# Variance

```block Variance "Calculates the empirical variance of its input signal"
extends Modelica.Blocks.Icons.Block;

parameter Modelica.SIunits.Time t_eps(min = 100 * Modelica.Constants.eps) = 1e-7 "Variance calculation starts at startTime + t_eps"
Modelica.Blocks.Interfaces.RealInput u "Noisy input signal"
annotation (Placement(transformation(extent = {
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Modelica.Blocks.Interfaces.RealOutput y "Variance of the input signal"
annotation (Placement(transformation(extent = {
{100, -10},
{120, 10}})));
protected
Real mu "Mean value (state variable)";
Real var "Variance (state variable)";
parameter Real t_0(fixed = false) "Start time";
initial equation
mu = u;
t_0 = time;
var = 0;
equation
y = noEvent(if t_0 + t_eps <= time then max(var, 0) else 0);
der(mu) = noEvent(if t_0 + t_eps <= time then (u - mu) / (time - t_0) else 0);
der(var) = noEvent(if t_0 + t_eps <= time then ((u - mu) ^ 2 - var) / (time - t_0) else 0);

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>\nThis block calculates the empirical variance of its input signal. It is based on the formula\n(but implemented in a more reliable numerical way):\n</p>\n<blockquote>\n<pre>y = mean(  (u - mean(u))^2  )</pre>\n</blockquote>\n\n<p>The parameter t_eps is used to guard against division by zero (the variance computation\nstarts at &lt;<em>simulation start time</em>&gt; + t_eps and before that time instant y = 0).</p>\n<p>The variance of a signal is also equal to its mean power.</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>"),
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end Variance;

```