GATE EC 2016 Question Paper (31-Jan-2016) (Shift 2)

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as



The range of $K$ for which the system is stable is

A second-order linear time-invariant system is described by the following state equations

$\frac{d}{dt}{x}_1(t)+2x_1(t)=3u(t)$
$\frac{d}{dt}{x}_2(t)+x_2(t)=u(t)$

where $x_1(t)$ and $x_2(t)$ are the two state variables and $u(t)$ denotes the input. If the output $c(t)=x_1(t)$, then the system is

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as

$G(s)=\frac{K(s+2)}{s^2+2s+2}$ and $H(s)=1$,

respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is _______________

A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau )$, then the autocorrelation function $R_Y(\tau )$ of the output $Y(t)$ is equal to

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density $\frac{\eta }{2}=2.5\times 10^{-5}$ Watt per Hz. If information at the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit-energy $E_b$ (in mJ/bit) necessary is ____________