WOLFRAM SYSTEM MODELER
This information is part of the Modelica Standard Library maintained by the Modelica Association.
A summary of the common properties of the noise blocks is provided in the documentation of package Blocks.Noise. This BandLimitedWhiteNoise block generates reproducible, random noise at its output according to a band-limited white noise distribution. This is performed by using a normal distribution with mu=0 and sigma = sqrt(noisePower/samplePeriod).
In order for this block to produce meaningful results, you should set the following parameters:
Ideal white noise contains all frequencies, including infinitely high ones. However, these usually cannot be observed in physical systems, since all physical systems in one way or the other contain low-pass filters. It is thus sufficient to generate a limited range of frequency content in the noise signal, as long as it exceeds the frequencies of the subsequent dynamics by a sufficiently high factor (of e.g. 100).
Ideal white noise has a flat, i.e. constant, power spectral density for all frequencies. It has thus infinitely high power, because the total power of a signal can be obtained by integrating the power spectral density over all frequencies. The following three ways to think of the power of a signal may be helpful:
In order to set the correct level of the band-limited white noise power spectral density,
the variance of its normal distribution can thus be influenced directly.
Recalling that the samplePeriod of the noise signal generates frequency content in the
range ±0.5/samplePeriod, the variance must be increased to generate sufficient
total signal power. The total power must match the product of the noisePower and its
frequency bandwidth 1/samplePeriod:
signal power = signal variance = noisePower / samplePeriod.
Example NoiseExamples.DrydenContinuousTurbulence demonstrates how to utilize this block to model wind gust.
Type: Period (s)
Description: Period for sampling the raw random numbers
Description: =true: y = noise, otherwise y = y_off
Description: y = y_off if enableNoise=false (or time<startTime, see below)
Description: = true: use global seed, otherwise ignore it
Description: = true: use automatic local seed, otherwise use fixedLocalSeed
Description: Local seed (any Integer number)
Type: Time (s)
Description: Start time for sampling the raw random numbers
Description: The actual localSeed
Description: Power of white noise signal
Description: Connector of Real output signal
Description: Definition of global seed via inner/outer
Demonstrates how to model wind turbulence for aircraft with the BandLimitedWhiteNoise block (a simple model of vertical Dryden gust speed at low altitudes < 1000 ft)