Band-Limited White Noise

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.

The main difference between this block and the Random Number block is that the Band-Limited White Noise block produces output data at a specific sampling rate. This frequency is related to the correlation time of the noise.