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A bandpass random signal can be represented by

where the PSD of s(t) is shown in Fig. P6–48. θc is an independent random variable that is uniformly distributed over (0, 2p). Assume that f3 – f2 = f2 – f1. Find the PSD for x(t) and y(t) when
(a) fc = f1. This is USSB signaling, where y(t) = (t).
(b) fc = f2. This represents independent USSB and LSSB signaling with two different modulations.
(c) f1 c 2. This is vestigial sideband signaling.
(d) For which, if any, of these cases are x(t) and y(t) orthogonal?

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