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

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.

[Jason Xie]

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.

Answer 1

[Honglei Chen]

You may want to look at the Algorithm section of the following doc page

https://www.mathworks.com/help/simulink/slref/bandlimitedwhitenoise.html

Basically the variance can be considered as 0.1/(1/0.001) which equals 100.

HTH

[Joan Vazquez]

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".

[SV]

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]

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..

[DGM]

Flagged by Mohsen Mardani on 26 Apr 2024:

0.1/(1/0.001) is not 100.