Is the signal u[n] +u[-n] periodic?

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In my Signals&Systems book it is written that sum of discrete time unit step function and its time reversal is periodic.

$x[n]=u[n]+u[-n]$

I just couldn't understand how $\;x[n]\;$ can be periodic even if it has the value 2 at 0 which doesn't recur anywhere else. Maybe I am missing something, I will appreciate any help.

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1 Answer

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$$x[n]=u[n]+u[-n]$$ isn't periodic because of the reason stated by OP.

But if $$x[n]={u[n]+u[-n}] \ \forall n\ \ne0$$ and if you define $x[0]=1,$ then it will be a constant function.

And as stated here in the other answer, constant functions are periodic and don't have any fundamental periods.

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