John Larkin posted a model in LTspice using four stages of rand() functions and then a low pass to generate a gaussian 1 Vrms noise source.
When I went back to reply to that post, yes, I deleted everything, so here is new thread.
Synapses, the generator consisted of an amplitude times a function containing four rand functions with their arguments having very diverse prime? multipliers. The output of that generator then fed into a simple low pass to generate approximately 1 Vrms output between 1Hz and 1kHz
With .tran 0 1 0 10u; took a LONG time on my system to run! but ok...
Yes, output is 1Vrms. Yes, output distribution is a fair representation of a gaussian source, within statistical limits for small sample set, just slightly squashed peak of 1.2 instead of 1.8, but within limits.
BUT, the spectrum decidedly tilts downwards! between 1Hz to 100Hz drops over 1 dB, then another 2dB by 500Hz, and then rounds down almost 6dB!!! To make up for this tilted spectral distribution the low frequency end is higher magnitude than a true gaussian source, almost 3X larger to compensate and still produce 1 Vrms.
To convince yourself, plot V(out) in FFT, but manually change scales to
1kHz maximum and use linear, not decibel, to exacerbate the effect. You'll see a descending line to the right and a significant drop near 1kHz.Almost forgot, the noise distribution near 300Hz was VERY 'ratty' instead of a spectrum of constant fuzz like one would expect, the spectrum has a 'lump' near 300Hz where the 'noise' of the noise is greater. Have no idea of the significance, if any, of that.