201. If the function
     H₁(z) = (1 + 1.5z^{– 1} – z^{– 2}) and H₁(z) = (z² + 1.5z – 1) then—

1. 1. the poles and zeros of the functions will be the same

   
   
   

   2. the poles of the functions will be identical but not zeros

   
   
   

   3. the zeros of the functions will be identical but not the poles
      

   
   
   

   4. neither the poles nor the zeros of the two functions will be identical

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given H₁(z) = 1 + 1·5z^{– 1} – z^{– 1}…(A)
   and H₂(z) = z² + 1·5z – 1 …(B)
   Equation (A) can be written as
   

   H1(z) =	z2 + 1·5z – 1
   	z2

   
   poles at z = 0, 0
   zeros are z² + 1·5z – 1 = 0
   or 2z² + 3z – 2 = 0
   or 2z² + 4z – z – 2 = 0
   2z(z + 2) – 1(z + 2) = 0
   (2z – 1) (z + 2) = 0
   

   z =	1	and – 2
   	2

   
   However, in equation (B)
   H₂(z) = z² + 1·5z – 1
   There is no poles
   zeros are at z² + 1·5z – 1 = 0
   

   or z =	1	and – 2
   	2

   
   Hence, the alternative (C) is the correct choice.

   Correct Option: C

   Given H₁(z) = 1 + 1·5z^{– 1} – z^{– 1}…(A)
   and H₂(z) = z² + 1·5z – 1 …(B)
   Equation (A) can be written as
   

   H1(z) =	z2 + 1·5z – 1
   	z2

   
   poles at z = 0, 0
   zeros are z² + 1·5z – 1 = 0
   or 2z² + 3z – 2 = 0
   or 2z² + 4z – z – 2 = 0
   2z(z + 2) – 1(z + 2) = 0
   (2z – 1) (z + 2) = 0
   

   z =	1	and – 2
   	2

   
   However, in equation (B)
   H₂(z) = z² + 1·5z – 1
   There is no poles
   zeros are at z² + 1·5z – 1 = 0
   

   or z =	1	and – 2
   	2

   
   Hence, the alternative (C) is the correct choice.

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202. The trigonometric Fourier series expansion of an odd function shall have—

1. 1. only sine terms

   
   
   

   2. only cosine terms

   
   
   

   3. odd harmonics of both sine and cosine terms

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Odd function will have only sine terms.

   Correct Option: A

   Odd function will have only sine terms.

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203. A function can sampled at Nyquist rate f_s = 2f₀. The function can be recovered from its samples only if it is a/an—

1. 1. Sine wave of frequency f₀

   
   
   

   2. Triangular wave of fundamental frequency f₀

   
   
   

   3. Periodic square wave of fundamental frequency f₀

   
   
   

   4. Unit step function

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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204. Frequency domain of a periodic triangular function is a—

1. 1. discrete sampling function

   
   
   

   2. discrete sinc function

   
   
   

   3. continuous sampling function

   
   
   

   4. continuous sampling square function

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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205. An impulse function consists, of—

1. 1. entire frequency range with same relative phase

   
   
   

   2. infinite bandwidth with linear phase variations

   
   
   

   3. pure d.c.

   
   
   

   4. large d.c. along with weak harmonics

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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