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 _______________________________________________ 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.
