Download AKTU B-Tech 8th Sem 2015-16 051 EME 051 Operations Research Question Paper

Code: 13A05305

B.Tech II Year I Semester (R13) Supplementary Examinations June 2022

SIGNALS AND SYSTEMS

(Electronics and Communication Engineering)

Time: 3 hours Max. Marks: 70

Answer all FIVE Questions

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All questions carry equal marks

1. Define signal and system. Explain different types of signals and systems with examples.

   OR

   Determine whether the system described by the following input-output relations are linear, time-invariant, causal and stable:

   1. y(t) = x(t) + 3

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   2. y(t) = t x(t)

2. Derive the expression for trigonometric Fourier series and explain the properties of Fourier series.

   OR

   Determine the Fourier transform of the following signals:

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   1. x(t) = e^-at u(t)
   2. x(t) = t e^-at u(t)

3. State and prove sampling theorem for band limited signals. Explain the effects of under sampling.

   OR

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   Explain the concept of signal reconstruction through interpolation.

4. Define Laplace transform and ROC. Explain the properties of Laplace transform.

   OR

   Find the inverse Laplace transform of the following:

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   1. X(s) = 1 / (s² + 3s + 2), ROC: -2 < Re{s} < -1
   2. X(s) = s / (s² + 4), ROC: Re{s} > 0

5. Define Z-transform. State and prove the properties of Z-transform.

   OR

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   Determine the Z-transform of the following sequences:

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

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