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:

    “Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
    —Elaine Heffner (20th century)

    “Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
    —Nadine Gordimer (b. 1923)

    “... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
    —George Eliot [Mary Ann (or Marian)