Root Mean Square (RMS) Function

An Root Mean Square (RMS) Function is a metric function defined as [math]\displaystyle{ x_{\mathrm{rms}} = \sqrt {{{x_1}^2 + {x_2}^2 + \cdots + {x_n}^2} \over n}. }[/math]

• AKA: RMS, Quadratic Mean Function.
• Context:
  • It can be used to calculated a RMS Error Function.
  • …
• Counter-Example(s):
  • an Accuracy Function.
• See: Mean Squared Error, Mean Squared Error, Number Generating Process.

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References

2011

• http://en.wikipedia.org/wiki/Root_mean_square
  • In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids. RMS is used in various fields, including electrical engineering. It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. It is a special case of the generalized mean with the exponent p = 2.

    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 [math]\displaystyle{ n }[/math] values [math]\displaystyle{ \{x_1,x_2,\dots,x_n\} }[/math], the RMS value is given by: :[math]\displaystyle{ x_{\mathrm{rms}} = \sqrt {{{x_1}^2 + {x_2}^2 + \cdots + {x_n}^2} \over n}. }[/math]

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