Create a white noise process

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.

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
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

WhiteNoise(Normal(mu = 0, sigma = 1))

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()