116. For the signal X(n) =			1		n	u(n– 3) the X(z) will be—
     			5

1. 1. 		z– 3			|z| >	1
      		1 –	1	z– 1		5
      			5

   
   
   

   2. 	1		3	z– 3			|z| >	1
      	5			1 –	1	z– 1		5
      					5

   
   
   

   3. 	1		3	z– 3			|z| <	1
      	5			1 –	1	z– 1		5
      					5

   
   
   

   4. 	1		3	z– 3			|z| <	1
      	5			1 +	1	z– 1		5
      					5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that x(n) =			1		n	u(n– 3) can be written as
   			5

   
   

   x(n) =			1		n – 3	·			1		3	u(n – 3)
   			5						5

   
   By using shifting property
   If x(n) ← z→ X(z)
   x(n – n₀) ←z→ z^{– n₀}.x(z)
   Therefore,
   

   			1		3	·			1		n – 3
   			5						5

   
   

   	1		3	z– 3			|z| >	1
   	5			1 –	1	z– 1		5
   					5

   
   Hence, alternative (B) is correct choice.

   Correct Option: B

   Given that x(n) =			1		n	u(n– 3) can be written as
   			5

   
   

   x(n) =			1		n – 3	·			1		3	u(n – 3)
   			5						5

   
   By using shifting property
   If x(n) ← z→ X(z)
   x(n – n₀) ←z→ z^{– n₀}.x(z)
   Therefore,
   

   			1		3	·			1		n – 3
   			5						5

   
   

   	1		3	z– 3			|z| >	1
   	5			1 –	1	z– 1		5
   					5

   
   Hence, alternative (B) is correct choice.

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117. Energy of a signal depends upon—

1. 1. Magnitude spectrum of Fourier transform only

   
   
   

   2. Phase spectrum of Fourier transform only

   
   
   

   3. Both Magnitude and phase spectrum of Fourier transform

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the Parsevel’s theorem for energy signals.
   

   i.e., E =		∞	|F(ω)|2df
   		- ∞

   
   From this relation it is clear that energy of a signal depends only upon the magnitude spectrum of Fourier transform.

   Correct Option: A

   According to the Parsevel’s theorem for energy signals.
   

   i.e., E =		∞	|F(ω)|2df
   		- ∞

   
   From this relation it is clear that energy of a signal depends only upon the magnitude spectrum of Fourier transform.

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118. Mathematically discrete time unit impulse can be obtained as—

1. 1. δ[n] = u[n]

   
   
   

   2. δ[n] = u[n] – u[n – 1]

   
   
   

   3. δ[n] = u[n] + u[n + 1]

   
   
   

   4. δ[n] = u[n] – u[n – 2]

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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119. The relation between the u|n| and δ[m] can be given by—

1. 1. 	n
      u[n] =		δ[m2]
      	m = – ∞

   
   
   

   2. 	n
      u[n] =		δ[m]
      	m = – ∞

   
   
   

   3. 	∞
      δ[m] =		u[n]
      	n = ∞

   
   
   

   4. 	∞
      δ[m] =		u[n]
      	n = –∞

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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120. y(t) = 2 x(t) is an invertible system whose inverse system H^–1 is—

1. 1. 	1	x(t)
      	2

   
   
   

   2. 	1	x2(t)
      	2

   
   
   

   3. 	3	y(t)
      	2

   
   
   

   4. 	1	y(t)
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   From given figure
   
   y(t) = H x(t)
   H^{– 1} 2x(t) = y′(t)
   y(t)=2x(t)
   Again from figure
   y′(t) = y(t). H^{– 1}
   

   or y′(t) = 2. x(t)	1
   	2

   
   or y′(t) = x(t)
   Therefore, it is clear that the system is invertible.
   Hence, alternative (D) is the correct choice.

   Correct Option: D

   From given figure
   
   y(t) = H x(t)
   H^{– 1} 2x(t) = y′(t)
   y(t)=2x(t)
   Again from figure
   y′(t) = y(t). H^{– 1}
   

   or y′(t) = 2. x(t)	1
   	2

   
   or y′(t) = x(t)
   Therefore, it is clear that the system is invertible.
   Hence, alternative (D) is the correct choice.

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