GATE ECE

Random Signals and Noise

Communications

(Past Years Questions)

Marks 1

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Consider the random process x(t) = U + Vt. Where U is a zero mean Gaussian random variable and V is a random variable ...
GATE ECE 2017 Set 2
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival ...
GATE ECE 2014 Set 4
Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X...
GATE ECE 2012
The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X...
GATE ECE 2012
If E denotes expectation, the variance of a random variable X is given by
GATE ECE 2007
The PDF of a Gaussian random variable X is given by $${p_x}(x) = \,{1 \over {3\sqrt {2\pi } }}\,\exp \,[ - \,{(x - 4)^2}...
GATE ECE 2001
The amplitude spectrum of a Gaussian pulse is
GATE ECE 1998
The ACF of a rectangular pulse of duration T is
GATE ECE 1998
The probability density function of the envelope of narrow band Gaussian noise is
GATE ECE 1998
A probability density function is given by $$p(x) = \,K\,\,\exp \,\,( - \,{x^2}/2),\,\, - \,\infty \, The value of K sh...
GATE ECE 1997
For a narrow band noise with Gaussian quadrature and inphase components, the probability density function of its enveolo...
GATE ECE 1995

Marks 2

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Let $$X(t)$$ be a wide sense stationary random process with the power spectral density $${S_x}\left( f \right)$$ as show...
GATE ECE 2017 Set 1
A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrel...
GATE ECE 2016 Set 3
An information source generates a binary sequence $$\left\{ {{\alpha _n}} \right\}.{\alpha _n}$$ can take one of the two...
GATE ECE 2016 Set 2
Consider random process $$X(t) = 3V(t) - 8$$, where $$V$$ $$(t)$$ is a zero mean stationary random process with autocorr...
GATE ECE 2016 Set 2
An antenna pointing in a certain direction has a noise temperature of 50K. The ambient temperature is 290K. The antenna ...
GATE ECE 2016 Set 1
A random binary wave $$y(t)$$ is given by $$$y\left( t \right) = \sum\limits_{n = - \infty }^\infty {{X_n}p\left( {t ...
GATE ECE 2015 Set 3
A zero mean white Gaussian noise having power spectral density $${{{N_0}} \over 2}$$ is passed through an $$ LTI $$ filt...
GATE ECE 2015 Set 2
$$\mathop {\left\{ {{X_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } $$ is an independent and identically distri...
GATE ECE 2015 Set 2
Let $$X \in \left\{ {0,1} \right\}$$ and $$Y \in \left\{ {0,1} \right\}$$ be two independent binary random variables. If...
GATE ECE 2015 Set 2
Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$....
GATE ECE 2014 Set 3
A real band-limited random process $$X( t )$$ has two -sided power spectral density $$${S_x}\left( f \right) = \left\{ {...
GATE ECE 2014 Set 3
Let $${X_1},\,{X_2},$$ and $${X_3}$$ be independent and identically distributed random variables with the uniform distri...
GATE ECE 2014 Set 3
The power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\ma...
GATE ECE 2014 Set 2
Consider a random process $$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$ where the ra...
GATE ECE 2014 Set 1
Let $$Q\left( {\sqrt y } \right)$$ be the BER of a BPSK system over an AWGN channel with two - sided noise power spectra...
GATE ECE 2014 Set 1
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for bot...
GATE ECE 2013
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for bot...
GATE ECE 2013
X(t) is a stationary random process with autocorrelation function Rx$$\left( \tau \right)$$= exp$$\left( { - \pi {\tau ...
GATE ECE 2011
X(t) is a stationary process with the power spectral density Sx(f) > 0 for all f. The process is passed through a syst...
GATE ECE 2010
Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-d...
GATE ECE 2008
A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then unif...
GATE ECE 2006
The following question refer to wide sense stationary stochastic process: It is desired to generate a stochastic p...
GATE ECE 2006
The following question refer to wide sense stationary stochastic process: The parameters of the system obtained in ...
GATE ECE 2006
Noise with uniform power spectral density of N0 W/Hz is passed through a filter H(ω ) = 2exp (-jωtd) followed by an ide...
GATE ECE 2005
An output of a communication channel is a random variable 'V' with the probability density function as shown in the figu...
GATE ECE 2005
A 1 mW video signal having a bandwidth of 100 MHz is transmitted to a receiver through a cable that has 40 dB loss. If t...
GATE ECE 2004
If the variance $$\sigma _d^2$$ of d(n) = x(n - 1) is one-tenth the variance $$\sigma _x^2$$ of a stationary zero-mean d...
GATE ECE 2002
For a random variable 'X' following the probability density function, p (x), shown in figure, the mean and the variance ...
GATE ECE 1992
Two resistors $$\,{R_1}$$ and $$\,{R_2}$$ (in ohms) at temperatures $${T_1}{}^ \circ K$$ and $${T_2}{}^ \circ K$$ respec...
GATE ECE 1991
Zero mean Gaussian noise of variance N is applied to a half wave rectifier. The mean squared value of the rectifier outp...
GATE ECE 1989
A part of a communication system consists of an amplifier of effective noise temperature, $$Te = \,\,21\,\,{}^ \circ K\,...
GATE ECE 1989
White Gaussian noise is passed through a linear narrow band filter. The probability density function of the envelope of...
GATE ECE 1987
The variance of a random variable X is $$\sigma _x^2\,.$$ Then the variance of - kx (where k is a positive constant ) is...
GATE ECE 1987

Marks 4

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White Gaussian noise with zero mean and double - sided power spectral density $$\eta /2$$ is the input $$x(t)$$ to a lin...
GATE ECE 1988

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