[time-nuts] A simple sampling DMTD

[jimlux]

On 11/27/19 9:48 AM, Joseph Gwinn wrote:
> 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.
>

There are also some very nice low sidelobe, rectangular top, windows 
like the Blackman-Harris, Nuttall, Solomon, etc.

Albrecht, 2001 has a collection of windows with max sidelobe levels more 
than 200dB down.

fred harris has a great 32 page summary paper in the Jan 1978 
Proceedings of IEEE which collects a bunch of the windows and their 
properties.  "On the use of windows for harmonic analysis with discrete 
fourier transform"  v66, #1, pp51-83
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