Download AKTU B-Tech 5th Sem 2016-2017 Microprocessor Nec 503 Question Paper

Code: 13A05305

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

SIGNALS AND SYSTEMS

(Common to ECE and EIE)

Time: 3 hours Max. Marks: 70

Answer all FIVE Questions

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All Questions Carry Equal Marks

1. (a) Distinguish between energy and power signals with examples.

   (b) Determine whether the following signals are periodic or not. If periodic, find the fundamental period.

   1. $x(t) = cos(t) + sin(\sqrt{2}t)$
   2. $x(t) = cos(2\pi t) + sin(5\pi t)$

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   OR

2. (a) State and prove the properties of the Fourier series.

   (b) Find the exponential Fourier series for the signal $x(t) = Acos(\omega_0t)$.

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3. (a) Define Fourier transform. Derive the relation between Fourier transform and Fourier series.

   (b) Find the Fourier transform of $f(t) = e^{-at}u(t)$, a > 0.

   OR

4. (a) State and prove the properties of Fourier transforms.

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   (b) Determine the Fourier transform of the gate function.

5. (a) Define system. Explain the classification of systems with examples.

   (b) Discuss the concept of distortion less transmission through a system.

   OR

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6. (a) Define convolution. Explain the properties of convolution.

   (b) Find the convolution of $x(t) = e^{-at}u(t)$ and $h(t) = u(t)$.

7. (a) Define sampling theorem. Explain the types of sampling.

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   (b) What is aliasing? How can aliasing effect be reduced?

   OR

8. (a) Define the following:

   1. Natural sampling

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   2. Flat top sampling
   3. Instantaneous sampling

   (b) Explain the reconstruction of signal from its samples.

9. (a) Define Laplace transform. Explain the properties of Laplace transform.

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   (b) Find the Laplace transform of $f(t) = e^{-at}sin(\omega t) u(t)$.

   OR

10. (a) Explain the concept of ROC in Laplace transform.

    (b) Determine the inverse Laplace transform of $X(s) = \frac{1}{s(s+1)}$.

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