Sub: Rigol's DHO800 Oscilloscope (Gibbs Effect & Aliasing Misunderstanding)

[nctnico]

Here is some evidence that Gibbs ears are real and can be seen on the output of a passive analogue filter.

yes! i was about to sketch similar picture for Fungus to understand, but since you provided proven one, thanks! i didnt rule out the possibility of it existing... so thats why i asked for evidence. from picture its about 1us delay. mind to tell what filter is that? or if that feasible to put on DSO front end?

Again, what wasedadoc is showing are not Gibbs ears!

dont be pedantic friend... if someone give your kid an elephant toy and they call it ohh its an elephant! and then you say, its not an elephant, elephant is in jungle, you screw it man.. ok fine! it just looks like Gibbs ear, but not Gibbs ear... or else what proper term for it? ever-increasing-magnitude-apparently-seems-non-causal-ringing? cheers.

For the umpteenth time: Gibbs ears are never in the actual signal. They are a digital filtering artefact from sin x / x that can show up on the display of a DSO. But Gibbs ears are never present in a real world signal you feed into a DSO. So you can't make Gibbs ears appear by performing any kind of operation on a real signal.

[Mechatrommer]

For the umpteenth time: Gibbs ears are never in the actual signal. They are a digital filtering artefact from sin x / x that can show up on the display of a DSO. But Gibbs ears are never present in a real world signal. So you can't make Gibbs ears appear by performing any kind of operation on a real signal.

i created this issue remember? so i ought to do the reading, thanks for emphasizing that for me btw elephant toy is not an elephant... cheer.

[Fungus]

its not Gibbs, but we could be mistakenly think is...

No we couldn't, because we know that "Gibbs" doesn't happen in a circuit.

Pre-ringing might, but that's not "Gibbs".

[ebastler]

For the umpteenth time: Gibbs ears are never in the actual signal. They are a digital filtering artefact from sin x / x that can show up on the display of a DSO. But Gibbs ears are never present in a real world signal you feed into a DSO. So you can't make Gibbs ears appear by performing any kind of operation on a real signal.

I dont think that is correct. If you build a higher-order, linear-phase lowpass filter and send a square wave through it -- frequency chosen such that e.g. the fundamental and the 3rd and 5th harmonic pass the filter -- what would you expect as the filter output signal?

You might use something like the LTC1064-7, for example: https://www.analog.com/media/en/technical-documentation/data-sheets/lt10647fb.pdf

[Mechatrommer]

its not Gibbs, but we could be mistakenly think is...

No we couldn't, because we know that "Gibbs" doesn't happen in a circuit.

i know, but it happened on monitor, monitor as you saw in the attached picture is not circuit. i can show you what never happened and existed in this real world on your monitor

[2N3055]

As an example I can show 10 MHz square wave signal, sampled at very low 25MS/s in dot mode. Signal is band limited with 200 MHz filter, so there are no frequencies (odd harmonics up to 19th in this case) above that. Simple edge trigger. Scope is my Siglent SDS6000.
Reference image is same signal, just sampled at 5GS/s.

Signal sampled with 25MS/s is perfectly reconstructed.
Can you explain why?

Let's start with that. Then we will proceed from there. Explain that first.

sorry i miss this post... i was distracted by other posts

from eyeballing your picture, sampling at 25MSps, nyquist limit is 50MHz, but you claimed 200MHz limited. by theory, its should already violates nyquist law and unable to reconstruct, yet you showed perfect reconstruction, somethings not right. is your scope can switch down to 50MHz BW at front end? i'm unable to make conclusion, not enough data and something not add up, such as....

in your other "properly designed" scope, even 100MSps sampling on "properly cutoff" 200MHz scope, it cannot reconstruct 1MHz square accurately, we got nasty Gibbs! can you answer why? before i can make firm conclusion. here comparison:

1) sampling 10MHz square, 25MSps = perfect
2) sampling 1MHz square, 100MSps = bad
why? please elaborate. i suspect you hide some setup i'm not aware of... you didnt explain anything in your post where i usually linked.

Stating that I'm hiding things is offensive, especially because it is your refusal to try to read and understand what other people are saying.
I'm not hiding a thing, you pompous baboon...

As I explained one is made with dot mode, other one is with Sin(x/x) interpolation...

Do you, in your infinite wisdom and omnipotent knowledge know why it was possible?

[ebastler]

[...] we know that "Gibbs" doesn't happen in a circuit.
Pre-ringing might, but that's not "Gibbs".

Prey tell, what is the difference? If we filter a square wave to let only its fundamental and a couple of harmonics pass, and do so with a linear-phase lowpass filter -- in which way is the output signal not a direct demonstration of the Gibbs phenomenon?

[rf-loop]

As an example I can show 10 MHz square wave signal, sampled at very low 25MS/s in dot mode. Signal is band limited with 200 MHz filter, so there are no frequencies (odd harmonics up to 19th in this case) above that. Simple edge trigger. Scope is my Siglent SDS6000.
Reference image is same signal, just sampled at 5GS/s.

Signal sampled with 25MS/s is perfectly reconstructed.
Can you explain why?

Let's start with that. Then we will proceed from there. Explain that first.

sorry i miss this post... i was distracted by other posts

from eyeballing your picture, sampling at 25MSps, nyquist limit is 50MHz, but you claimed 200MHz limited. by theory, its should already violates nyquist law and unable to reconstruct, yet you showed perfect reconstruction, somethings not right. is your scope can switch down to 50MHz BW at front end? i'm unable to make conclusion, not enough data and something not add up, such as....

in your other "properly designed" scope, even 100MSps sampling on "properly cutoff" 200MHz scope, it cannot reconstruct 1MHz square accurately, we got nasty Gibbs! can you answer why? before i can make firm conclusion. here comparison:

1) sampling 10MHz square, 25MSps = perfect
2) sampling 1MHz square, 100MSps = bad
why? please elaborate. i suspect you hide some setup i'm not aware of... you didnt explain anything in your post where i usually linked.

