# Why the mean squared value of a random noise signal at a single precise frequency is zero?

I am reading about noise from this lecture (page 9/31). However, I don't understand this point. Could anyone explain why mean squared value is zero?

The mean squared value of a random noise signal at a single precise frequency is zero.

• If the mean squared value wasn't zero, it would be a systematic error, not a random one. Oct 28 '16 at 20:11
• I think the key word here is "random" noise. Meaning over time you should have the same amount of random positive magnitude noise as negative magnitude noise. Law of large numbers means that this cancels out eventually. Since it is also randomly spread across frequencies, it will balance everywhere (on average). Oct 28 '16 at 20:11

Noise is continuous spectrum in this case and measured here in $\mu V/Hz^{0.5}$