GATE EC 2014 Question Paper (16-Feb-2014) (Shift 1)

The steady state error of the system shown in the figure for a unit step input is ---------

The state equation of a second-order linear system is given by:

ẋ(t) = Ax(t), x(0) = x₀

For x_0 = ≤ft[ {*20c 1\\ - 1 } ], x≤ft( t ) = ≤ft[ {*20c {e^ - t}\\ { - e^ - t} } ] and for

x_0≤ft[ {*20c 0\\ 1 } ], x≤ft( t ) = ≤ft[ {*20c {e^ - t - e^ - 2t}\\ { - e^ - t + 2e^ - 2t} } ]

When x_0 = ≤ft[ {*20c 3\\ 5 } ], x(t) is

In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?

Let (𝑡) be a wide sense stationary (WSS) random process with power spectral density 𝑆${}_{\text{X}}$ (𝑓). If Y(t) is the process defined as 𝑌(𝑡) = 𝑋(2𝑡 − 1), the power spectral density 𝑆${}_{\text{Y}}$ (𝑓) is

A real band-limited random process (𝑡) has two-sided power spectral density

S_X≤ft( f ) = ≤ft\{ {*20c {10^ - 6≤ft( 3000 - ≤ft| f | )Watts/Hz for ≤ft| f | ≤ 3 kHz}\\ 0 otherwise } .

where 𝑓 is the frequency expressed in Hz. The signal X(t) modulates a carrier cos 16000𝜋t and the resultant signal is passed through an ideal band-pass filter of unity gain with the centre frequency of 8 kHz and bandwidth of 2 kHz. The output power (in Watts) is _______.