The z-Transform of a sequence x[n] is given as X(z) = 2z

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The z-Transform of a sequence x[n] is given as X(z) = 2z + 4 – 4/z + 3/z². If y[n] is the first difference of x[n], then Y(z) is given by

1. 2z + 2 – 8/z + 7/z² – 3/z³
2. – 2z + 2 – 6/z + 1/z² – 3/z³
3. – 2z – 2 + 8/z – 7/z² + 3/z³
4. 4z – 2 – 8/z – 1/z² + 3/z³

Correct Option: A

y[n] is first difference of x[n]
∴ y[n] = x(n)– x(n – 1)
From z transform
∴ Y(z) = x(Z) (1 – z – 1) = X(z) – z^–1X(z)
∴ Y(z) = [2z + 4 – 4z^–1 + 3z^–2] – [2 + 4z^–1 – 4z^–2]
= 2z + 4 – 4z^–1 +3 z^–2 – 2 – 4z^–1 + 4z^–2 – 3z^–3
= 2z + 2 – 8z^–1 + 7z – 2 – 3^–3

= 2z + 2 -	8	+	7	-	3
	z		z²		z³