246. I x I << 1, coth (x) can be a proximated as

A. x

B.b) x11

C. ?x 12

D. x10

247. inn is sin(0 / 2) q-4.0 0

A.0.5

B.1

C.2

D. not defined

248. If R(T) is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is NOT true? x(t) ? 5 (sin 2n 1000t )3 + 7 ( nt sin In 1000t )3 nt would be (a) 2 x 103 (c) 6 x 103 A(t) Same Y2(t)

A. R(T) = R(-T) YU) m(t)y(t)

B. I R(T) I5 11(0) 2__.

C. R(T) = - R(-T) -130 +B f

D. The mean square value of the process is R(0)

249. The 3-dB bandwidth of the low-pass signal e-t u(t), where u(t) is unit step function, is given by

A. ?2n Hz

B. ?2n 1/2--1z

C. co

D. 1 Hz

250. The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unit roll-off factor is given by sin4nWt p(t) =47rWt(1 - 16W 2 t 2 ) (biBt) Y(f) 0 +B +2B

A.

B.

C.

D.

251. In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(/) of y(t) will be-aL The ratio of the average energy of Constellation 1 to the average energy of Constellation 2 is

A. 4a2

B.4

C.2

D.8

252. If these constellations are used for digital communications over an AWGN channel, then which of the following statements is true?

A. Probability of symbol error for Constellation 1 is lower

B. Probability of symbol error for Constellation 1 is higher

C. Probability of symbol error is equal for both the constellations

D. The value of No will determine which of the two constellations has a lower probability of symbol error

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