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Band-Limited White Noise - Introduce white noise into continuous system

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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 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 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 f_max is the bandwidth of the system in rad/sec.

Algorithm

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. This block approximates the covariance of white noise as the Noise power divided by tc.

Data Type Support

The Band-Limited White Noise block outputs real values of type double.

Parameters and Dialog Box

Opening this dialog box causes a running simulation to pause. See Changing Source Block Parameters During Simulation.

Noise power

The height of the PSD of the white noise. The default value is 0.1.

Sample time

The correlation time of the noise. The default value is 0.1. See How to Specify the Sample Time.

Seed

The starting seed for the random number generator. The default value is 23341.

Interpret vector parameters as 1-D

Output a 1-D array if the block's parameters are vectors. Otherwise, output a 2-D array one of whose dimensions is 1. See Determining the Output Dimensions of Source Blocks.

Characteristics

Sample Time	Specified in the Sample time parameter
Scalar Expansion	Yes, of Noise power and Seed parameters and output
Dimensionalized	Yes
Zero Crossing	No

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