White and Coloured Noise
Snapshot of the front panel of the simulator:
Description of the simulated system
A noise signal, v(k), being a uniformly distributed random signal is generated. Thus, v is white noise, which means it varies principally completely randomly between the samples. This signal is sent to the following discrete-time signal filter - also denoted shaping filter:
x(k) = a*x(k-1) + K*v(k)
where a is a filter parameter and K is a gain. With a = 0, the filter output signal, x, is also white noise. With parameter between 0 and 1, x becomes coloured noise, which means it does not vary completely randomly between the samples. The autocorrelation of x, Rxx(L), is plotted. L is the lag parameter. Rxx(L) shows the "colour" of x.
White noise and coloured noise are important signals in stochastic systems. For example, in applications as minimum variance optimal control and in state estimation using a Kalman filter the noise signals acting on the system (for control or estimation) are assumed to be white. If the noise is coloured, it can be regarded as the output of a dynamic signal filter typically called a shaping filter.