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Parseval's relation states that

  • A.Convolution in time corresponds to multiplication in frequency
  • B.Energy is the same in either domain
  • C.The spectrum of a real signal is always symmetric about zero frequency
  • D.Bandwidth is inversely proportional to pulse duration for any waveform

Answer: B

Parseval equates the energy computed from the time waveform with the energy computed from the spectrum, which is the formal statement that a transform preserves energy. Conjugate symmetry of a real signal's spectrum is a separate and equally useful property. The time-bandwidth relation is a consequence of the transform but is not Parseval's statement. And the convolution theorem is a third distinct property, often confused with this one because both relate the two domains.

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