Download Goa University BA LLB-5 Years 2016 Oct 6th Semester Labour Law I Question Paper

Code: 13A05305

B.Tech II Year I Semester (R13) Supplementary Examinations June 2017

SIGNALS & SYSTEMS

(Common to ECE and EIE)

Time: 3 hours Max. Marks: 70

Answer all five units by choosing one question from each unit (5 x 14 = 70 Marks)

UNIT – I

1. (a) Define signal. Explain various types of signals with examples.

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

   1. x(t) = cos(t) + sin(v2t)
   2. x[n] = cos(pn/4) + sin(pn/6)

   OR

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2. (a) Define system. Explain various types of systems with examples.

   (b) Determine whether the following system is linear, time-invariant, causal and stable. y(t) = x(t) + tx(t-3)

UNIT – II

3. (a) State and prove the following properties of Fourier Transform:

   1. Time Shifting

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   2. Convolution in Time domain

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

   OR

4. (a) Explain about Dirichlet’s conditions for existence of Fourier series.

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   (b) Find the exponential Fourier series for the function x(t) = A for 0 < t < T/2 and x(t) = -A for T/2 < t < T.

UNIT – III

5. (a) Define Hilbert Transform. Explain properties of Hilbert Transform.

   (b) Find the Hilbert Transform of x(t) = cos ?t.

   OR

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6. (a) Explain the concept of pre-envelope and complex envelope representation of band pass signals.

   (b) Consider the signal x(t) = 10 cos(2000pt) cos(8000pt). Find:

   1. Spectrum of x(t)
   2. Spectrum of pre-envelope x+(t)

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UNIT – IV

7. (a) State and prove sampling theorem for band limited signals.

   (b) Explain the effects of under sampling.

   OR

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8. (a) Define the terms:

   1. Autocorrelation
   2. Cross correlation

   (b) Find the autocorrelation of x(t) = Arect(t/T).

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UNIT – V

9. (a) Define probability, conditional probability and statistical independence.

   (b) Find the mean and variance of uniform random variable.

   OR

10. (a) Explain the properties of power spectral density.

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    (b) Find the power spectral density of x(t) = Acos(?₀t + ?), where ? is a random variable uniformly distributed in the interval (-p, p).

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