[time-nuts] Simulation of oscillator noise

Magnus Danielson magnus at rubidium.dyndns.org
Fri Nov 29 17:00:50 EST 2013


Jim,

On 11/29/2013 07:27 PM, Jim Lux wrote:
> On 11/29/13 8:50 AM, Magnus Danielson wrote:
>> 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.
>>
>
> That's essentially what the Kasdin-Walter paper talks about. The
> number of taps/sections is adjusted to approximate whatever curve you
> want "well enough".
... which fails to reference the right papers:

NBS Report 9284 "The generation and recognition of flicker noise" by Jim
Barnes.
http://tf.boulder.nist.gov/general/pdf/190.pdf‎

NBS Technical Note 604 "Efficient Numerical and Analog Modeling of
Flicker Noise Processes" by Jim Barnes.
http://tf.nist.gov/timefreq/general/pdf/29.pdf‎

Jim Barnes and Chuck Greenhall "Large sample simulation of flicker noise"
http://tycho.usno.navy.mil/ptti/1987papers/Vol 19_19.pdf
This one has nice plots about different amount of stages, however you
*really* want the follow-up correction and addenda
http://tycho.usno.navy.mil/ptti/1992papers/Vol 24_44.pdf

This is the W. Riley list of references:
http://www.wriley.com/Refs.htm
> Then, they sort of shunt all that with an FFT based method.. Generate
> white noise, filter it with a FFT convolution scheme where you've
> loaded the bins of the FFT with the desired power spectrum.
The paper which is filename is FlfmSimPtti.pdf has the propper title
"FFT-Based Methods for Simulating Flicker FM" by Charles A. Greenhall of
JPL. Should have remembered Chuck's name in the previous post, but I was
tired. The Kasdin-Walter paper was proposed as a replacement, there are
similarities, but do read Chuck's fine paper!

This Greenhall paper is found here:
http://trs-new.jpl.nasa.gov/dspace/handle/2014/11024
http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/11024/1/02-2912.pdf
>
>> It's non-trivial to do well.
>
> And, I suspect, non-trivial to do with low computational complexity.
It is. Hence it is important to read-up.
>>
>> There are many many methods to do this. Everyone has a favorite.
>
> No doubt about it.
Not sure which is my favorite just yet.

Cheers,
Magnus


More information about the time-nuts mailing list