# Causality of the given system

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?

## 1 Answer

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 $$n=2$$.

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