[time-nuts] A simple sampling DMTD

[Joseph Gwinn]

On Sun, 01 Dec 2019 01:01:34 -0500, time-nuts-request at lists.febo.com 
wrote:
Re: time-nuts Digest, Vol 185, Issue 1

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> 
> Message: 1
> Date: Sat, 30 Nov 2019 12:23:07 -0500
> From: Joseph Gwinn <joegwinn at comcast.net>
> To: time-nuts at lists.febo.com
> Subject: Re: [time-nuts] A simple sampling DMTD
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> Re: time-nuts Digest, Vol 184, Issue 40
> On Fri, 29 Nov 2019 20:37:02 -0500, time-nuts-request at lists.febo.com 
> wrote:
> 
> [snip]
>> Message: 6
>> Date: Fri, 29 Nov 2019 20:37:16 +0100
>> From: Gerhard Hoffmann <dk4xp at arcor.de>
>> To: time-nuts at lists.febo.com
>> Subject: Re: [time-nuts] A simple sampling DMTD
>> Message-ID: <f34ec823-04f2-a92f-b7a1-85ab165cdc6a at arcor.de>
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[snip]
> The fundamental problem to be solved is to estimate the phases of two 
> beatnotes, one per channel (ref, signal under test), the phase 
> difference being converted into a relative time delay.  So, we are 
> estimating phase twice, against an unknown but common internal 
> reference, and the key question here is how best to measure those two 
> phases.  Detection of zero crossings is one way, but there are others. 

FYI, while looking for something unrelated, I recently ran across a 
relevant article from the NIST of Japan, published in 2007:

"Frequency-Stability Measurement System Using High-Speed ADCs and 
Digital Signal Processing", Ken Mochizuki, Masaharu Uchino, and Takao 
Morikawa, IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 
56, NO. 5, OCTOBER 2007, pages 1887-1893, Digital Object Identifier 
10.1109/TIM.2007.895588.

This can be implemented using a modern Software Defined Radio system.

No zero-crossing detecter is used.  Computation of the time difference 
is detailed in reference [16] therein:

[16] M. Uchino and K. Mochizuki, "Frequency stability measuring 
technique using digital signal processing," Electron. Commun. Jpn., 
vol. 87, no. 1, pp. 21–33, 2004.   IEEE Xplore has it.

Searching for Uchino et al led me to the following:

"Oscillator metrology with software defined radio, Jeff A. Sherman and 
Robert Jördens (of NIST),  Review of Scientific Instruments 87, 054711 
(2016); https://doi.org/10.1063/1.4950898.  (Open version: 
<https://arxiv.org/pdf/1605.03505.pdf>)

Joe Gwinn


> We know the frequencies of the beatnotes quite accurately, and that the 
> waveforms are sine waves (which we will have band-pass filtered in 
> hardware before conversion to digital data).  Here, I will assume that 
> the frequencies are the same.  The only free variables are thus 
> amplitude and phase; these can be estimated using least squares applied 
> to successive batches of I&Q samples.  Windowing is still useful to 
> reduce end splice effects, as previously discussed.  Given that we are 
> working in the numerical domain, it's probably adequate to apply the 
> window function to the product of the proposed match and the actual 
> data, and then sum the windowed products.
> 
> As a quality check, if the estimated amplitude is too small (or too 
> large), reject the phase estimate and try again.  If this condition 
> persists too long or becomes too common, something is broken.
> 
> I doubt that anything of the 8-bit class is practical for this, and 
> certainly not for a small-volume product, because programming effort 
> increases sharply if the chosen processor is too limited.  Ardinuo and 
> maybe StrawberryPi seem more like it.
> 
> As for emulation of floating point, the least-squares algorithm defined 
> above can certainly be implemented in fixed-point arithmetic, called 
> fractional integers above.  
> <https://en.wikipedia.org/wiki/Fixed-point_arithmetic>
> 
> In the extreme, this kind of algorithm will work with data clipped to a 
> few bits per sample.  The underwater sonar folk are masters of this, 
> especially back in the days when signal processors were necessarily 
> bespoke hardware.  The search term is "one-bit correlator" (without the 
> quotes).
> 
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