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

jimlux jimlux at earthlink.net
Mon Nov 27 18:03:08 EST 2017

On 11/27/17 2:45 PM, Magnus Danielson wrote:

> 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” 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.

It actually took a fair amount of work to *prove* that a 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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