[time-nuts] A simple sampling DMTD

[Joseph Gwinn]

Re: time-nuts Digest, Vol 184, Issue 35
On Wed, 27 Nov 2019 12:00:02 -0500, time-nuts-request at lists.febo.com 
wrote:
--------------------------------
> 
> Message: 8
> Date: Wed, 27 Nov 2019 00:29:19 +0100
> From: Jan-Derk Bakker <jdbakker at gmail.com>
> To: Discussion of precise time and frequency measurement
> 	<time-nuts at lists.febo.com>
> Subject: Re: [time-nuts] A simple sampling DMTD
> Message-ID:
> 	<CAEoGJM=DwGUzAuTAAw13948HuAGdZo+YSxymozDnWD07G94Oiw at mail.gmail.com>
> Content-Type: text/plain; charset="UTF-8"
> 
> [This thread has started about three months ago; first post with design
> considerations is here:
> https://www.mail-archive.com/time-nuts@lists.febo.com/msg04265.html ]
> 
> Dear all,
> 
> In the past month I have managed to get the PLL working, and found a
> lightweight way to eliminate most if not all of the offset/drift.
> 
> After the discussions with Attila and Bob I have expanded the PLL bandwidth
> to 0.5Hz (with a 10Hz PFD frequency I can't go very much higher). The
> damping factor is 0.7 for now; I intend to do more tests on how an
> increased damping affects the ZCD. To get sufficient ECD drive resolution I
> have implemented a 3rd order multibit sigma/delta modulator driving a
> 12-bit ADC (with passive filtering and active buffering). The result of the
> measured beat note period can be seen at
> 
http://www.lartmaker.nl/time-nuts/PSD%20of%20measured%20ZCD%20period%20with%20PLL%20active.pdf
> ; peaking is shown to be limited.
> 
> With an active PLL the beat note spectrum became much narrower (compare
> 
http://www.lartmaker.nl/time-nuts/PSD%20of%20HP10811%20into%20the%20LTC2140%20with%20PLL%20active.pdf
> to
> http://www.lartmaker.nl/time-nuts/DMTD%20self-noise%20input%20spectrum.pdf
> ). This made it possible to use a comb filter to suppress even-order
> harmonics (before adding hardware notch filtering at the input).
> 
> The 1001-point FIR band pass filter is a good reference to get an idea of
> the best case performance of the system, but it is computationally
> infeasible to run on an 8-bit processor. While a cheap comb filter can take
> a bite out of the HF noise, canceling offset/drift is harder. Early on I
> was looking into ways to average all samples of a single period of the beat
> note, but I had trouble finding a closed form solution to the fact that the
> beat note period is never an exact integer multiple of the sampling rate.
> Through numerical methods I did end up finding a good estimator for the
> "leakthrough" caused by the fractional part of the beat note period (as a
> function of the measured period and the phase offset), which was fairly
> inexpensive to implement. This has yielded a combined "simple" signal
> processing path of a differentiator, a double comb filter and the offset
> estimator, which is getting very close in performance to the "ideal" band
> pass filter (OADEV of 3.77e-13 at tau=1s versus 3.25e-13 at tau=1s for the BPF;
> full plot:
> 
http://www.lartmaker.nl/time-nuts/DMTD%20self-noise%20OADEV%20with%20PLL%20and%20various%20filters.pdf
> for this 600000-second recording:
> 
http://www.lartmaker.nl/time-nuts/600ksec%20run%20with%20PLL,%2010811%20through%20splitter.png
> . OADEV past ~1000sec is severely compromised by the fact that the
> measurement setup is in my home lab which sees temperature swings of up to
> 20 degrees C and which does get bumped from time to time. Longer runs in a
> more controlled setting forthcoming).

In the radar world, the standard solution to the leakthrough problem is 
to batch the data and apply a windowing function to the data in each 
batch.  Typically, the batches overlap such that every sample appears 
in two batches.  The window functions largely eliminate the splice 
error due to the FFT, which is fact splices each batch into a circle, 
causing a discontinuity at the splice.  If the window function is very 
small at the splice, there is little discontinuity power sprayed into 
innocent FFT bins.

In radar, Taylor windows are used, as well as Dolph-Chebyshev if very 
low sidelobes are needed.

.<https://en.wikipedia.org/wiki/Window_function#Dolph%E2%80%93Chebyshev_window>

Taylor is mentioned in the above D-C description, and a link is 
provided.

Joe Gwinn