The system represented by equations—(i) N

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The system represented by equations—
(i)
_{N – 1}
y(n) = 1/N x(n – m)
^{m = 0}

(ii) y(n) = [x(n)]²

1. (i) is linear, (ii) non-linear
2. (i) is non-linear (ii) is linear
3. both (i) and (ii) are linear
4. both (i) and (ii) are non-linear

Correct Option: A

	_{N – 1}
(i) y(n) = 1/N		x(n – m)
	^{m = 0}

	_{N – 1}
Let y₁(n) = 1/N		x₁(n – m)
	^{m = 0}

	_{N – 1}
and y₂(n) = 1/N		x₂(n – m)
	^{m = 0}

then y(n) = y₁(n) + y₂(n)

	_{N – 1}		_{N – 1}
= 1/N		x₁(n – m) + 1/N		x₂(n – m)
	^{m = 0}		^{m = 0}

	_{N – 1}
= 1/N		[x₁(n – m) + x₂(n – m)]
	^{m = 0}

	_{N – 1}
= 1/N		x(n – m)
	^{m = 0}

Therefore, this system is linear. (ii) y[n] = [x(n)]² is non-linear already discussed in previous question.
Hence, alternative (A) is the correct choice.