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 }}}}

Read more about this topic:  Root Mean Square

Famous quotes containing the words frequency and/or domain:

    “The frequency of personal questions grows in direct proportion to your increasing girth. . . . No one would ask a man such a personally invasive question as “Is your wife having natural childbirth or is she planning to be knocked out?” But someone might ask that of you. No matter how much you wish for privacy, your pregnancy is a public event to which everyone feels invited.”
    —Jean Marzollo (20th century)

    “Every sign is subject to the criteria of ideological evaluation.... The domain of ideology coincides with the domain of signs. They equate with one another. Wherever a sign is present, ideology is present, too. Everything ideological possesses semiotic value.”
    —V.N. (Valintin Nikolaevic)