BandLimited White Noise
Introduce white noise into continuous system
 Library:
Simulink / Sources
Description
The BandLimited White Noise block generates normally distributed random numbers that are suitable for use in continuous or hybrid systems.
Simulation of White Noise
Theoretically, continuous white noise has a correlation time of 0, a flat power spectral density (PSD), and a total energy of infinity. In practice, physical systems are never disturbed by white noise, although white noise is a useful theoretical approximation when the noise disturbance has a correlation time that is very small relative to the natural bandwidth of the system.
In Simulink^{®} software, you can simulate the effect of white noise by using a random sequence with a correlation time much smaller than the shortest time constant of the system. The BandLimited White Noise block produces such a sequence. The correlation time of the noise is the sample rate of the block. For accurate simulations, use a correlation time much smaller than the fastest dynamics of the system. You can get good results by specifying
$$tc\approx \frac{1}{100}\frac{2\pi}{{f}_{max}},$$
where f_{max} is the bandwidth of the system in rad/sec.
Comparison with the Random Number Block
The primary difference between this block and the Random Number block is that the BandLimited White Noise block produces output at a specific sample rate. This rate is related to the correlation time of the noise.
Usage with the Averaging Power Spectral Density Block
The BandLimited White Noise block specifies a twosided spectrum, where the
units are Hz. The Averaging Power Spectral Density block specifies a
onesided spectrum, where the units are the square of the magnitude per unit radial
frequency: mag^2/(rad/sec). When you feed the output of a BandLimited White
Noise block into an Averaging Power Spectral Density block, the average
PSD value is π times smaller than the Noise power of the
BandLimited White Noise block. This difference is the result of
converting the units of one block to the units of the other, 1/(1/2)(2π
) = 1/π
, where:
1/2 is the factor for converting from a twosided to onesided spectrum.
2
π
is the factor for converting from Hz to rad/sec.
Ports
Output
Parameters
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
To produce the correct intensity of this noise, the covariance of the noise is scaled to reflect the implicit conversion from a continuous PSD to a discrete noise covariance. The appropriate scale factor is 1/tc, where tc is the correlation time of the noise. This scaling ensures that the response of a continuous system to the approximate white noise has the same covariance as the system would have to true white noise. Because of this scaling, the covariance of the signal from the BandLimited White Noise block is not the same as the Noise power (intensity) parameter. This parameter is actually the height of the PSD of the white noise. This block approximates the covariance of white noise as the Noise power divided by tc.