GATE ECE 2011 | Random Signals and Noise Question 30 | Communications

GATE ECE 2011

MCQ (Single Correct Answer)

-0.6

X(t) is a stationary random process with autocorrelation function R_x$$\left( \tau \right)$$= exp$$\left( { - \pi {\tau ^2}} \right)$$. This process is passed through the system shown below. The power spectral density of the output process Y(t) is GATE ECE 2011 Communications - Random Signals and Noise Question 45 English

GATE ECE 2011 Communications - Random Signals and Noise Question 45 English

$$\left( {4\,{\pi ^2}{f^2} + 1} \right)\,\exp \left( { - \pi {f^2}} \right)$$

$$\left( {4\,{\pi ^2}{f^2} - 1} \right)\,\exp \left( { - \pi {f^2}} \right)$$

$$\left( {4\,{\pi ^2}{f^2} + 1} \right)\,\exp \left( { - \pi f} \right)$$

$$\left( {4\,{\pi ^2}{f^2} - 1} \right)\,\exp \left( { - \pi f} \right)$$

GATE ECE 2010

MCQ (Single Correct Answer)

-0.6

X(t) is a stationary process with the power spectral density S_x(f) > 0 for all f. The process is passed through a system shown below. GATE ECE 2010 Communications - Random Signals and Noise Question 46 English

GATE ECE 2010 Communications - Random Signals and Noise Question 46 English

Let S_y(f) be the power spectral density of Y(t). Which one of the following statements is correct?

S_y(f) > 0 for all f

S_y(f) > 0 for $$\left| f \right|$$ > 1 kH

S_y(f) > 0 for f = nf₀, f₀ = 2kHz, n any integer

S_y(f) > 0 for f = (2n + 1)f₀, f₀ = 1 kHz, n any integer

GATE ECE 2008

MCQ (Single Correct Answer)

-0.6

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

K f_c

K $$\pi $$ f_c

$$\infty $$

GATE ECE 2006

MCQ (Single Correct Answer)

-0.6

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 t_s = 0.03 msec. The samples so obtained would be

correlated

statistically independent

uncorrelated

orthogonal

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