16. The periodic function shown in the figure below
    

1. 1. is even and has no half-wave symmetry

   
   
   

   2. is odd and has no half-wave symmetry

   
   
   

   3. is even and has half-wave symmetry

   
   
   

   4. is odd and has half-wave symmetry

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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17. The Fourier series of the square wave given by the following figure where given a_k, b_k are nonzero, is
    

1. 1. a₀ + a₁ cos ω₀ t + a₂ 2 cos ω₀ t + .....

   
   
   

   2. b₁ sin ω₀ t + b₂ 2sin ω₀ t + b₃ + 2 sin ω₀ t + .....

   
   
   

   3. a₁ cos ω₀ t + a₃ cos 3 ω₀ t + a₅ cos 5 ω₀ t +.....

   
   
   

   4. b₁ sin ω₀ t + b₃ sin 3 ω₀ t + b₅ + sin 5 ω₀ t + .....

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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18. 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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19. 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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20. A periodic signal x(t) of period T_o is given by
    

    x(t) =		1,		|t| < T1
    		0,		T1 < |t| < T0/2

    
    The d.c. component of x(t) is

1. 1. T1

      T0

   
   
   

   2. T1

      2T0

   
   
   

   3. 2T1

      T0

   
   
   

   4. T0

      T1

   
   
   

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1. View Hint View Answer Discuss in Forum

   The periodic signal X(t) of period T₀
   X(t) = 1,      | t| < T₁
   X(t) = 0,      T₁ < | t| < T₀/2
   

   Correct Option: C

   The periodic signal X(t) of period T₀
   X(t) = 1,      | t| < T₁
   X(t) = 0,      T₁ < | t| < T₀/2
   

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