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I am given the following discrete system

$$y[n]=x[-n]$$

where

$$x[n]=n+3$$.

Now from what I understand, since

$$y[n]=x[-n]$$

therefor the system is causal as the output is depending on the past values of the input. Right?

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You are correct that $y[n]$ only depends on past input values for $n \gt 0$, but when $n \lt 0$, that is not the case --- then $y[n]$ is dependent on future input values, regardless of what $x$ is.

To see this: $$ y[-2] = x[-(-2)] = x[2] $$ so the output at time $n=-2$ is dependent on the input at time $n=2$.

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  • $\begingroup$ Really sorry to bother you again and again, but is it non causal? Is that what you are trying to say? $\endgroup$ – Ahmad Qayyum Oct 9 '18 at 16:59
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    $\begingroup$ @AhmadQayyum yes; the system $y[n] = x[-n]$ is non-causal... $\endgroup$ – Fat32 Oct 9 '18 at 20:09

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