B.Tech II Year I Semester Examinations, December - 2018

SIGNALS AND SYSTEMS

Time: 3 hours Max. Marks: 75

Note: This question paper contains two parts A and B.

Part A is compulsory which carries 25 marks. Answer all questions in Part A.

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Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks.

PART - A (25 Marks)

1. 1. Define signal and system. (2M)
   2. What is the relationship between step and impulse function? (3M)
   3. Define Fourier series. (2M)
   4. Write the properties of Fourier transform. (3M)

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   5. Define Laplace transform. (2M)
   6. List the properties of ROC of Laplace transform. (3M)
   7. Define sampling theorem. (2M)
   8. What is aliasing? How can it be avoided? (3M)
   9. Define Z-transform. (2M)

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   10. State initial and final value theorem of Z-transform. (3M)

PART - B (50 Marks)

(Answer any one full question from each unit)

UNIT - I

1. Determine whether the following signals are periodic or not. If periodic determine the fundamental period.

   1. x(t) = 3cos(4t + p/3) (5M)

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   2. x(t) = cos t + sin v2 t (5M)

   OR

2. Check whether the systems described by the following input-output relations are

   1. y(t) = tx(t) (5M)

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   2. y(n) = x(-n+2) (5M)

   i) static or dynamic ii) linear or non-linear iii) causal or non-causal iv) time variant or invariant v) stable or unstable.

UNIT - II

1. State and prove properties of Fourier series.

   OR

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2. Find the Fourier transform of gate function and signum function.

UNIT - III

1. Find the Laplace transform of

   1. t sin at (5M)

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   2. t² e^-at u(t) (5M)

   OR

2. Find the inverse Laplace transform of the following

   1. X(s) = 1/(s+1)(s+2) (5M)

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   2. X(s) = s/(s²+4) (5M)

UNIT - IV

1. Explain about band limited signals and signal reconstruction.

   OR

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2. Explain about flat top sampling and natural sampling.

UNIT - V

1. State and prove properties of Z-transform.

   OR

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2. Determine the Z-transform of

   1. x(n) = aⁿ u(n) (5M)
   2. x(n) = -bⁿ u(-n-1) (5M)

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