$y(n) = x(-n)$ , causal or not , memory or memoryless?

Question

$y(n) = x(-n)$ , causal or not , memory or memory-less ?

it's a question in digital signal processing course .

My guess it's memory less , causal because $x(-n)$ is only the inverse of the function ?

Memoryless System A system is memoryless if the output y[n] at every value of n depends only on the input x[n] at the same value of n

Causality A system is causal it’s output is a function of only the current and previous samples

Answer 1

• It is not causal. Consider $n=-1$. The output $y(-1)$ depends on the input at $n=1$, which is only available in future.
• It is not memoryless. Consider any $n > 0$. The output $y$ depends on the input at $-n$ which was applied in the past. Thus the system has memory.