11. Which of the following cannot be the Fourier series expansion of a periodic signal?

1. 1. x(t) = 2cos t + 3 cos 3t

   
   
   

   2. x(t) = 2cos πt + 7 cos t

   
   
   

   3. x(t) = cos t + 0.5

   
   
   

   4. x(t) = 2cos 1.5πt + sin 3.5πt

   
   
   

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1. View Hint View Answer Discuss in Forum

   x(t) = 2cos πt + 7 cost, does not satisfy the Dirichlet condition, therefore, it can't be expanded as Fourier series.

   Correct Option: B

   x(t) = 2cos πt + 7 cost, does not satisfy the Dirichlet condition, therefore, it can't be expanded as Fourier series.

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12. Consider the voltage waveform shown in the figure. The equation for V(t) is
    

1. 1. u (t – 1) + u (t – 2) + u (t – 3)

   
   
   

   2. u (t – 1) + 2u (t – 2) + 3u (t – 3)

   
   
   

   3. u (t) + u (t – 1) + u (t – 2) + u (t – 4)

   
   
   

   4. u (t– 1) + u (t – 2) + u (t – 3) – 3u (t – 4)

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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13. A periodic function f(t) has the exponential series
    

    ƒ(t) =

    A

    +

    2A

    +

    e-j3ω

    +

    e-jω

    +

    ejω

    +

    ej3ω

    .........

    2

    π²

    (- 3)²

    (- 1)²

    1²

    3²

    
    The trigonometric form of the series is

1. 1. ƒ(t) =	A	+	2A	Σ	cos k ω0t	for all integers
      	2		π		k²

   
   
   

   2. ƒ(t) =	A	+	2A	Σ	cos k ω0t	for k odd
      	2		π²		k²

   
   
   

   3. ƒ(t) =	A	+	4A	Σ	cos k ω0t	for k odd
      	2		π²		k²

   
   
   

   4. ƒ(t) =	A	+	4A	Σ	cos k ω0t	for k even
      	2		π²		k²

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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14. The fourier series of the periodic function ƒ(t) shown in the figure below has coefficients a_k, b_k. The series has
    

1. 1. both cosine and sine terms but only for odd values of k

   
   
   

   2. only cosine terms for odd values of k

   
   
   

   3. only sine terms for odd values of k

   
   
   

   4. a constant and sine terms for odd values of k

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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15. The amplitude and phase spectr a for the harmonics of a periodic signal of time period shown in the figure below, are
    
    
    
    
    

1. 1. cos

      2πt -

      π

      + 0.75 cos

      6πt +

      π

      + 0.1 cos

      10πt +

      π

      ...............

      4

      2

      6

   
   
   

   2. cos

      t

      -

      π

      + 0.75 cos

      t

      +

      π

      + 0.1 cos

      t

      +

      π

      ...............

      2π

      4

      6π

      2

      10π

      6

   
   
   

   3. cos		2πt -	π		+ 0.75 cos		6πt +	π		+ 0.1 cos		10πt +	π	.	1		...............
      			4					2					6		6

   
   
   

   4. - cos

      2πt -

      π

      + 0.75 cos

      6πt +

      π

      + 0.1 cos

      10πt +

      π

      ...............

      4

      2

      6

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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