Discussion
The spectrum of a real-valued signal has which symmetry?
Answer: C
Real signals have conjugate-symmetric spectra: the amplitude is even and the phase odd about zero frequency. That is why only the positive-frequency half is ever plotted, the negative half carrying no additional information. Odd amplitude would allow negative amplitudes, which is not what the magnitude spectrum means. Periodicity affects whether the spectrum is discrete, not its symmetry. And symmetric phase would imply the signal is also even in time, a much stronger condition.
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