Band limited white noise vs random number
$toffel
random number generator in simulink ?
Christophe
Paul Kinnucan
> What is the difference between band limited white noise generator and the
> random number generator in simulink ?
>
Hi Christophe,
The Band-Limited White Noise Generator allows you to create a better
approximation to an ideal white noise source than is possible
using the Random Number Generator alone. An ideal white noise
source has a correlation of 0 (i.e., it is completely random)
and a constant PSD across the spectrum. The Random Noise Generator
block's correlation is not 0 (it is not completely random) and
it is band-limited (i.e., it is not constant over the spectrum
but falls off outside a band determined by the periodicity of
the random number generator). Thus it departs from the ideal
white noise generator. The Band-Limited White Noise
Generator block allows you create a better approximation
by allowing you to generate a signal whose correlation
is as close to the ideal as you like. It does this by outputting at a fixed
sample rate that you can specify. The correlation of the signal
output by the block is equal to the sample time. Thus you can
make the correlation as small as you like, within limits
of the periodicity of the random number generator, by decreasing
the block's sample time. Although you can make the sample
time, and the correlation time, of the signal as small as
you like, the cost is an increase in simulation time. Generally,
making the sample time about a 100th of the time constant of a system
is sufficient to provide a good approximation to a white noise
source.
The block also allows you to specify the covariance of the white
noise. The block scales its output so that the power output remains
constant regardless of the sample time that you choose.
More specifically, the output
of the Band-Limited White Noise Generator block is
Ywn = Yr(n * St) * (COV/ST) for n=0,1,2,..N
where N is the number of samples in the simulation run,
Yr is the output of the Random Number Generator block,
ST is the sample time that you specify in the Sample Time
field of the Band-Limited White Noise block and COV is
the covariance that you specify in the Noise Power field of
the block. Put another way, the White Noise block is simply
a Random Number Generator block constrained to have a discrete
sample time and whose output is scaled to keep its power
output independent of the sample time. To see this,
copy an instance of the White Noise block into a model
and look under its mask.
Because it is based on the Random Number Generator block,
the output of the White Noise block is band-limited, i.e.,
its output is limited to a specific band of frequencies
instead of being spread equally across the entire
spectrum like an ideal white source. Hence, the name of
the Band-Limited White Noise block.
- Paul
$toffel
Christophe
Ante
and what happens if i use a 'Random Number' block and run my simulation with a fixed time step, say Ts. Then my 'Random Number Generator' block calculates every Ts a random sample. This gives me the same correlation time as a band-limited white noise source. Is this right? Is in this case the spectrum of the random number generator also band-limited to 1/Ts/2?
If i multiply the noise sequency with a factor say sigma, my noise power is sigma^2 (with zero mean and variance equal to one inside the random number block).
I do not understand how the power is related to the sampling time?
Thanks for your help!