The DTFT of the given signal— x[n] =3nu[n – 4]4

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The DTFT of the given signal—
x[n] = 3 ⁿ u[n – 4]
4

1. 3 e^{– jΩ} ⁴
  4
  1 – 3 e^{– jΩ}
  4
2. 3 e^jΩ ⁴
  4
  1 – 3 e^jΩ
  4
3. 3 e^{– jΩ} ⁴
  4
  1 + 3 e^jΩ
  4
4. None of these

Correct Option: A

The DTFT of signal x[n] is given as

	_∞
X(e^jΩ) =		x[n].e^{– jΩn}
	^{n = – ∞}

	_∞
=		(3/4)ⁿ.e^{– jΩn}
	^{n = 4}

	_∞
=		[(3/4)e^{– jΩn}]ⁿ.
	^{n = 4}

=		3	e^{– jΩ}		⁴
		4

	1 –	3	e^{– j Ω}
		4