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Pocket-Sized 6 GHz 1 TS/s ET Scope
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SJL-Instruments:

--- Quote from: joeqsmith on February 29, 2024, 04:49:19 pm ---I enjoyed watching their review.  I almost wish they had given you another week to work on it.  Even from the time of the video's release you have made several improvements.   It's too bad that the speckles are a focal point.   I was talking out loud as he started trying different settings to improve it,  crank up the triggers!!   :-DD 

--- End quote ---
Yep, we're happy with how his review turned out. Of course, the performance has improved since the review - such is the nature of any actively developed product.


--- Quote from: joeqsmith on February 29, 2024, 04:49:19 pm ---For starts I need to sort out how to plot the PDF.  I collected raw PAM4 data and attempted to post process it. Any tips on how you converted the PDF back into the voltages you plot? 

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Shown is looking at the raw PDF data for the PAM8 signal.  While I can see the 8 distinct levels, obviously this is not correct.   
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Looking at the PAM4 data (20k triggers, 100  CDF samples, basically the same settings that with your software will produce a decent looking eye.   I was surprised how much the PDF varies.  On the right side, you can see the sorted PDF values (48,000 total), represented by 366 unique levels ranging from 1264 to 0.   Negative PDFs were set to 0. 

--- End quote ---
The PDF values shouldn't be sorted. Each PDF value corresponds to the region between the two voltage values from which it was derived. The interval within this region should be shaded with intensity proportional to the PDF value.
This is why there is one less PDF value than the count of voltages you start with.


--- Quote from: joeqsmith on February 29, 2024, 09:16:26 pm ---Sorting the highest PDF values and then indexing to their corresponding voltage, I get the display on the left (pure guess on my part that is what you are doing).   I then look at the PDF distribution (right histogram) and sort for the areas with the highest peaks.  I then search for only data that falls within a small percentage of these, which gives me the plot in the center.  Does a fair job de-speckling the data but we are also missing some of the good data....  So not a good solution.    I tried a few other simple corrections.  My take away, it's not a super simple problem.   :-DD

--- End quote ---
Filtering each individual PDF distribution is not a good approach, as you've found, since it biases the data downwards. This will remove rare features and lead to inaccurate visualization of the data.

The approach we mentioned before does not introduce any bias, and only improves convergence properties. In more precise terms, the expectation value is unaffected, and we're just changing the inference prior. This will remove any random/uncorrelated noise (speckles) while preserving the signal. We think this has a good chance of working well.

Of course, the firmware and software changes should largely fix the root issue, and the above technique will just deal with the residual statistical noise.
SJL-Instruments:

--- Quote from: Lukas on February 29, 2024, 10:41:32 pm ---I was building pretty much this about 12 years ago: https://www.eevblog.com/forum/projects/diy-ghz-sampling-head-for-lt100mhz-scopes/msg971961/#msg971961 but didn't really get around to finish it.  (that post is much newer than the project itself). I didn't know how to do FPGAs back then, so there's a bit more discrete ECL logic on my design. Really nice to see that someone took that concept and turned it into a well-polished modern product!

I built the ring oscillator out of a meandering trace rather than the adjustable delay line since I thought that it'd have lower jitter.

Since there was no FPGA in my design and everything was controlled by an MCU, the triggering rate was much slower. To somewhat compensate for that, I didn't sweep the comparator threshold to build the CDF. Instead I used the comparator to build a SAR ADC that does one bit per trigger event. This approach obviously falls apart when there's significant noise or jitter on the measured signal, but worked well enough for my purposes.

--- End quote ---
Interesting work! Yep, the basic concept is quite simple - just a precisely triggered comparator. The hard part is of course the precision, and achieving it fast.

The timing core represents about three years of work. Freshly calibrated, we can get precision down to 50 femtoseconds RMS. It's actually somewhat of a shame that the comparator supports an analog bandwidth of only ~6 GHz, since the timing accuracy would support a Nyquist bandwidth of ~500 GHz. Foreshadowing...   ;D
joeqsmith:

--- Quote from: SJL-Instruments on March 01, 2024, 12:04:08 am ---The PDF values shouldn't be sorted. Each PDF value corresponds to the region between the two voltage values from which it was derived. The interval within this region should be shaded with intensity proportional to the PDF value.
This is why there is one less PDF value than the count of voltages you start with.
...
Filtering each individual PDF distribution is not a good approach, as you've found, since it biases the data downwards. This will remove rare features and lead to inaccurate visualization of the data.
...
Of course, the firmware and software changes should largely fix the root issue, and the above technique will just deal with the residual statistical noise.

--- End quote ---

Top graph should be what you describe above complete with speckles which is not really what I am after.   Sorting for high PDFs was to removed points having less of an effect,  speckles.   

It reminds me of the game of life.  I had read about it in one of Steven Levy's books and coded it into an FPGA. 
https://youtu.be/5OUfx2F43ek?t=515

Wiki
https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life

I could treat these speckles similar to cells that live in secluded areas and die off.   :-DD
joeqsmith:
Doing a vertical scan that requires cells above and below to be active, we are already loosing a fair amount of good data.  I would need to do a horizontal scan as well.  It could certainly be done but what a mess...   
KE5FX:
Looks like a job for a median filter to me.  Or if you want to get a little fancier...
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