From numerical simulation and regression analysis I discovered that the root-mean-square amplitude of white noise with bandwidth $\Delta\!f$ is proportional to $\sqrt{\!\Delta\!f}$. How can this be derived mathematically ?
2026-03-25 01:35:35.1774402535
White noise RMS vs. its bandwidth
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I think I found and grasped the explanation... In white noise the energy (power) is the same for each frequency - by definition. So for a bunch of successive frequencies (bandwidth) the average RMS power will become proportionally larger. Electric power is proportional to voltage squared. Thus the voltage (RMS amplitude) of white noise will be proportional to the square root of its bandwidth.
Correct me if my reasoning is wrong.