Root Mean Square - Definition

Definition

The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean (average) of the squares of the original values (or the square of the function that defines the continuous waveform).

In the case of a set of values, the RMS value is given by this formula:


x_{\mathrm{rms}} =
\sqrt{ \frac{1}{n} \left( x_1^2 + x_2^2 + \cdots + x_n^2 \right) }

The corresponding formula for a continuous function (or waveform) defined over the interval is


f_{\mathrm{rms}} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {}^2\, dt}},

and the RMS for a function over all time is


f_\mathrm{rms} = \lim_{T\rightarrow \infty} \sqrt {{1 \over {T}} {\int_{0}^{T} {}^2\, dt}}.

The RMS over all time of a periodic function is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a series of equally spaced samples. Additionally, the RMS value of various waveforms can also be determined without calculus, as shown by Cartwright.

In the case of the RMS statistic of a random process, the expected value is used instead of the mean.

Read more about this topic:  Root Mean Square

Famous quotes containing the word definition:

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    ... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.
    Adrienne Rich (b. 1929)