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Pocket-Sized 6 GHz 1 TS/s ET Scope
joeqsmith:
I tell people that when I wrote that software for the VNAs, the time spent actually writing/maintaining the software is very little when compared to researching all the math behind it. And while there are many good papers on-line, published by the leaders of the industry, they are not perfect and so you run into bugs, compounding the problem.
Your example code does the easy part. Collecting all the chunks. It's what you do with these chunks that I would have liked to see a simple walk through. If your example code were to set the Q (samples per CDF) to 30, we get 30 chunks for each sample interval consisting of 30 voltages and 30 F(V ;Δt) multiplied by 255. In your example of 5ns @ 100ps resolution, you end up with 50 of these sets of chunks. Now we do something with this mess to get it back to a meaningful signal. That IMO, it the part that would be good to include.
No doubt, the stats book is one option. Like the VNA, certainly possible to do that research. I'm looking for a shortcut. If there is one trait I have, it's being lazy.
SJL-Instruments:
We've attached an explicit example of how to process each chunk.
We describe simplest method that gets you a viewable waveform - it should be a good first "test" if you're writing custom software.
This will be added to the upcoming revision of the manual. Let us know if this explanation is clear.
joeqsmith:
Big thanks. I took decided to go ahead and attempt to talk with it. How hard can it be? :-DD
I have not divided the CDF values by 255 yet. The waveform is not using the 0.5 CDF but rather just the average of the three center values. I'll go ahead and add that along with time axis. Doesn't seem to bad to code up.
--- Quote ---For single-valued signals (e.g. a simple periodic waveform), you can more-or-less average the two neighboring voltages where F(V; Δt) first goes from <0.5 to >0.5 to find the location of the step (V0). (The software does something fancier, fitting a Gaussian error function.)
--- End quote ---
Do you always use a Gaussian fit to get the centroid?
SJL-Instruments:
Nice work with the custom software! :-+
--- Quote from: joeqsmith on January 17, 2024, 01:37:32 am ---Do you always use a Gaussian fit to get the centroid?
--- End quote ---
A bit complicated, but details if you're interested: to a first approximation, you can use the interpolation procedure we described in the last post. This usually gets you close, but the noise performance is poor since you're only using two samples.
Fitting a Gaussian error function is theoretically the best thing to do (in the sense of Fisher information), but in practice is overly sensitive to outliers on the wings. What we've found works well in practice is to fit a line to the inverse Gaussian CDF applied to the data, but truncated within a certain region (say 10-90%) of the CDF, with the truncation also seeded by the interpolation method. (This is also faster on the CPU.) You need to weight samples with some care to maintain equal sensitivity to all values (which minimizes the total propagated noise, and improves outlier robustness).
This gives a significantly lower noise floor than the interpolation method alone, but is still robust to spurious errors.
joeqsmith:
I didn't want you to feel that your posts and updates to the manual were a wasted effort. It was an evenings work to see that GHz sinewave. Says a lot about your choice of a protocol.
The remaining parts for the delay line arrived today. I plan to assemble it over the weekend, so no rush on the s-parameter support.
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