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Zooming *IN* [actually: signal reconstruction]

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balnazzar:
Zooming IN with the scope can be dangerous too, if done carelessly...:

https://youtu.be/W4twnd-YQQ4

Note that the KS, having *less* memory depth, automatically turns Sinc interpolation off...

But an interesting thing I'd like experienced people to clarify (or our host hisself), is that Dave gives us some numbers (position 8:10 circa): "sinc int. works well when we have more than a 4 samples per period".
Note that the scope is sampling at 2.5:1 ratio, and indeed the signal's reconstruction is far from perfect. This seems to give credit to Dave's rule of thumb, and, as he turns off the 2nd channel, the signal looks virually perfectly reconstructed (5 samples per period), while linear interpolation still sucks.

But look at this: https://www.tek.com/en/documents/application-note/real-time-versus-equivalent-time-sampling

Basically it says that Tek scopes can reconstruct the signal with just 2.5 samples per period.

This seems to be confirmed by Chris Rehorn at KS, who in https://siglent.fi/data/technical-common/Sin(x)x_Agilent.pdf says:

In reality, as long as the rules of Nyquist are not violated, an oscilloscope can reconstruct a user’s signal identically. This reconstruction process is often referred to as sin(x)/x interpolation. Whether the sample rate is 25x the Nyquist frequency, or 2.5x the Nyquist frequency, interpolation can be used to reproduce the waveform exactly as it appeared at the oscilloscopes input connector, removing all doubt about a signal’s behaviour between samples.

And:

Nyquist’s most famous theoremproposes that a signal can be reconstructed perfectly from discrete samples if the following two rules are observed:
1. The highest frequency component sampled must be less than half the sampling frequency and
2. Samples must be acquired in equally spaced intervals

Note that nothing is said about an infinite number of samples, presumably because he wants to talk about oscilloscopes (hence not 2X, but just 2.5X).

I'd like to know which of these hypotheses did the scope in Dave's video violate. Maybe the front end was ineffective at discarding the high frequency components due to roll off from being at maximum (3 db) frequency, as he seems to hint? If so, would you elaborate upon this particular point? Thanks.

Fungus:

--- Quote from: balnazzar on October 21, 2022, 05:43:12 pm ---Note that the scope is sampling at 2.5:1 ratio, and still the signal reconstruction is far from perfect.

I'd like to know which of these hypotheses did the scope in Dave's video violate.

--- End quote ---

At around 7:30-8:00 in the video?

I think the problem is that sin(x)/x is an infinitely wide function and oscilloscopes have to be practical so they only apply a small window of it (the central part of the sinc curve) in their reconstructions. Some manufacturers will have a wider window than others.

ie. 2.5x is correct in theory but putting it into practice can be difficult.

Dave's "4x" number doesn't come from theory, it's pulled out of thin air based on practical experience working with that particular 'scope (and maybe some others), hence the overlayed comment at 8:20 that starts with "In practice..."


--- Quote from: balnazzar on October 21, 2022, 05:43:12 pm ---Maybe the front end was ineffective at discarding the high frequency components due to roll off from being at maximum (3 db) frequency, as he seems to hint?

--- End quote ---

The 'scope's bandwidth rolloff doesn't apply when the input is a pure sine wave, there's no harmonics to break Nyquist.

DavidAlfa:
How in earth is this dangerous? Innacurate, yes.

Try zooming a 1MHz wave sampled at 50us/div with any average scope, good luck with that!
Only high-end equipment will be able to zoom-in so much with accuracy, definitely not the average sub-$600 scope, though these devices are getting better each year and I could be wrong.

tautech:

--- Quote from: DavidAlfa on October 21, 2022, 06:20:58 pm ---How in earth is this dangerous? Innacurate, yes.

--- End quote ---
Youtuber clickbaiters just don't care, they only want views.

bdunham7:
I have a problem with any statement that refers to Nyquist and to 'perfect' reconstruction.  The reconstruction is never, ever perfect.  There are always errors such as mathematical truncation (you can't compute everything to an infinite number of decimal places...), quantization (8-bits has its limitations), noise, input amplifier distortion and group delay, width of signal memory and the sinc function as applied, and probably more things.  The more samples you have, the less the reconstruction depends on any one sample or calculation so it becomes easier and easier to get a good (again--not perfect, ever!) result.

As a practical matter, reconstruction from 2.01 samples per cycle would only be practical for on-paper mathematical examples calculated to many decimal places, whereas reconstruction from 100 samples per cycle will work no matter how bad the method--even just showing the dots would obviously work fine.  In between those two extremes you have practical limits.  With ideal conditions 2.5X is possible, but even a little bit of noise will make the results distorted and jumpy.  4-5X typically gives good results under most conditions, although again it is never perfectly correct.   I don't know exactly what caused the result in the video that you mention, but I think if he had done continuous acquisition instead of a single shot you'd see a noisy, jumpy signal.

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