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

band-limited white noisenoise powerrandom number generatorsimulinkvariance

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.

Best Answer

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

Related Solutions

MATLAB: Have a “Band Limited” White Noise Generator block instead of just a White Noise Generator block

Before this block was created, "White Noise" was being fed into CONTINUOUS-time blocks. The

resulting answer was not agreeing with what theory predicted.

The theory relates the Power Spectral Densities and the Transfer Function:

   PSD_Output(w) = TransferFunctionMagSquared(w) * PSD_Input(w)

Keep in mind that this analysis is in the continuous-time domain.

Passing ideal white noise through a zero-order-hold creates a stair-case signal with random tread heights. When viewed from the continuous-time domain, the PSD of this random stair-case is very different from that of ideal white noise. The ideal white noise will have a flat PSD:

   PSD_ideal_white(w) = P     % same value for all w

The exact same white noise passed through a zero-order-hold will have PSD

    PSD_staircase_white =  P * Tsamp * ( sinc( w * Tsamp ) )^2

Not only does the PSD falloff at higher frequencies with the behavior of sinc() squared, it also has a different value a DC frequency, namely P * Tsamp instead of P.

The Band-Limited White-Noise block restores the low frequency amplitude of the PSD by multiplying the individual samples by 1/sqrt(Tsamp). As a result, the Band-Limited White-Noise block will have PSD:

    PSD_bandlimited_white =  P * ( sinc( w * Tsamp ) )^2

At sufficiently low frequencies, the PSD is approximately

    PSD_bandlimited_white =  P   % w sufficiently small

so the Band-Limited-White-Noise will seem like ideal white noise to continuous-time blocks at these sufficiently low frequencies.

MATLAB: How to generate band-limited Gaussian white noise?

You cannot generate band-limited "white" Gaussian noise. "White" noise means that the power spectral density is flat, which contradicts the notion of a passband.

You can generate band-limited Gaussian noise. I'm not sure what you mean by "...signal ranging from 0 to 3 with a frequency of 0-6Hz", so I'll assume that you want a passband of 0 to 6 Hz. You did not tell us your sampling frequency, I'll assume 100 Hz.

      Fs = 100;
      d = fdesign.lowpass('Fp,Fst,Ap,Ast',6,10,0.5,40,Fs);
      B = design(d);
      % create white Gaussian noise the length of your signal
      x = randn(1000,1);
      % create the band-limited Gaussian noise
      y = filter(B,x);

The output, y, is a band-limited Gaussian noise with a passband of 0 to 6 Hz.

Best Answer

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MATLAB: Have a “Band Limited” White Noise Generator block instead of just a White Noise Generator block

MATLAB: How to generate band-limited Gaussian white noise?

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