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Why RMS value of a periodic signal is equal to sqrt of linear spectrum divided normalized equivalent bandwidth?

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Hi everyone!
I'm reading a book on noise and vibration analysis. And i knew that how to calculate a RMS value of periodic signal (x(n)) by:
xRMS = sqrt(sum(XL^2(k)) / Ben)
xRMS is RMS value of the sampled signal x(n).
XL(k) is single-sided linear spectrum of the signal x(n)
Ben is normalized equivalent noise bandwidth.
Note that:
XL(k) = sqrt(Axx(k)), with Axx(k) is single-side auto-power spectrum of signal.
Axx(k) = Aw^2/N^2*abs(Xw(k)^2)
Aw is amplitude correction factor of the window, w(n).
N is number of samplings
Xw(k) is scaled DFT to RMS of windowed signal xw(n), or:
Xw(k) = Aw/(N*sqrt(2))*FFT(xw(n))
xw(n) = x(n)*w(n),
w(n) is a window function.
Thank you so much.

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