '21 at 22:00
• But why does it depend on the future inputs, for any $n$ the summation goes up to $n$ too. Is there an example that can make it more clear. Thank you. Oct 28 '21 at 22:02
• From what i've searched if $n_0$ was $-\infty$ it would be causal. But since $n_0$ can be anything and summation when $n < n_0$ is possible resulting in zero, I don't know. Oct 28 '21 at 22:22
• As you say, normally the range (for example) 5:3 is empty. However, someone may define it as [5, 4, 3], where $n$ is 3, so it'd be looking into the future. It'd be a completely non-standard definition, though, and probably quite useless too.
– MBaz
Oct 28 '21 at 22:26
• BTW, in case it's not clear: this system is causal, following widely accepted conventions for the $\Sigma$ operation.
– MBaz
Oct 28 '21 at 22:28