Note

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# Create a white noise processΒΆ

This example details how to create and manipulate a white noise. A second order white noise is a stochastic process of dimension such that the covariance function where is the covariance matrix of the process at vertex and the Kroenecker function.

A process is a white noise if all finite family of locations , is independent and identically distributed.

The library proposes to model it through the object *WhiteNoise* defined
on a mesh and a distribution with zero mean and finite standard
deviation.

If the distribution has a mean different from zero, The library writes message to prevent the User and does not allow the creation of such a white noise.

```
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
```

Define the distribution

```
sigma = 1.0
dist = ot.Normal(0.0, sigma)
```

Define the mesh

```
tgrid = ot.RegularGrid(0.0, 1.0, 100)
```

Create the process

```
process = ot.WhiteNoise(dist, tgrid)
process
```

Draw a realization

```
realization = process.getRealization()
graph = realization.drawMarginal(0)
graph.setTitle("Realization of a white noise with distribution N(0,1)")
view = viewer.View(graph)
```

Draw a sample

```
sample = process.getSample(5)
graph = sample.drawMarginal(0)
graph.setTitle(
str(sample.getSize()) + " realizations of a white noise with distribution N(0,1)"
)
for k in range(sample.getSize()):
drawable = graph.getDrawable(k)
drawable.setLegend("realization " + str(k + 1))
graph.setDrawable(drawable, k)
view = viewer.View(graph)
plt.show()
```