1
GATE ECE 2014 Set 3
Numerical
+2
-0
A real band-limited random process $$X( t )$$ has two -sided power spectral density
$$${S_x}\left( f \right) = \left\{ {\matrix{
{{{10}^{ - 6}}\left( {3000 - \left| f \right|} \right)Watts/Hz} & {for\left| f \right| \le 3kHz} \cr
0 & {otherwise} \cr
} } \right.$$$
Where f is the frequency expressed in $$Hz$$. The signal $$X( t )$$ modulates a carrier cos $$16000$$ $$\pi t$$ and the resultant signal is passed through an ideal band-pass filter of unity gain with centre frequency of $$8kHz$$ and band-width of $$2kHz$$. The output power (in Watts) is ______.
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2
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
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 defined as $$Y(t) = X(2t - 1)$$, the power spectral density $${S_y}\left( f \right)$$ is
.
3
GATE ECE 2014 Set 3
Numerical
+2
-0
Let $${X_1},\,{X_2},$$ and $${X_3}$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,\,1} \right]$$. The probability $$P\left\{ {{X_1} + {X_2} \le {X_3}} \right\}$$ is ___________ .
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4
GATE ECE 2014 Set 2
Numerical
+2
-0
The power spectral density of a real stationary random process X(t) is given by
$$${S_x}\left( f \right) = \left\{ {\matrix{
{{1 \over W},\left| f \right| \le W} \cr
{0,\left| f \right| > W} \cr
} } \right.$$$
The value of the expectation
$$$E\left[ {\pi X\left( t \right)X\left( {t - {1 \over {4W}}} \right)} \right]$$$
is ---------------.
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Questions Asked from Random Signals and Noise (Marks 2)
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GATE ECE 2024 (2)
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GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Communications
Electromagnetics
General Aptitude