Section A
Q1.
(a) A certain speech signal is sampled at 8 kHz and coded with DPCM, the output of which belongs to a set of 8 symbols s1 - s8. The probabilities of these symbols are p(s1) = 0.4, p(s2) = p(s3) = 0.2, p(s4) = 0.1, p(s5) = 0.05, p(s6) = p(s7) = 0.02 and p(s8) = 0.01. Calculate the entropy in bits/sec. If all the symbols are equiprobable, what will be the entropy?
(b) In the figure shown below, G(s) = (K)/((\tau s + 1)) has a time constant of 0.5 seconds, and has unity DC gain. An integral controller is placed in forward path as Gc(s) = (K1)/(s) such that the open loop transfer function G(s) Gc(s) has a velocity error constant KV = 1. Find the sensitivity of the closed loop system transfer function with respect to K1 at omega = 1 rad/sec.
(c)
List and define various scheduling performance criteria used for comparing various CPU-scheduling algorithms. Compute and compare the average process waiting time of First come First serve, Shortest task first and Priority scheduling algorithms for the processes with their details as listed in the table. Burst Time Process Arrival Time Priority
P0 0 3 1
P1 2 2 2
P_{2} 3 3 4
P3 4 7 1
(d) A uniform plane wave is propagating in z-direction with velocity 1.4 × 108 m/s in a perfect dielectric medium of intrinsic impedance 474 \Omega. If Ex(z, t) = 1750 cos (106 pit – \betaz) V/m represents instantaneous electric field, what will be the magnetic field ? Determine the wavelength and average power of the wave.
