[time-nuts] Resampling/decimating (was: Frequency standards for different tau in Allen Dev measurement)

[Attila Kinali]

On Fri, 21 Feb 2020 12:09:53 -0800
"Gary E. Miller via time-nuts" <time-nuts at lists.febo.com> wrote:

> Anyone have any references to how to decimate properly?

(Disclaimer: This is not my forte and I only know the basics,
so take with a grain of salt)

The basic way is to filter the input signal through a band-pass
or low-pass filter, such that the Nyquist sampling criterion will hold
after the resampling. Then you take every n-th sample. The most comonly
used filter, for its low processing cost, is a CIC filter, also knowns
as Hogenauer filter. If you google for that, you will find lots of
resources. "Multi-rate signal processing" is also a good key-word.
There should be also quite a few books on that in your local library.

The "engineering" way to do it, is to split the filter into
multiple steps. E.g. if you want to decimate by 100, you split
it into one decimation step of 25 and one decimation step of 4.
Or maybe even into two steps of 5 and one step of 4. There are
two reasons for this splitting. The first one is to keep the
processing per step small and easier to handle. The second reason
is that this allows to insert a FIR/IIR filter with  steeper
slopes in before the decimation, especially before the last step,
limiting the aliasing into the signal band. There are a few more
tricks that you can play, depending on the decimation factor,
to better shape the noise folding and aliasing. 


			Attila Kinali
-- 
<JaberWorky>	The bad part of Zurich is where the degenerates
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