Signal Magnitude Area
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In
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, the signal magnitude area (abbreviated SMA or sma) is a
statistical Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
measure of the
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
of a varying quantity.


Definition

The SMA value of a set of values (or a
continuous-time In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "poi ...
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitude Scale (ratio), scales and of any dis ...
) is the normalized
integral In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...
of the original values. In the case of a set of ''n'' values \ matching a time length ''T'', the SMA : x_\text = \sum_^n x_i In the continuous domain, we have for example, with a 3-axis signal with an offset correction ''a'' for each axis, the following equation: : f_\text= \int_0^T , x(t)-a_x, +, y(t)-a_y, +, z(t)-a_z, \, dt


See also

*
Root mean square In mathematics, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square. Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denote ...


References

{{Reflist Computational statistics