Stating that I'm hiding things is offensive, especially because it is your refusal to try to read and understand what other people are saying.
I'm not hiding a thing, you pompous baboon...

As I explained one is made with dot mode, other one is with Sin(x/x) interpolation...

Do you, in your infinite wisdom and omnipotent knowledge know why it was possible?

And, to Mechatrommer.

This dots mode, SARI (Sequential Acquistion Random Inteleaving), (not same as LeCroy RIS ut its litlle cousin) have explained and handled in many threads over years when we have handled these things about  Siglent scopes.

So you need not even think yourself, just look old threads. They ara allthere and multiple times and places.

Also many years ago here.


Sorry sides are finnish language but if you look images 9 and 10...(note signal frequency and samplerate)  perhaps you hit it.
And note. this old oscilloscope was quite slow in zoom mode and tb (but also this slow update give it better visible what happen there
in random interleaved sequential acquisition (interleaving happen due to wfm/s speed where in same frame is overlayed many acquistions. In image 10 there is red highlighted ONE acquisition... and if scope is now faster etc there can be so many acq on one image frame that it looks nearly continuous line. 

[Mechatrommer]

Stating that I'm hiding things is offensive

i wrote "i suspect"

As I explained one is made with dot mode, other one is with Sin(x/x) interpolation...

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.

[wasedadoc]

For the umpteenth time: Gibbs ears are never in the actual signal. They are a digital filtering artefact from sin x / x that can show up on the display of a DSO. But Gibbs ears are never present in a real world signal you feed into a DSO. So you can't make Gibbs ears appear by performing any kind of operation on a real signal.

Nonsense.  Digital filtering and sin(x)/x are not the only ways to create Gibbs ears. I no longer have access to an analogue Cathode Ray Oscilloscope, but before 1980 (when Digital Sampling Oscilloscopes were but a gleam in someone's eye) I could observe the same effect when passing video test signals through a low pass filter and looking at the result on a Tektronix waveform monitor. (Similar to one in the photo.)

[nctnico]

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.

[ebastler]

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.

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?

[nctnico]

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.

[Mechatrommer]

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.

tracing back history, it came from Fourier Series itself Jean-Baptiste Joseph Fourier (1768–1830), and then the Gibbs Phenomenon discovered by Henry Wilbraham (25 July 1825 – 13 February 1883)... so, since i guess Sinc is using some of Fourier derivative, so the effect as well... Sinc is too math complicated for me, but i have FFT library that can easily produce this effect by band limiting in digital (FFT) and do the inverse FFT. i dont care whether if its a "conceptual", "theoretical", or "mathematical" property, as long as we can mimick it in reality, then we call it that... just as singularity, we call black hole is a singularity, not because its the truth singularity, but thats a reality we dont understand about where all the mathematical formulations, scientifical theory and logics collapse. i dont have time with this literalism

[Mechatrommer]

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.

yes you can get perfect square with fourier series, except the order N = infinity...

[nctnico]

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.

yes you can get perfect square with fourier series, except the order N = infinity...

Nope.

[ebastler]

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.

 

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.

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?

[2N3055]

Stating that I'm hiding things is offensive

i wrote "i suspect"

As I explained one is made with dot mode, other one is with Sin(x/x) interpolation...

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.

I give up...

[wasedadoc]

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.

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.

[nctnico]

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.

 

So how is this different from what I said? A square wave cannot be exctly 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.

It is not about truncating the series, you can never approach a perfect square wave using fourier series to start with. If you truncate the fourier series, you are left with a bandwidth limited signal.

[ebastler]

It is not about truncating the series, you can never approach a perfect square wave using fourier series to start with. If you truncate the fourier series, you are left with a bandwidth limited signal.

I keep reading "that is not the Gibbs effect, because that is not the Gibbs effect" from you.
Please state your definition, thanks!

And the statement in bold is just plain wrong, under any definition, sorry. Look at the limit for pushing the number of Fourier components towards infinity, and measure e.g. an RMS deviation between the square wave and its Fourier series. What would you claim the limiting value is?

[Mechatrommer]

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.

yes you can get perfect square with fourier series, except the order N = infinity...

Nope.

there are differences between theoretical science and applied science applied scientists try to make theoritical applicable. one of it is FFT. knowing there are limitations what a real world can do, or what we can achieve, we know where to stop as "good enough". theoritical by itself is useless if it cannot be applied. imho ymmv.

[wasedadoc]

Nope. Your scope is showing the real signal. Not 'virtual' Gibbs ears. The dead-giveaway is that the signal doesn't change between vector, dot and sin x /x mode.

That is not a dead-giveaway.  The square wave frequency is 100kHz. The sample rate is 250MHz.  That means 2500 samples for every period.  There would not be any visible change between modes.

[wasedadoc]

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.

 

So how is this different from what I said? A square wave cannot be exctly 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.

It is not about truncating the series, you can never approach a perfect square wave using fourier series to start with. If you truncate the fourier series, you are left with a bandwidth limited signal.

And how did the mathematicians produce the Gibbs ears?  They added a limited number of harmonics.  Are you disputing that is not "bandwidth limited"?