GATE EC 2017 Question Paper (05-Feb-2017) (Shift 1)

A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are Q${}_A$ Q${}_B$ = 00,01,10, and 11.



Assume that X${}_{IN}$ is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state Q${}_A$ Q${}_B$ = 00 and clocked, after a few clock cycles, it starts cycling through

A linear time invariant (LTI) system with the transfer function

$G\left(s\right)=\frac{K\left(s^2+2s+2\right)}{\left(s^2-3s+2\right)}$

Is connected in unity feedback configuration as shown in the figure



For the closed-loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed-loop system is stable for

Which one of the following options correctly describes the locations of the roots of the equation s⁴ + s² + 1 = 0 on the complex plane?

The Nyquist plot of the transfer function $G\left(s\right)=\frac{K}{\left(s^2+2s+2\right)\left(s+2\right)}$

Does not encircle the point (–1 + j0) for K = 10 but does encircle the point (-1 + j0) for K = 100 . Then the closed-loop system (having unity gain feedback) is

In binary frequency shift keying (FSK), the given signal waveforms are

u₀(t) = 5 cos(20000πt); 0 ≤ t ≤ T, and

u1(t) = 5 cos(22000πt); 0 ≤ t ≤ T

where T is the bit-duration interval and t is in seconds. Both u₀(t) and u₁(t) are zero outside the interval 0 ≤ t ≤ T. With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u₀(t) and u₁(t) uncorrelated is