## Relationship between noise power in a Band-Limited White Noise block VS Variance in a Random Number block

### Joan Vazquez (view profile)

on 18 Apr 2019
Latest activity Commented on by Joan Vazquez

on 23 Apr 2019

### Honglei Chen (view profile)

What is the relationship between Noise Power in a Band-Limited White Noise block and the Variance in a Random Number block?
For example, if we use 0.1 for the former and 100 for the latter, with a sampling time of 0.001, we get the same results (besides the band limitation, which is not apparent here, but can be seen if we do a PSD; it will have a small effect, but let's forget about it).
After some numerical experiments, I guess that it is:
But what is reason/formula behind it?
I went over the documentation and googled it, but I do not find a simple formula to compute one from the other, and I feel this should be pretty simple.
Thanks
PS: the motivation is to translate specs from another software into Matlab.

R2017b

### Honglei Chen (view profile)

on 18 Apr 2019

You may want to look at the Algorithm section of the following doc page
Basically the variance can be considered as 0.1/(1/0.001) which equals 100.
HTH

Joan Vazquez

### Joan Vazquez (view profile)

on 23 Apr 2019
Thanks, it makes sense now. I will copy the section here for reference:
"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) 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."
Where the correlation time tc is the parameter "Sample time".