The z-transform F(z) of the function f(nT) = anT is—

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The z-transform F(z) of the function f(nT) = a^nT is—

1. z
  z – a^T
2. z
  z + a^T
3. z
  z – a^{– T}
4. z
  z + a^{– T}

Correct Option: A

The z-transform of function f(n) is given by relation

	_∞
z[f(n)] =	∑	f(n)·z^{– n}
	^{n = – ∞}

	_∞
z[f(nT)] =	∑	a^nt·z ^{– n}
	^{n = – ∞}

= 1 + a^T z^{– 1} + a^2T z ^{– 2} + …

=	1
	1 – a^T z^{– 1}

=	z
	z – a^T

Hence, alternative (A) is the correct choice.