Band-Limited White Noise
Continuous white noise.
Description
The Band-Limited White Noise block generates normally distributed random numbers that are suitable for use in continuous or hybrid systems.
White Noise Modelling
In theory, continuous white noise has a correlation time equal to 0, a flat power spectral density (PSD) and a total energy equal to infinity. In practice, physical systems never experience perturbations in the form of white noise, yet white noise is a useful theoretical approximation in cases where the perturbation has a correlation time that is very small compared to the natural bandwidth of the system.
You can simulate the effect of white noise by using a random sequence with a correlation time much smaller than the smallest system time constant. The Band-Limited White Noise block creates just such a sequence. Its noise correlation time is the same as the block’s sampling frequency. For accurate modelling, use a correlation time much smaller than the time constant of the fastest part of the system. You can get good results by specifying
where
- is the throughput of the system in `rad/sec.
Comparison with Random Number block
The main difference between this block and the Random Number block is that the Band-Limited White Noise block produces output at a specific sampling rate. This rate is related to the correlation time of the noise.
Parameters
Noise power - white noise power spectral density
0.1 (by default) | scalar | vector | matrix
White noise power spectral density as a scalar, vector or matrix.
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Seed - initial value
23341 (by default) | scalar | vector | matrix
An initial number for a random number generator, specified as a scalar, vector or matrix. The values must be positive, valid, and finite. If the starting number is constant, the generated output sequence will not change.
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By default |
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Sample time - interval between calculation steps
0.1 (by default) | scalar
Specify the interval between calculation steps as a non-negative number. To inherit a calculation step, set this parameter to -1.
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Value |
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By default |
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Algorithms
To produce the correct noise intensity, the noise covariance is scaled to reflect an implicit transformation from the continuous power spectral density to the discrete noise covariance. The corresponding scaling factor is 1/tc, where tc is the noise correlation time. This scaling ensures that the response of a continuous system to approximate white noise has the same covariance as the system to real white noise. Because of this scaling, the covariance of the signal from the Band-Limited White Noise block is different from the Noise power parameter. This parameter is actually the height of the white noise power spectral density. This block approximates the white noise covariance as the noise power divided by `tc'.