[time-nuts] practical details on generating artificial flicker noise

[Bob Camp]

Hi

About all I’d say is that if Jim Barnes said that’s the way to do it. then that’s the way to do it. There are only a very few people who I’d say that about. 

Bob

> On Nov 23, 2014, at 9:05 AM, Jim Lux <jimlux at earthlink.net> wrote:
> 
> I'm writing a short simulation program to generate samples from a analog system with some op amps, etc., and I'm wondering if anyone has some practical experience on picking parameters for the generator.
> 
> I'm generating minutes worth of data sampled at 1 kHz, and my opamps have their flicker/white knee at around 3-4 Hz (at least that's what the LT1679 data sheet claims.. we shall see if the model matches the data sheet matches what I measure on the actual hardware)
> 
> I'm using a Barnes-Jarvis (or Barnes-Greenhall) type generator for the flicker noise, which basically sums up a bunch of stages to create an arbitrarily smooth representation.  See threads:
> https://www.febo.com/pipermail/time-nuts/2010-April/046926.html
> https://www.febo.com/pipermail/time-nuts/2013-November/081534.html
> 
> The actual PTTI paper is
> 
> http://tycho.usno.navy.mil/ptti/1987papers/Vol%2019_19.pdf has the details
> http://tycho.usno.navy.mil/ptti/1992papers/Vol 24_44.pdf has some corrections, but is a partial page..
> 
> You need to pick a few parameters:  how many stages to cover your frequency band of interest, how big the frequency steps are (e.g. octaves), and where's the "top band" filter cutoff (typically 0.3 to 0.5 relative to the sample rate)
> 
> If you picked 4 stages, with a starting frequency of 0.4, and octaves(R=2), then the individual filter cutoffs would be
> 0.4
> 0.2
> 0.1
> 0.05
> 
> I'm interested in the behavior down in the 1 Hz and below range, say, to 0.01 Hz.  So to cover 0.01 Hz to 1000Hz, one would need about 16-17 octaves which is an enormous number of stages and I've got to believe you'd have all sorts of numerical problems
> 
> And I think I don't need to do this
> I can add white noise to establish the noise floor to match lab measurements (there's sources other than the op amps) for higher frequencies, say in the 20-1000 Hz area.
> 
> It would seem, then, that I can start the first filter at around 5 Hz and go down from there, if my assumption that most of the flicker noise is coming from the opamp and it's flicker noise comes above the thermal noise at 3-4 Hz.
> 
> Then, going in, say, octave jumps, I can get down to 0.01 Hz in about 8 steps.  (this seems to match Figure 2 in the paper.. they used a 8 stages with a frequency ratio of 2.4, and the spectrum looks pretty flat for a good 5 decades.
> 
> I suppose I could just write it and see what comes out, but if someone out there has worked with this kind of thing before, a bit of practical guidance would be useful.
> 
> 
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