36. A Fourier transform pairs is as follows
    
    

    Where;       x(t) =		1		|t| < |
    		0		otherwise

    
    Determine the Fourier transform of the signal y(t) shown in figure below
    

1. 1. ej2ω sin2ω

      2ω

   
   
   

   2. e-j2ω sin2ω

      ω

   
   
   

   3. 4e-j2ω sin ω/2

      ω

   
   
   

   4. 4ej2ω sin ω/2

      ω

   
   
   

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1. View Hint View Answer Discuss in Forum

   y(t) = x		t - 2
   		2

   
   ⇒ Y(jω) = e ^{– j2ω} X(j2ω)
   

   Y(jω) =	e – j2ω sin 2ω
   	2ω

   Correct Option: B

   y(t) = x		t - 2
   		2

   
   ⇒ Y(jω) = e ^{– j2ω} X(j2ω)
   

   Y(jω) =	e – j2ω sin 2ω
   	2ω

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37. Consider a causal LTI system with frequency response
    

    H(jω) =	1
    	jω + 3

    
    This system produces the output to input x(t) as follows
    y(t) = e^{– 2t} u(t) – e^{– 4t} u(t)
    The input x(t) is

1. 1. (2e^{– 4t} – 3e^{– 3t})u(t)

   
   
   

   2. e^{– 4t} u(t)

   
   
   

   3. (3e^{– 4t} – 2e^{– 3t})u(t)

   
   
   

   4. – e^{– 4t} u(t)

   
   
   

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1. View Hint View Answer Discuss in Forum

   x(t) = cos (4πt + θ)
   X(jπ) = e^jθ πδ(ω – 2π) + e ^-jθπδ(ω + 2π)
   The non zero portion of X(jω) lie outside the range – 3π ≤ ω ≤ 3π. This implies that
   Y(jω) = X(jω) H(jω) = 0
   ∴ Y(t) = 0.

   Correct Option: B

   x(t) = cos (4πt + θ)
   X(jπ) = e^jθ πδ(ω – 2π) + e ^-jθπδ(ω + 2π)
   The non zero portion of X(jω) lie outside the range – 3π ≤ ω ≤ 3π. This implies that
   Y(jω) = X(jω) H(jω) = 0
   ∴ Y(t) = 0.

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38. Fourier transform of the signal
    x(t) = sin 2πt e^–t u(t) is

1. 1. 1		1	-	1
      2		1 + j(ω - 2π)		1 + j(ω + 2π)

   
   
   

   2. 1		1	-	1
      2j		1 + j(ω - 2π)		1 + j(ω + 2π)

   
   
   

   3. 1		1	-	1
      2j		1 + j(ω + 2π)		1 + j(ω - 2π)

   
   
   

   4. 1		1	-	1
      2		1 + j(ω + 2π)		1 + j(ω - 2π)

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: B

   

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39. Fourier trans form of the signal x(t) = e^{– 4}| t| is

1. 1. 8

      16 + ω²

   
   
   

   2. - 8

      16 + ω²

   
   
   

   3. 4

      16 + ω²

   
   
   

   4. - 4

      16 + ω²

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: A

   

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40. The wave for m that results from addition of 10 sinωt, 5 sin2ωt, 3.33 sin3ωt, 2.5 sin 4ωt, 2 sin 5ωt, 1.66 sin 6ωt, 1.43 sin 7ωt, 1.25 sin 8ωt and 1.11 sin9ωt is

1. 1. a saw tooth waveform of a radian frequency (ω) having a finite average value.

   
   
   

   2. a saw tooth waveform of radian frequency (ω) with zero average value.

   
   
   

   3. a square waveform of radian frequency (ω)

   
   
   

   4. a complex waveform

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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