141. Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in figure.
     
     Then Y(f) is—

1. 1. –	1	X		f		e– j2πf
      	2			2

   
   
   

   2. –	1	X		f		ej2πf
      	2			2

   
   
   

   3. – X		f		ej2πf
      		2

   
   
   

   4. – X		f		e– j2πf
      		2

   
   
   

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1. View Hint View Answer Discuss in Forum

   From fig. we see that y(t) is a compressed version of x(t). But in frequency domain it will be represented by expansion i.e., shifting of two unit left side.
   First shifting then
   
   Scaling and then
   
   Amplitude reflection i.e.,
   x(t) = – x(t)
   

   we get – X		f		e–j2πf
   		2

   Correct Option: D

   From fig. we see that y(t) is a compressed version of x(t). But in frequency domain it will be represented by expansion i.e., shifting of two unit left side.
   First shifting then
   
   Scaling and then
   
   Amplitude reflection i.e.,
   x(t) = – x(t)
   

   we get – X		f		e–j2πf
   		2

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142. The Fourier transform of V(t) = cos ω₀t is given by—

1. 1. V(f) =	1	δ(f – f0)
      	2

   
   
   

   2. V(f) =	1	δ(f + f0)
      	2

   
   
   

   3. V(f) =	1	[δ(f – f0) – δ(f + f0)]
      	2

   
   
   

   4. V(f) =	1	[δ(f – f0) + δ(f + f0)]
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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143. Match List-I {x(n)} with List-II {X(z)} and select the correct answer using the codes given below the Lists—
     

1. 1. A B C D
      2 4 3 1

   
   
   

   2. A B C D
      1 3 4 2

   
   
   

   3. A B C D
      1 4 3 2

   
   
   

   4. A B C D
      2 3 4 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   A. αn u(n) ←z→	1	, |z| > |α|
   	(1 – αz–1)

   
   

   B. - αn u(- n - 1) ←z→	1	, |z| < |α|
   	(1 – αz–1)

   
   

   c. – nαn u(- n - 1) ←z→	αz–1	, |z| < |α|
   	(1 – αz–1)

   
   

   D. nαn u(n) ←z→	αz–1	, |z| > |α|
   	(1 – αz–1)2

   
   Hence, alternative (D) is the correct choice.

   Correct Option: D

   A. αn u(n) ←z→	1	, |z| > |α|
   	(1 – αz–1)

   
   

   B. - αn u(- n - 1) ←z→	1	, |z| < |α|
   	(1 – αz–1)

   
   

   c. – nαn u(- n - 1) ←z→	αz–1	, |z| < |α|
   	(1 – αz–1)

   
   

   D. nαn u(n) ←z→	αz–1	, |z| > |α|
   	(1 – αz–1)2

   
   Hence, alternative (D) is the correct choice.

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144. A periodic triangular wave is shown in the figure. Its Fourier components will consist only of—
     
     
     

1. 1. all cosine terms

   
   
   

   2. all sine terms

   
   
   

   3. odd cosine terms

   
   
   

   4. odd sine terms

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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145. Convolution of x(t + 4) with impulse function δ(t – 6) is equal to—

1. 1. x(t – 10)

   
   
   

   2. x(t + 2)

   
   
   

   3. x(t – 2)

   
   
   

   4. x(t – 4)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the convolution of x(t + 4) and δ(t – 6) is y(t)
   y(t) = x(t + 4)^* δ(t – 6)
   

   	x(t)*δ(t) = x(t)
   	x(t)*δ(t + t 0) = x(t + t 0)

   
   or
   y(t) = x(t – 6 + 4)
   or
   y(t) = x(t – 2)
   Hence, alternative (C) in the correct choice.

   Correct Option: C

   Let the convolution of x(t + 4) and δ(t – 6) is y(t)
   y(t) = x(t + 4)^* δ(t – 6)
   

   	x(t)*δ(t) = x(t)
   	x(t)*δ(t + t 0) = x(t + t 0)

   
   or
   y(t) = x(t – 6 + 4)
   or
   y(t) = x(t – 2)
   Hence, alternative (C) in the correct choice.

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