51. The inverse transform of
    is

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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52. The fourier transform of the function sgn(t) defined in the figure is
    

1. 1. - 2

      jω

   
   
   

   2. 4

      jω

   
   
   

   3. 2

      jω

   
   
   

   4. 1	+ 1
      jω

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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53. X[k] is shown in the figure below
    

1. 1. 2cos		6π	n -	π
      		7		2

   
   
   

   2. 2sin		6π	n -	π
      		7		2

   
   
   

   3. 2cos		6π	n +	π
      		7		2

   
   
   

   4. 2sin		6π	n +	π
      		7		2

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: A

   

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54. The determine-time Fourier-coefficients X[k] for
    

    X[n] = 2sin		4π	n		+ cos		4π	n		+ 1 will be
    		19					19

1. 1. - jδ[k + 2] + jδ[k - 2] +	1	+ [k + 5] +	1	δ[k - 5] + δ [k]
      	2		2

   
   
   

   2. - jδ[k + 2] + jδ[k - 2] +	1	+ [k + 5] +	1	δ[k - 5] + 1
      	2		2

   
   
   

   3. - jδ[k - 2] + jδ[k + 2] +	1	+ [k - 5] +	1	δ[k + 5] + δ[k]
      	2		2

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   x[n] = 2 sin		4π	n		+ cos		10 π	n		+ 1
   		19					19

   
   

   =	1		ej(4π/19)n - e-j(4π/19)n		+	1		ej(10π/19)n - e-j(10π/19)n		+ 1
   	j					2

   
   

   Correct Option: C

   x[n] = 2 sin		4π	n		+ cos		10 π	n		+ 1
   		19					19

   
   

   =	1		ej(4π/19)n - e-j(4π/19)n		+	1		ej(10π/19)n - e-j(10π/19)n		+ 1
   	j					2

   
   

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55. For the waveform for one period shown in the figure below, the trigonometric fourer series will be
    

1. 1. A	+	2A	(sint -	1	sin 3t +	1	sin 5t...........)
      2		π		3		5

   
   
   

   2. A	+	2A	(cos t -	1	cos 2t +	1	cos 3t...........)
      2		π		2		3

   
   
   

   3. A	+	2A	(cos t -	1	cos 3t +	1	cos 5t...........)
      2		π		3		5

   
   
   

   4. A	+	2A	(sin t + cos t +	1	sin 3t +	1	cos 3t...........)
      2		π		3		3

   
   
   

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1. View Hint View Answer Discuss in Forum

   x(t) is even. So it contain cosine terms only. It also have half wave symmetry if A/2 is subtracted. So it contains only odd harmonics.

   Correct Option: C

   x(t) is even. So it contain cosine terms only. It also have half wave symmetry if A/2 is subtracted. So it contains only odd harmonics.

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