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GATE EC : Communications Champion Quiz 1
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Question 1
The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X2(t)] and |E[X(t)]|, respectively, are
Question 2
The force on a point charge + q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity 
is
isQuestion 3
X(t) is a stationary random process with autocorrelation function 
. This process is passed through the system shown below. The power spectral density of the output process Y(t) is
. This process is passed through the system shown below. The power spectral density of the output process Y(t) is Question 4
A low-pass filter having a frequency response H(jω) = A(ω) e jφ(ω) does not produce any phase distortion if
Question 5
The signal cos 
is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response 
. The filter output is
is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response . The filter output is Question 6
A zero mean white Gaussian noise having power spectral density
is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t = 4 is
is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t = 4 is Question 7
The efficiency of Huffman code is linearly proportional to
Question 8
Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3dB cut-off frequency of fc. The noise power at the filter output is
Question 9
A random binary wave y(t) is given by
Where p(t) = u(t) – u(t –T), u(t) is the unit function and f is an independent random variable with uniform distribution in [0, T]. The sequence {Xn} consists of independent and identically distributed binary valued random variables with P{Xn = +1} = P{Xn = –1} = 0.5 for each n.
The value of autocorrelation
equals______.
Where p(t) = u(t) – u(t –T), u(t) is the unit function and f is an independent random variable with uniform distribution in [0, T]. The sequence {Xn} consists of independent and identically distributed binary valued random variables with P{Xn = +1} = P{Xn = –1} = 0.5 for each n.
The value of autocorrelation
equals______.Question 10
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 period ts = 0.03 m sec. the samples so obtained would be
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Jun 2ESE & GATE EC
