Products > Test Equipment
Sub: Rigol's DHO800 Oscilloscope (Gibbs Effect & Aliasing Misunderstanding)
nctnico:
--- Quote from: Mechatrommer on October 29, 2023, 04:17:25 pm ---
--- Quote from: nctnico on October 29, 2023, 04:12:12 pm ---Read the Wikipedia article carefully. It says that a square wave can not be constructed from a fourier series because a square wave is a discontinuous function. As a result you get artificial ringing near the edges. The discontinuity gets you artificial pre-ringing when using sin x /x reconstruction.
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yes you can get perfect square with fourier series, except the order N = infinity...
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Nope.
ebastler:
--- Quote from: nctnico on October 29, 2023, 04:12:12 pm ---Read the Wikipedia article carefully. It says that a square wave can not be constructed from a fourier series because a square wave is a discontinuous function. As a result you get artificial ringing near the edges.
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???
So how is this different from what I said? A square wave cannot be exactly represented as a finite Fourier series. If you truncate the series somewhere, you will see the Gibbs effect. The ringing near the edges is the Gibbs effect.
A real-world sqaure wave is, of course, already an approximation of a "perfect" square wave, due to its limited risetime. Nevertheless, a sharp low-pass filter will remove higher harmonics and hence will truncate the Fourier series further. The resulting approximation of a square wave will show the Gibbs effect. (Provided that the low-pass filter treats the phases of the incoming harmonics in the right way.)
Edit: Typos
ebastler:
@nctnico -- somehow we have our wires crossed here, and it may just be a matter of assuming different definitions. I have given my definition of the Gibbs Phenomenon; I think it would really be helpful if you stated yours.
--- Quote from: ebastler on October 29, 2023, 04:06:49 pm ---My definition of the Gibbs Phenomenon or "Gibbs ears" is the following:
The effect of approximating a signal with sharp jumps (e.g. a square wave) by its partial Fourier series, i.e. by its fundamental frequency and a limited number of harmonics.
Such an approximate representation can be generated in the real world in an additive way (by adding sine functions) or in a subtractive way (by starting with a square wave and removing higher harmonics via low-pass filtering). In either case, the resulting output is an example of the Gibbs phenomenon in my book, and will show the characteristic "ears".
Your definition of the Gibbs Phenomenon seems to be different from mine. Could you state what it is, and where you got it from?
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2N3055:
--- Quote from: Mechatrommer on October 29, 2023, 03:24:51 pm ---
--- Quote from: 2N3055 on October 29, 2023, 02:59:48 pm ---Stating that I'm hiding things is offensive
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i wrote "i suspect"
--- Quote from: 2N3055 on October 29, 2023, 02:59:48 pm ---As I explained one is made with dot mode, other one is with Sin(x/x) interpolation...
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oic, so you are comparing elephant to apple then... i got distracted again... in that case... my answer is...
1) there is no Sinc in dot mode, no wonder! there is no "reconstruction" actually happened in there, its just try to overlap REAL sampled data too many times, of course no Gibbs effect! read nctnico post. or even literatures i've provided earlier. Gibbs only happened when you turn on fancy interpolation such as Sinc. when we talk about "reconstruction", it means Sinc interpolation. not overlapping real data to many times, thats statistical. different animal! no Sinc, no "reconstruction" (interpolation) period. sorry if you dont understand that earlier.
2) now 2nd pic Sinc is turned ON (5GSps), but 1st pic not (25MSps), thats why i said comparing elephant to apple. my answer is... at 2nd picture, at 5GSps is 0.2ns samples interval, that means 500 points for each cycle, you showed 5 cycles, meaning 2500 points, that means more dots than your monitor can handle, lets just assume for simplicity the dots are 1080 dots filling your monitor. even if there is Gibbs, its too small to see the interpolation on sub-pixel level ;) do you have any idea what you are posting?
here what i suggested for you to do earlier.... check my challenge posts earlier. dial back to where you got the gibbs effect like in this picture you showed here...
screen capture it again to show the gibbs effect as reference... and then.... this is the most important part you need to get right.... change your scope to Sinc OFF, dot mode ON, and single trigger it, until it triggered and stopped. so we can see few points on screen paused, not overlapping around. and do the 2nd capture, and post here again for comparison and analysis... cheers.
here an example of the 2nd capture i need, like tautech have made... (i would love to see same time scale as the one you got the gibbs effect above 200ns/div)
or like this as an example except i need it at 200ns/div same as gibbs effect setup above.. except the settings i've mentioned.
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I give up...
wasedadoc:
--- Quote from: nctnico on October 29, 2023, 03:56:03 pm ---If you are low-pass filtering, you are removing higher harmonics. The ringing on a bandwidth limited square wave are not Gibbs ears. Just less harmonics. Because Gibbs ears are a digital signal processing artefacts from using sin x /x reconstruction, you can't get these on an analog scope because the whole digital signal processing step isn't there.
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No. Just waiting for someone else who does have a completely analogue scope to produce the same result as I have shown.
In the "additive method" used by mathematicians, Gibbs ears appear when you start with a fundamental frequency and add a non-infinite number of harmonics of suitable amplitude and phase.
Fourier says that a real world square wave is a fundamental frequency plus many harmonics. Where "many" is enough to make the wave appear square.
The low pass filter removes the higher harmonics. It is important that the filter is linear phase. That means the fundamental and the remaining harmonics suffer equal delay. What remains in this "subtractive method" is the same as the "additive method". They both result in Gibbs ears.
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