1
GATE ECE 2023
Numerical
+2
-0

Let X(t) be a white Gaussian noise with power spectral density $$\frac{1}{2}$$W/Hz. If X(t) is input to an LTI system with impulse response $$e^{-t}u(t)$$. The average power of the system output is ____________ W (rounded off to two decimal places).

Your input ____
2
GATE ECE 2022
Numerical
+2
-0

Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), as shown in the figure.

GATE ECE 2022 Communications - Random Signals and Noise Question 7 English

Consider a 1 bit quantizer that maps positive samples to value $$\alpha$$ and others to value $$\beta$$. If $$\alpha$$* and $$\beta$$* are the respective choices for $$\alpha$$ and $$\beta$$ that minimize the mean square quantization error, then ($$\alpha$$* $$-$$ $$\beta$$*) = ___________ (rounded off to two decimal places).

Your input ____
3
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
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 $$f$$ is in Hertz $$(Hz)$$. The random process $$X(t)$$ is input to an ideal low pass filter with the frequency response $$$H\left( f \right) = \left\{ {\matrix{ {1,} & {\left| f \right| \le {1 \over 2}Hz} \cr {0,} & {\left| f \right| > {1 \over 2}Hz} \cr } } \right.$$$

As shown in Figure (b). The output of the low pass filter is $$y(t)$$.

GATE ECE 2017 Set 1 Communications - Random Signals and Noise Question 28 English 1 GATE ECE 2017 Set 1 Communications - Random Signals and Noise Question 28 English 2

Let $$E$$ be the expectation operator and consider the following statements :
$$\left( {\rm I} \right)$$ $$E\left( {X\left( t \right)} \right) = E\left( {Y\left( t \right)} \right)$$
$$\left( {{\rm I}{\rm I}} \right)$$ $$\,\,\,\,\,\,\,\,E\left( {{X^2}\left( t \right)} \right) = E\left( {{Y^2}\left( t \right)} \right)$$
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\,$$ $$\,\,\,\,\,\,E\left( {{Y^2}\left( t \right)} \right) = 2$$

Select the correct option:

A
only $${\rm I}$$ is true
B
only $${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ are true
C
only $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ are true
D
only $${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ are true
4
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
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-amplifier that has a noise figure of 2dB and an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise temperature Te for the amplifier and the noise power Pao at the output of the preamplifier, respectively, are
A
$${T_e} = 169.36K\,\,\,$$ and $${P_{ao}} = 3.73 \times {10^{ - 10}}\,\,W$$
B
$${T_e} = 170.8K\,\,\,$$ and $${P_{ao}} = 4.56 \times {10^{ - 10}}\,\,W$$
C
$${T_e} = 182.5K\,\,\,$$ and $${P_{ao}} = 3.85 \times {10^{ - 10}}\,\,W$$
D
$${T_e} = 160.62K\,\,\,$$ and $${P_{ao}} = 4.6 \times {10^{ - 10}}\,\,W$$
GATE ECE Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12