ANURAG GROUP OF INSTITUTIONS

(Autonomous)

B.Tech III Year I Semester (R18) Regular Examinations November / December - 2021

SIGNALS AND STOCHASTIC PROCESSES

Time: 3 Hours Max. Marks: 70

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PART A: 5 * 2 = 10 Marks

Answer all questions.

1. Define signal and classification of signals.
2. Define Fourier series.
3. Define and write properties of Fourier Transform.

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4. Define random variable.
5. Define cross correlation and auto correlation.

PART B: 4 * 15 = 60 Marks

Answer all questions. Each question carries 15 Marks.

1. a) Explain about elementary signals. [7M]

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   b) Determine whether the following signals are periodic or not. If periodic, find the fundamental period. [8M]

   1. x(t) = cos(t) + sin(2t)
   2. x(t) = cos(2πt) + sin(5πt)

   OR

   a) Explain about various operations on signals with examples. [7M]

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   b) Determine whether the following signal is periodic or not. If periodic, find the fundamental period. [8M]

   x(n) = cos(πn/4) + sin(πn/6)

2. a) Find the exponential Fourier series for the following signal. [7M]

   b) State and prove properties of Fourier series. [8M]

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   OR

   a) Explain about trigonometric Fourier series. [7M]

   b) Find the Fourier transform of the gate function defined by [8M]

   f(t) = A for -T/2 < t < T/2

   f(t) = 0 otherwise

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3. a) State and prove properties of Laplace transform. [7M]

   b) Find the Laplace transform of the function f(t) = e^-atu(t). [8M]

   OR

   a) State and prove properties of Z-transform. [7M]

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   b) Find the Z-transform of the function f(n) = aⁿu(n). [8M]

4. a) Define probability density function and write its properties. [7M]

   b) Two dice are thrown. Let X assign to each outcome (a, b) the value a + b. Determine the probability distribution of X. [8M]

   OR

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   a) Explain about Gaussian random variable. [7M]

   b) Find auto correlation function of X(t) = A cos(ωt + θ) where A and ω are constant and θ is uniformly distributed random variable in the range of (0, 2π). [8M]

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