# StandardDeviation

```block StandardDeviation "Calculates the empirical standard deviation of its input signal"
extends Modelica.Blocks.Icons.Block;

parameter Modelica.SIunits.Time t_eps(min = 100 * Modelica.Constants.eps) = 1e-7 "Standard deviation calculation starts at startTime + t_eps"
Modelica.Blocks.Interfaces.RealInput u "Noisy input signal"
annotation (Placement(transformation(extent = {
{-140, -20},
{-100, 20}})));
Modelica.Blocks.Interfaces.RealOutput y "Standard deviation of the input signal"
annotation (Placement(transformation(extent = {
{100, -10},
{120, 10}})));
Modelica.Blocks.Math.Variance variance(t_eps = t_eps) annotation (Placement(transformation(extent = {
{-60, -10},
{-40, 10}})));
Modelica.Blocks.Math.Sqrt sqrt1 annotation (Placement(transformation(extent = {
{-20, -10},
{0, 10}})));
equation
connect(sqrt1.u,variance.y) annotation (Line(
points = {
{-22, 0},
{-39, 0}},
color = {0, 0, 127}));
connect(sqrt1.y,y) annotation (Line(
points = {
{1, 0},
{110, 0}},
color = {0, 0, 127}));
connect(variance.u,u) annotation (Line(
points = {
{-62, 0},
{-120, 0}},
color = {0, 0, 127}));

annotation (
Documentation(
revisions = "<html>\n<table border=1 cellspacing=0 cellpadding=2>\n<tr><th>Date</th> <th align=\"left\">Description</th></tr>\n\n<tr><td> June 22, 2015 </td>\n    <td>\n\n<table border=0>\n<tr><td>\n         <img src=\"modelica://Modelica/Resources/Images/Blocks/Noise/dlr_logo.png\">\n</td><td valign=\"bottom\">\n         Initial version implemented by\n         A. Kl&ouml;ckner, F. v.d. Linden, D. Zimmer, M. Otter.<br>\n         <a href=\"http://www.dlr.de/rmc/sr/en\">DLR Institute of System Dynamics and Control</a>\n</td></tr></table>\n</td></tr>\n\n</table>\n</html>",
info = "<html>\n<p>This block calculates the standard deviation of its input signal. The standard deviation is the square root of the signal&#39;s variance:</p>\n<blockquote>\n<pre>y = sqrt( variance(u) )</pre>\n</blockquote>\n<p>\nThe <a href=\"modelica://Modelica.Blocks.Math.Variance\">Variance</a> block is used to\ncalculate variance(u).\n</p>\n<p>The parameter t_eps is used to guard against division by zero (the computation of the standard deviation\nstarts at &lt;<em>simulation start time</em>&gt; + t_eps and before that time instant y = 0).\n</p>\n\n<p>\nThis block is demonstrated in the examples\n<a href=\"modelica://Modelica.Blocks.Examples.NoiseExamples.UniformNoiseProperties\">UniformNoiseProperties</a> and\n<a href=\"modelica://Modelica.Blocks.Examples.NoiseExamples.NormalNoiseProperties\">NormalNoiseProperties</a>.\n</p>\n</html>"),
Icon(graphics = {
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color = {192, 192, 192}),
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color = {215, 215, 215}),
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fillColor = {192, 192, 192},
fillPattern = FillPattern.Solid),
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lineColor = {192, 192, 192},
fillColor = {192, 192, 192},
fillPattern = FillPattern.Solid),
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points = {
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fillPattern = FillPattern.Solid)}));
end StandardDeviation;

```