1
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral density $${{{N_0}} \over 2}$$. The received signal is passed through a filter with impulse response h(t). Let $${E_s}$$ and $${E_n}$$ denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter $$\left( {SN{R_{\max }}} \right)$$, which of the following holds?
A
$${E_s} = \,{E_h};\,\,SN{R_{\max }} = \,{{2{E_s}} \over {{N_0}}}$$
B
$${E_s} = \,{E_h};\,\,SN{R_{\max }} = \,{{{E_s}} \over {2{N_0}}}$$
C
$${E_s} > \,\,{E_h};\,\,SN{R_{\max }} > \,\,{{2{E_s}} \over {{N_0}}}$$
D
$${E_s} < \,\,{E_h};\,\,SN{R_{\max }} = \,\,{{2{E_h}} \over {{N_0}}}$$
2
GATE ECE 2016 Set 1
Numerical
+2
-0
The open-loop transfer function of a unity-feedback control system is $$$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$ For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is __________.
Your input ____
3
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation.

X: The system is stable …
Y: The system is unstable …
Z: The test breaks down …

P: … when all elements are positive
Q: … when any one element is zero
R: … when there is a change in sign of coefficients

A
X→P, Y→Q, Z→R
B
X→Q, Y→P, Z→R
C
X→R, Y→Q, Z→P
D
X→P, Y→R, Z→Q
4
GATE ECE 2016 Set 1
Numerical
+2
-0
The open-loop transfer function of a unity-feedback control system is $$$G\left(s\right)=\frac K{s^2+5s+5}$$$ The value of K at the breakaway point of the feedback control system's root-locus plot is _____________
Your input ____
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