The sign functionextracts the sign of a real valued signal, i.e.,

(a) Let s[n] = s₁[n] + s₂[n], x[n] = n, where s₁[n] is causal and s₂[n] anti-causal; find their Z-transforms and indicate the corresponding ROCs.

(b) Determine the Z-transform S(z).

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-1 x[n] < 0 s[n] = sign(x[n]) = {0 x[n] = 0 x[n] > 0