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The power spectral density of a random signal is obtained as

  • A.The transform of its autocorrelation
  • B.The square of the Fourier transform of one sample record
  • C.The derivative of its cumulative distribution function
  • D.The autocorrelation of its Fourier transform

Answer: A

The Wiener-Khinchin relation gives the power spectral density as the Fourier transform of the autocorrelation function, which is how a random signal, having no deterministic spectrum, is nonetheless described in the frequency domain. Squaring the transform of one record gives a periodogram, a noisy estimate rather than the quantity itself. The distribution function describes amplitude statistics, not spectral content. And the last option reverses the operations.

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