As far as I have grasped the concept is that if we are given the expression
y[n]=(2x[n]−x2[n])2,
it is a memory less system because even if we give negative values of n, we still get the overall result in the positive sign, right?
And this expression is memory system because we get the negative answer for negative values of n, right?
y[n]=(2x[n]−x2[n]).
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