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]$$. The probability of th... The amplitude spectrum of a Gaussian pulse is The probability density function of the envelope of narrow band Gaussian noise is The ACF of a rectangular pulse of duration T is A probability density function is given by$$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$$i... A wide sense stationary random process$$X(t)$$passes through the$$LTI$$system shown in the figure. If the autocorrelation function of$$X(t)$$is... An information source generates a binary sequence$$\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...
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...
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