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

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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.
  1 Comment
Jason Xie
Jason Xie on 2 Feb 2022
The 'bandlimited white noise source' is specified by white noise's Power Spectrum Density (PSD), which is Power per Unit Frequency (V^2/Hz, power is indicated by V^2 usually in circuit design). (It is termed as Noise Power in the setting, but it is actually Power Spectrum Density)
Suppose your smallest time step (or sample time) in your Simulink is dt, then the maximum frequency range you can get is 0 to 1/dt. Noise power is specified by V^2 = (Voltage_standard_deviation)^2 = Variance. If your simulation length is N (fixed time step solver), then your frequency resolution or Unit Frequency is Fs/N.
So, set PSD = (Voltage_std)^2 / (1/dt), and set SAMPLE time as dt, run Simulink, send white noise output to workspace (array), run std() to see Voltage_std that you just set.
Plot PSD
f = Fs*linspace(0,1,N)
semilogx(f, 20*log10(abs(fft(noise)))
By doing so, it is equivalent to using 'rand number generator' by setting the same VARIANCE and SAMPLE TIME.

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Accepted Answer

Honglei Chen
Honglei Chen 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
  3 Comments
SV
SV on 14 Nov 2019
I have to found the relationship between the noise power and the variance. if i have the variance, for example 0.003, and the sample time Ts =1, the noise power is equal to the variance? the formula above is right?
Thanks.
632541
632541 on 18 Feb 2021
To feed the band limited whilte noise , what value should i give in noise power section of the block if i want to produce the noise with noise floor of 0.5nV/rtHz.?
Please clarify this..

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