[time-nuts] Allan variance by sine-wave fitting

Jim Lux jimlux at earthlink.net
Mon Nov 27 18:05:55 EST 2017

-----Original Message-----
>From: Magnus Danielson <magnus at rubidium.dyndns.org>
>Sent: Nov 27, 2017 2:45 PM
>To: time-nuts at febo.com
>Cc: magnus at rubidium.se
>Subject: Re: [time-nuts] Allan variance by sine-wave fitting

<giant snip>

>There is nothing wrong about attempting new approaches, or even just 
>test and idea and see how it pans out. You should then compare it to a 
>number of other approaches, and as you test things, you should analyze 
>the same data with different methods. Prototyping that in Python is 
>fine, but in order to analyze it, you need to be careful about the details.
>I would consider one just doing the measurements and then try different 
>post-processings and see how those vary.
>Another paper then takes up on that and attempts analysis that matches 
>the numbers from actual measurements.
>So, we might provide tough love, but there is a bit of experience behind 
>it, so it should be listened to carefully.

It is tough to come up with good artificial test data - the literature on generating "noise samples" is significantly thinner than the literature on measuring the noise.

When it comes to measuring actual signals with actual ADCs, there's also a number of traps - you can design a nice approach, using the SNR/ENOB data from the data sheet, and get seemingly good data. 

The challenge is really in coming up with good *tests* of your measurement technique that show that it really is giving you what you think it is.

A trivial example is this (not a noise measuring problem, per se) - 

You need to measure the power of a received signal - if the signal is narrow band, and high SNR, then the bandwidth of the measuring system (be it a FFT or conventional spectrum analyzer) doesn't make a lot of difference - the precise filter shape is non-critical.  The noise power that winds up in the measurement bandwidth is small, for instance.

But now, let's say that the signal is a bit wider band or lower SNR or you're uncertain of its exact frequency, then the shape of the filter starts to make a big difference.  

Now, let’s look at a system where there’s some decimation involved - any decimation raises the prospect of “out of band signals” (such as the noise) aliasing into the post decimation passband.  Now, all of a sudden, the filtering before the decimator starts to become more important. And the number of bits you have to carry starts being more important.  And some assumptions about noise being random and uncorrelated start to fall apart.

It actually took a fair amount of work to *prove* that a recent system I was working on
a) accurately measured the signal (in the presence of other large signals)
b) that there weren’t numerical issues causing the strong signal to show up in the low level signal filter bins
c) that the measured noise floor matched the expectation

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