Random Processes - Communications - Electronics & Communication Engineering Previous Year Questions

1

2007 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2007

If \(R(\tau)\) is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is NOT true?

A

\(R(\tau) = R(-\tau)\)

B

\(|R(\tau)| \leq R(0)\)

C

\(R(\tau) = -R(-\tau)\)

D

The mean square value of the process is \(R(0)\)

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2

2007 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2007

If \(S(f)\) is the power spectral density of a real, wide-sense stationary random process, then which of the following is ALWAYS true?

A

\(S(0) \geq S(f)\)

B

\(S(f) \geq 0\)

C

\(S(-f) = -S(f)\)

D

\(\int_{-\infty}^{\infty} S(f) df = 0\)

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3

2007 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2007

The values of a and b are

A

a = 1/6 and b = 1/12

B

a = 1/5 and b = 3/40

C

a = 1/4 and b = 1/16

D

a = 1/3 and b = 1/24

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4

2008 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2008

Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3 dB cut-off frequency of f_c. The noise power at the filter output is

A

K

B

K f_c

C

K π f_c

D

∞

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5

2009 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2009

If the power spectral density of stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is

A

A rectangular pulse

B

A triangular pulse

C

A half-cosine pulse

D

A sinc pulse

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6

2011 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2011

X(t) is a stationary random process with autocorrelation function $R_X(\tau) = \exp(-\pi\tau^2)$. This process is passed through the system shown below. The power spectral density of the output process Y(t) is

A

$(4\pi^2 f^2 + 1)\exp(-\pi f^2)$

B

$(4\pi^2 f^2 - 1)\exp(-\pi f^2)$

C

$(4\pi^2 f^2 + 1)\exp(-\pi f)$

D

$(4\pi^2 f^2 - 1)\exp(-\pi f)$

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7

2012 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2012

The power spectral density of a real process \(X(t)\) for positive frequencies is shown below. The values of \(E[X^2(t)]\) and \(|E[X(t)]|\), respectively, are

A

6000/π, 0

B

6400/π, 0

C

6400/π, 20/π√2

D

6000/π, 20/π√2

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8

2018 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2018

A random variable \(X\) takes values \(-0.5\) and \(0.5\) with probabilities \(\frac{1}{4}\) and \(\frac{3}{4}\), respectively. The noisy observation of \(X\) is \(Y = X + Z\), where \(Z\) has uniform probability density over the interval \((-1, 1)\). \(X\) and \(Z\) are independent. If the MAP rule based detector outputs \(\hat{X}\) as

\[ \hat{X} = \begin{cases} -0.5, & Y < \alpha \\ 0.5, & Y \ge \alpha, \end{cases} \]

then the value of \(\alpha\) (accurate to two decimal places) is ________.

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9

2019 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2019

Let a random process Y(t) be described as Y(t) = h(t) * X(t) + Z(t), where X(t) is a white noise process with power spectral density S_X(f) = 5 W/Hz. The filter h(t) has a magnitude response given by |H(f)| = 0.5 for -5 ≤ f ≤ 5, and zero elsewhere. Z(t) is a stationary random process, uncorrelated with X(t), with power spectral density as shown in the figure. The power in Y(t), in watts, is equal to ___________ W (rounded off to two decimal places).

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10

2023 · Electronics & Communication Engineering · Communications · Random Processes

Electronics & Communication Engineering (EC) 2023

For a real signal, which of the following is/are valid power spectral density/densities?

A

\(S_X(\omega) = \frac{2}{9 + \omega^2}\)

B

\(S_X(\omega) = e^{-\omega^2} \cos^2 \omega\)

C

D

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