[time-nuts] Question about noisetypes and ADEV

Anders Wallin anders.e.e.wallin at gmail.com
Sat Oct 27 03:08:57 EDT 2018


> Is this some elemental effect of integration (sqrt(n) or some such), or am
> I seeing the effects of bandwidth and/or bias-functions or other esoterica?
>

FWIW the python "colorednoise" (aka. Kasdin-Walter) repo has a figure:
https://github.com/aewallin/colorednoise
and code that generates the figure:
https://github.com/aewallin/colorednoise/blob/master/example_noise_slopes.py

there are probably two issues to look at:
1. If you simply integrate with cumsum() the PSDs will cross at a frequency
of 1/(2*pi) (not 1 Hz) (assuming a sample rate of one).
The PSDs will cross at the nyquist frequency if you integrate with x2 =
sqrt(2*pi)*cumsum(x1)
2. the ADEV pre-factors for different noise-types are not the same. If you
want ADEV curves that cross at tau=1 you have to tune the PSDs specifically
for that.
The pre-factors for ADEV are e.g. here:
https://github.com/aewallin/colorednoise/blob/master/colorednoise.py#L69
or ieee-1139: https://ieeexplore.ieee.org/document/4797525
or Dawnkins et al https://ieeexplore.ieee.org/document/4225303

Anders


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