GATE EC 2014 Question Paper (15-Feb-2014) (Shift 2)

An unforced linear time-invariant (LTI) system is represented by:

≤ft[ {*20c {x_1}\\ {x_2} } ] = ≤ft[ {*20c - 1&0\\ 0& - 2 } ]≤ft[ {*20c x_1\\ x_2 } ]

If the initial condition are x₁(0) = 1 and x₂(0) = -1, the solution of the state equation is

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.



If the system is connected in a unity negative feedback configuration the steady-state error of the closed-loop system, to a unit ramp input, is _______.

Consider the state space system expressed by the signal flow diagram shown in the figure.



The corresponding system is

The input to a 1-bit quantizer is a random variable 𝑋 with pdf (𝑥) = 2𝑒${}^{-2\text{x}}$ for 𝑥 ≥ 0 and 𝑓${}_{\text{X}}$ (𝑥) = 0 for 𝑥 < 0. For outputs to be of equal probability, the quantizer threshold should be_____

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms 𝑠₁(𝑡) = 𝛼 cos 2𝜋𝑓₁𝑡 and 𝑠₂(𝑡) = 𝛼 cos 2𝜋𝑓₂𝑡, where 𝛼 = 4 mV. Assume an AWGN channel with two-sided noise power spectral density $\frac{N_0}{2}=0.5\times 10^{-12}W/Hz$. Using an optimal receiver and the relation $Q\left(v\right)=\frac{1}{\sqrt{2\pi }}\underset{v}{\overset{\infty }{\int }}{e}^{-u^2/2}du$, the bit error probability for a data rate of 500 kbps is