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".
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.
It's non-trivial to do well.
And, I suspect, non-trivial to do with low computational complexity.
There are many many methods to do this. Everyone has a favorite.
No doubt about it.
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