Root Mean Square - RMS in Frequency Domain

RMS in Frequency Domain

The RMS can be computed in the frequency domain, using Parseval's theorem. For a sampled signal,

where and is number of samples.

In this case, the RMS computed in the time domain is the same as in the frequency domain:

$RMS =\sqrt{\frac{1}{n}\sum\limits_{n}{{{x}^{2}}(t)}} = \sqrt{\frac{1}{n^2}\sum\limits_{n}{{{\left| X(f) \right|}^{2}}}} = \sqrt{\sum\limits_{n}{{{ \left|\frac{X(f)}{n}\right| ^ 2 }}}}$

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