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The autocorrelation of white noise is

  • A.Zero at every lag including zero
  • B.An impulse at zero lag
  • C.A constant at every lag
  • D.A sinusoid whose period is the inverse of the bandwidth

Answer: B

Flat spectral density transforms into an impulse at zero lag, so samples taken at any two different instants are uncorrelated: the formal meaning of whiteness. A constant at every lag would describe a direct-current signal. A sinusoidal autocorrelation belongs to a narrowband process, and indeed band-limited noise does show one. Zero at zero lag would mean zero power, so the noise would not exist.

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