In Figure P8.38(a), a communication system is shown that transmits a band-limited signal

Chapter 8, Problem 8.38

(choose chapter or problem)

In Figure P8.38(a), a communication system is shown that transmits a band-limited signal x(t) as periodic bursts of high-frequency energy. Assume that X(jw) = 0 for lwl > WM. Two possible choices, m1 (t) and m2(t), are considered for the modulating signal m(t). m1 (t) is a periodic train of sinusoidal pulses, each of duration D, as shown in Figure P8.38(b). That is, m1 (t) = L, p(t - kT), k= -oc where ( ) _ { COS Wet, ltl < (D/2) p t - 0, ltl > (D/2) . m2(t) is cos Wet periodically blanked or gated; that is, m2(t) = g(t) cos wet, where g(t) is as shown in Figure P8.38(b ). The following relationships between the parameters T, D, We, and WM are assumed: D> D' 27T T >2wM. Also, assume that [sin(x)]/x is negligible for x >> 1. Determine whether, for some choice of w1p, either m1 (t) or m2(t) will result in a demodulated signal x(t). For each case in which your answer is yes, determine an acceptable range for WJp