Discussion
The analytic signal formed from a real signal has a spectrum that
Answer: D
Adding \( j \) times the Hilbert transform to a real signal cancels the negative-frequency half, so the analytic signal is one-sided in frequency. It is the natural representation for a modulated signal, since its magnitude is the envelope and its phase the instantaneous phase, both of which are exactly what a demodulator recovers. Symmetry about zero is the property of the original real signal. A negative-only spectrum would follow from subtracting rather than adding. And the whole point is that the spectrum changes.
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