GATE ECE
Communications
Random Signals and Noise
Previous Years Questions

## Marks 1

The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure. Statement I : The system is necessarily a pure del...
Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), ...
Consider the random process x(t) = U + Vt. Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between ...
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, th...
Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X, Y] is less than 1/2 is
The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X^2}\,(t)} \right]$$ and $$E\,\l... If E denotes expectation, the variance of a random variable X is given by The PDF of a Gaussian random variable X is given by$${p_x}(x) = \,{1 \over {3\sqrt {2\pi } }}\,\exp \,[ - \,{(x - 4)^2}/18]$$. The probability of th... The amplitude spectrum of a Gaussian pulse is The ACF of a rectangular pulse of duration T is The probability density function of the envelope of narrow band Gaussian noise is A probability density function is given by$$p(x) = \,K\,\,\exp \,\,( - \,{x^2}/2),\,\, - \,\infty \, < \,x < \,\infty $$. The value of K shou... For a narrow band noise with Gaussian quadrature and inphase components, the probability density function of its enveolope will be ## Marks 2 Let$$X(t)$$be a wide sense stationary random process with the power spectral density$${S_x}\left( f \right)$$as shown in figure (a), where$$f$$i... An information source generates a binary sequence$$\left\{ {{\alpha _n}} \right\}.{\alpha _n}$$can take one of the two possible values −1 and +1 wit... Consider random process$$X(t) = 3V(t) - 8$$, where$$V(t)$$is a zero mean stationary random process with autocorrelation$${R_v}\left( \tau \r...
A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrelation function of $$X(t)$$ is...
An antenna pointing in a certain direction has a noise temperature of 50K. The ambient temperature is 290K. The antenna is connected to a pre-amplifie...
A zero mean white Gaussian noise having power spectral density $${{{N_0}} \over 2}$$ is passed through an $$LTI$$ filter whose impulse response $$h(...$$\mathop {\left\{ {{X_n}} \right\}}\nolimits_{n = - \infty }^{n = \infty } $$is an independent and identically distributed (i.i.d) random process w... Let$$X \in \left\{ {0,1} \right\}$$and$$Y \in \left\{ {0,1} \right\}$$be two independent binary random variables. If$$P\left( {X\,\, = 0} \right)...
A random binary wave $$y(t)$$ is given by $$y\left( t \right) = \sum\limits_{n = - \infty }^\infty {{X_n}p\left( {t - nT - \phi } \right)}$$$whe... Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$. If $$Y(t)$$ is the process de... A real band-limited random process $$X( t )$$ has two -sided power spectral density $${S_x}\left( f \right) = \left\{ {\matrix{ {{{10}^{ - 6}}\lef... Let$${X_1},\,{X_2},$$and$${X_3}$$be independent and identically distributed random variables with the uniform distribution on$$\left[ {0,\,1} \ri... The power spectral density of a real stationary random process X(t) is given by $${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f... Consider a random process$$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$where the random phase$$\varphi $$is uni... Let$$Q\left( {\sqrt y } \right)$$be the BER of a BPSK system over an AWGN channel with two - sided noise power spectral density N0/2. The parameter ... Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. ... Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. ... X(t) is a stationary random process with autocorrelation function Rx$$\left( \tau \right)$$= exp$$\left( { - \pi {\tau ^2}} \right)$$. This process i... X(t) is a stationary process with the power spectral density Sx(f) > 0 for all f. The process is passed through a system shown below. Let Sy(f... Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-dB cut-off frequency of fc. The... A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling pe... The following question refer to wide sense stationary stochastic process: It is desired to generate a stochastic process (as voltage process) wi... The following question refer to wide sense stationary stochastic process: The parameters of the system obtained in Q. 12 would be An output of a communication channel is a random variable 'V' with the probability density function as shown in the figure. The mean square value of '... Noise with uniform power spectral density of N0 W/Hz is passed through a filter H(ω ) = 2exp (-jωtd) followed by an ideal low pass filter of bandwidt... A 1 mW video signal having a bandwidth of 100 MHz is transmitted to a receiver through a cable that has 40 dB loss. If the effective one-sided noise s... If the variance$$\sigma _d^2$$of d(n) = x(n - 1) is one-tenth the variance$$\sigma _x^2$$of a stationary zero-mean discrete-time signal x(n), then... For a random variable 'X' following the probability density function, p (x), shown in figure, the mean and the variance are, respectively. ... Two resistors$$\,{R_1}$$and$$\,{R_2}$$(in ohms) at temperatures$${T_1}{}^ \circ K$$and$${T_2}{}^ \circ K$$respectively, are connected in serie... Zero mean Gaussian noise of variance N is applied to a half wave rectifier. The mean squared value of the rectifier output will be: A part of a communication system consists of an amplifier of effective noise temperature,$$Te = \,\,21\,\,{}^ \circ K\,$$, and a gain of 13 dB, follo... White Gaussian noise is passed through a linear narrow band filter. The probability density function of the envelope of the noise at the filter outpu... The variance of a random variable X is$$\sigma _x^2\,.$$Then the variance of - kx (where k is a positive constant ) is ## Marks 4 White Gaussian noise with zero mean and double - sided power spectral density$$\eta /2$$is the input$$x(t)$\$ to a linear system with impulse respon...
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