| Simulink Reference | |
Introduce white noise into a continuous system
Library
Description
The Band-Limited White Noise block generates normally distributed random numbers that are suitable for use in continuous or hybrid systems.
The primary difference between this block and the Random Number block is that the Band-Limited White Noise block produces output at a specific sample rate, which is related to the correlation time of the noise.
Theoretically, continuous white noise has a correlation time of 0, a flat power spectral density (PSD), and a covariance 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, 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 Band-Limited 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
where fmax is the bandwidth of the system in rad/sec.
The Algorithm Used in the Block Implementation
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 Band-Limited White Noise block is not the same as the Noise power (intensity) dialog box parameter. This parameter is actually the height of the PSD of the white noise. While the covariance of true white noise is infinite, the approximation used in this block has the property that the covariance of the block output is the Noise Power divided by tc.
Data Type Support
A Band-Limited White Noise block outputs real values of type double.
Parameters and Dialog Box
0.1.0.1. See Specifying Sample Time in the online documentation for more information.23341.Characteristics
| Sample Time |
Discrete |
| Scalar Expansion |
Of Noise power and Seed parameters and output |
| Dimensionalized |
Yes |
| Zero Crossing |
No |
| | Backlash | Bitwise Logical Operator | |