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The autocorrelation function of a signal at zero lag equals

  • A.Its peak amplitude
  • B.Its bandwidth
  • C.Its total energy divided by the observation time squared
  • D.Its average power

Answer: D

At zero lag the autocorrelation reduces to the mean square, which is the average power of the signal. That gives it a physical anchor and makes it the natural starting point for describing random signals, whose power spectral density is the Fourier transform of this function. Peak amplitude is not recoverable from the autocorrelation. Bandwidth follows from the shape of the transform rather than from a single value. And the last expression has the wrong dimensions.

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