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Why is white noise an idealisation rather than a physical signal?

  • A.Random signals cannot be described by a spectral density at all
  • B.A truly flat spectrum over infinite bandwidth carries infinite power
  • C.Noise cannot have a flat spectrum at any frequency
  • D.Thermal noise has a spectrum that falls with frequency

Answer: B

Because of the power it would imply. Flat density multiplied by infinite bandwidth gives infinite power, so the model must always be qualified as flat over the band of interest - which is a perfectly good approximation, since thermal noise is essentially flat up to frequencies far above any communication band. Real noise does have a flat region, so the second option is too strong. The quantum correction eventually rolls the density off, but not in a way that matters at radio frequencies. And random signals are described by spectral density precisely through the Wiener-Khinchin relation, which is what makes the whole framework work.

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