1
GATE ECE 2015 Set 3
Numerical
+2
-0
A random binary wave $$y(t)$$ is given by $$$y\left( t \right) = \sum\limits_{n = - \infty }^\infty {{X_n}p\left( {t - nT - \phi } \right)} $$$

where $$p(t) = u(t) - u(t - T)$$, $$u(t)$$ is the unit step function and $$\phi $$ is an independent random variable with uniform distribution in $$[0, T]$$. The sequence $$\left\{ {{X_n}} \right\}$$ consists of independent and identically distributed binary valued random variables with $$P\left\{ {{X_n} = + 1} \right\} = P\left\{ {{X_n} = - 1} \right\} = 0.5$$ for each $$n$$.

The value of the autocorrelation $${R_{yy}}\left( {{{3T} \over 4}} \right)\underline{\underline \Delta } E\left[ {y\left( t \right)y\left( {t - {{3T} \over 4}} \right)} \right]\,\,$$


equals ------------ .
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2
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
The impulse response of an LTI system can be obtained by
A
differentiating the unit ramp response
B
differentiating the unit step response
C
integrating the unit ramp response
D
integrating the unit step response
3
GATE ECE 2015 Set 3
Numerical
+2
-0
The characteristic equation of an LTI system is given by
F(s) = s5 + 2s4 +3s3 + 6s2 - 4s - 8 = 0.The number of roots that lie strictly in the left half s-plane is _____.
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4
GATE ECE 2015 Set 3
Numerical
+2
-0
For the system shown in the figure, s = –2.75 lies on the root locus if K is_____. GATE ECE 2015 Set 3 Control Systems - Root Locus Diagram Question 11 English
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