[time-nuts] Simulation of oscillator noise

[Magnus Danielson]

On 11/29/2013 04:11 PM, Jim Lux wrote:
> On 11/29/13 5:56 AM, Azelio Boriani wrote:
>> Unfortunately that was a contribution from Magnus in 2010
>>
>> (see  www.febo.com/pipermail/time-nuts/2010-April/046932.html )
>>
>> that I have simply reported without verifying the link and found that
>> link unusable after sending the message. My best guess is this:
>>
>> http://www.crya.unam.mx/radiolab/recursos/Allan/Kasdin-Walter.pdf
>>
>> based on a search on FLFM (flicker of frequency).
>
>
>
> one limitation of the Kasdin-Walter method is that it is "batch mode",
> and doesn't lend itself to an implementation which is continuous.
>
> The paper does have a nice discussion of why the "white noise into a
> filter" technique doesn't work very well if the slopes you need aren't
> integer powers of frequency. Integer powers in frequency correspond to
> rational functions in filter characteristics, which are
> straightforward, but how do you make a 1.5th order filter section or
> half a pole or zero?
>
> The fractal literature, though, may provide mechanisms that might be
> useful.
Actually, NIST (or actually this was in it's NBS days) did a few good
articles, comparing the Mandelbrot simulation method with their filter
method. Turns out that you need to dimension the filter to the
simulation length, as the number of lead-lag sections needs to cover the
range where 1/f slope is needed and then the density of them (lead-lag
pole/zeros per decade) will control how close it will approximate, that
is, how little "pass-band" ripple there is from the ideal. Also, you
need to apply the corrections to start the filter up in the correct state.

It's non-trivial to do well.

There are many many methods to do this. Everyone has a favorite.

Cheers,
Magnus