Download AKTU B-Tech 6th Sem 2014-2015 Power System Analysis 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) Define signals and systems. How are signals classified? Explain.
   (b) Check whether the following signals are periodic or not. If periodic find the fundamental period.
   (i) x(t) = cos(t) + sin(v2t)
   (ii) x(t) = cos(2t) + sin(3t)

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   OR

2. (a) Define unit step, ramp, impulse and exponential signals. Give their mathematical representation and sketch them.
   (b) Determine whether the following system is linear, causal, time invariant and stable.
   (i) y(t) = x(t) + tx(t-1)
   

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   (ii) y(t) = x(t) + x²(t)

3. (a) State and prove the following properties of Fourier transform.
   (i) Time shifting
   (ii) Convolution in time domain
   

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   (b) Find the Fourier transform of x(t) = e^-at u(t).

   OR

4. (a) Explain about Dirichlet's conditions for Fourier series.
   (b) Find the exponential Fourier series for the signal x(t) = Acos(?₀t).

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5. (a) Define convolution. Explain the properties of convolution.
   (b) Find the convolution of the signals x(t) = e^-at u(t) and h(t) = e^-bt u(t).

   OR

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6. (a) Explain about the detection of signals in the presence of noise.
   (b) Find the autocorrelation of the signal x(t) = Acos(?₀t).

7. (a) State and prove sampling theorem.
   (b) Explain about flat top sampling.

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   OR

8. (a) Explain about aliasing effect.
   (b) Explain about signal reconstruction through holding operation.

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9. (a) Find the Laplace transform of x(t) = e^-at u(t).
   (b) State and prove properties of Laplace transforms.

   OR

10. (a) Find the inverse Laplace transform of X(s) = 1/(s(s+1)).
    

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    (b) Explain the relation between Laplace transform and Fourier transform.

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