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 _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
