46. The Fourier transform of a unit step fnction is given by

1. 1. F(jω) =	j
      	ω

   
   
   

   2. F(jω) = jω

   
   
   

   3. F(jω) =	1
      	jω

   
   
   

   4. F(jω) =	j
      	ω

   
   
   

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   NA

   Correct Option: C

   NA

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47. Fourier transform of v(t) cos ω₀t is

1. 1. V(ƒ) =	1	δ(ƒ - ƒ0)
      	2

   
   
   

   2. V(ƒ) =	1	δ(ƒ + ƒ0)
      	2

   
   
   

   3. V(ƒ) =	1	[δ(ƒ - ƒ 0) - δ(ƒ + ƒ0)
      	2

   
   
   

   4. V(ƒ) =	1	[δ(ƒ - ƒ 0) + δ(ƒ + ƒ0)
      	2

   
   
   

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   NA

   Correct Option: D

   NA

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48. Fourier transform of the unit step signal
    u(t) = 1 for t > 0
    = 0 for t < 0 is
    

1. 1. πδ(ω)

   
   
   

   2. 1/jω

   
   
   

   3. 1	+ πδ(ω)
      jω

   
   
   

   4. 1	+ 2πδ(ω)
      jω

   
   
   

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   NA

   Correct Option: C

   NA

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49. The frequency response of a causal and stable LTI system is
    

    H(jω) =	1 - jω
    	1 + jω

    
    The group delay of the system is

1. 1. 2

      1 + ω²

   
   
   

   2. - 2

      1 + ω²

   
   
   

   3. 2 tan^{– 1}ω

   
   
   

   4. – 2 tan^{– 1}ω

   
   
   

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   Group delay τ(ω) = -	d	∠H(jω)
   	dω

   
   ∠H(jω) = tan^–1 (– ω) – tan^–1 ω = – 2 tan^–1 ω
   

   τ(ω) =	d	(- 2 tan–1 ω) =	2
   	dω		1 + ω²

   Correct Option: A

   Group delay τ(ω) = -	d	∠H(jω)
   	dω

   
   ∠H(jω) = tan^–1 (– ω) – tan^–1 ω = – 2 tan^–1 ω
   

   τ(ω) =	d	(- 2 tan–1 ω) =	2
   	dω		1 + ω²

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50. Which one of the following is the Fourier transform of the signal given in Fig. II, if the Fourier transform of the signal in Fig. I is given by
    

    2	sin ω T1	?
    	ω

    
    

1. 1. 2	sin ω T1	e+jωT1
      	ω

   
   
   

   2. 2	sin ω T1	e-jωT1
      	ω

   
   
   

   3. 	sin ω T1	e-jωT1
      	ω

   
   
   

   4. 	sin ω T1	e+jω(T1 - 2)
      	ω

   
   
   

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   NA

   Correct Option: B

   NA

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