Indian Institute of Technology Kharagpur (IIT-K) 2006 M.E Electronics and Telecommunications Gate ece - Question Paper

(A) (y)=(u(y+2.5)-u(y-2.5))
(B) i,(y)=O.5Y(y)+O.5Y(y—l)
(C) f(y)= O.255(y+2.5)+O.255(y —2.5)+O.55(y)
(D) f(y) = O.258(y+2.5)+O.258(y —2.5)+(u(y+2.5)—u(y —2.5))
42. A system with input x[nl and output y[n is provided as y[n=sinrnx(n). The
system is:
(A) linear, stable and invertible
(B) non-linear, stable and non-invertible
(C) linear, stable and non-invertible
(D) linear, unstable and invertible
43. The unit-step response of a system starting from rest is provided by
c(t)=1—e2 for t!=0
The transfer function of the system is:
(A)1 + 2s
(B) 2+s
(C) 2+s
(D) 2s one + 2s
44. The Nyquist plot of G(ja)H(ja)for a closed loop control system, passes through (—1, j0)
point in the GH plane. The gain margin of the system in dB is equal to
(A) infinite
(B) greater than zero
(C) less than zero
(D) zero
45. The positive values of “K” and “a” so that the system
oscillates at a frequency of two rad/sec respectively are
shown in the figure beneath
(A) 1, 0.75
(B) 2, 0.75
(C) 1, 1
(D) 2, 2
46. The unit impulse response of a system is:
For this system, the steady-state value of the output for unit step input is equal
to
(A) -1
(B) 0
(C) 1
(D)
47. A linear system is defined by the subsequent state formula
k(t)=Ax(t)+Bu(t), A=[°
The state-transition matrix of the system is:
(A) rcost sint
L—sint cost
(B) r_cost sint
L—sint —cost
(C) r_cost —sint
L—sint cost
(D) rcost —sint
Lcost sint
48. The minimum step-size needed for a Delta-Modulator operating at 32 K samples/sec to
track the signal (here u (t) is the unit-step function)
x(t)=125t(u(t)_u(t_1))+(250_125t)(u(t_1)_u(t_2))
So that slope-overload is avoided, would be
(A) two 10
(B) two 8
(C) two 6
(D) 2
49. A zero-mean white Gaussian noise is passed through an ideal lowpass filter of bandwidth
10 kHz. The output is then uniformly sampled with sampling period t = 0.03 msec. The
samples so found would be

Earning:   Approval pending.