41. f(t) is a pulse defined as ƒ(t) = 1 for 0 < 1 = 0 otherwise. The even part of ƒ(t) is
    

1. 1. 1	for 0 < t < 1 and zero otherwise
      2

   
   
   

   2. 1 for – 1 < t < 1 and zero otherwise

   
   
   

   3. 1	for - 1 < t < 1 and zero otherwise
      2

   
   
   

   4. 1 for -	1	< t <	1	and zero otherwise
      	2		2

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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42. Given the transform pair ƒ₁ (t) → ƒ₁(ω) ƒ₁(t)e^jω0t → ƒ₁ (ω - ω_o).
    

    Given ƒ1 (ω) =	2
    	1 + ω²

    
    The Fourier transform of ƒ₁(t) e^–jat is

1. 1. 2

      1 + a²

   
   
   

   2. 2

      1 - a²

   
   
   

   3. 2

      1 + (ω + a)²

   
   
   

   4. 2

      1 + (ω - a)²

   
   
   

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   NA

   Correct Option: C

   NA

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43. The transform of ƒ₁ (t) = e^{– t} u(t) is 1/(1 + jω). Then the transform of ƒ(t) = ƒ₁ (t) – ƒ₁ (– t) is

1. 1. 1

      jω²

   
   
   

   2. 2

      jω²

   
   
   

   3. jω

      jω²

   
   
   

   4. - 2jω

      jω²

   
   
   

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   NA

   Correct Option: D

   NA

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44. If the fourier transform of deterministic signal g(t) is G(ƒ), then the Fourier transform of g (t – 2) is

1. 1. G(ƒ) e^{– j4πƒ}

   
   
   

   2. G(2ƒ)

   
   
   

   3. 2G(2ƒ)

   
   
   

   4. G(ƒ – 2)

   
   
   

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   NA

   Correct Option: A

   NA

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45. Fourier transform of a function ƒ(at) is given by

1. 1. ƒ(at) = a ƒ(ω)

   
   
   

   2. ƒ(at) = 2/a ƒ(ω)

   
   
   

   3. ƒ(at) = (1/a) F(ω/a)

   
   
   

   4. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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