is it true, oscilloscope must reach at least 4x observed freq?

[robert.rozee]

It is what happens if you just ignore the Nyquist criterion. And then apply sinc-based interpolation anyway. Did you have to turn that on manually or is that actually the default? If so, that would seem to be either a bug or a strange design choice indeed.

the default behavior of a Siglent SDS1204X-E. i'd imagine most other similar modern DSOs would default to the same.

I wonder if the OPs question is well answered here?

he asked a simple question, and in return received a whole jumble of complex technical explanation that went straight over his head - and that was, indeed, irrelevant to the context in which his question sat. i'd imagine he is long gone, and will likely not be seen on the forums again.


to answer the OP's question: as the (broadly speaking) frequency of the signal you're sampling heads towards 1/2 of the scope's sampling rate, the image displayed by your DSO will approach a smooth undulation / sine curve. if you wish to observe fine detail in a complex waveform, you need to ensure that your DSO has a sampling rate at least several times the 'frequency' of that detail - as per the earlier posted screenshots.

if you are just wanting to observe a simple RF signal (such as AM modulation on an RF carrier), then you can get away with a sampling rate that is a tad over 2x the carrier frequency. just be wary that a DSO will 'smooth over' signal features that approach the scope's limits.


cheers,
rob   :-)

[Fungus]

It is what happens if you just ignore the Nyquist criterion. And then apply sinc-based interpolation anyway. Did you have to turn that on manually or is that actually the default? If so, that would seem to be either a bug or a strange design choice indeed.

It's mathematically correct. What else would it do?

[switchabl]

If the scope has a 200 MHz front-end and the sampling rate is set to 10 kSa/s like in the example, it is not mathematically correct (unless the user makes sure the signal itself is < 5kHz BW or it does decimation). Keysight scopes e.g. switch to linear interpolation in such a scenario which I think is a sane default. At the very least it gives you an immediate visual cue that you are sub-sampling. I guess the only mathematically correct option would be dot mode?

EDIT: I am not sure if the Siglent behaviour is a Lecroy-ism or if this is actually more widespread. It seems strange to me.

[Fungus]

Keysight scopes e.g. switch to linear interpolation in such a scenario

And are therefore less valuable when you're trying to learn signal theory. 

[nctnico]

If the scope has a 200 MHz front-end and the sampling rate is set to 10 kSa/s like in the example, it is not mathematically correct (unless the user makes sure the signal itself is < 5kHz BW or it does decimation). Keysight scopes e.g. switch to linear interpolation in such a scenario which I think is a sane default. At the very least it gives you an immediate visual cue that you are sub-sampling. I guess the only mathematically correct option would be dot mode?

IMHO switching to linear interpolation isn't a good solution either. It is entirely possible that the signal you are looking at still meets Nyquist at a lower sampling rate. The oscilloscope simply doesn't know that. This is a typical case where the user needs to know what he/she is doing.

[Fungus]

IMHO switching to linear interpolation isn't a good solution either. It is entirely possible that the signal you are looking at still meets Nyquist. The oscilloscope simply doesn't know that.

Yep.

The correct thing to do would be to put a (discreet) warning message on screen, not to try and "out-think" the user.

A user might know what they're doing or they might be trying to demonstrate/explore the limits of signal theory.

[2N3055]

If the scope has a 200 MHz front-end and the sampling rate is set to 10 kSa/s like in the example, it is not mathematically correct (unless the user makes sure the signal itself is < 5kHz BW or it does decimation). Keysight scopes e.g. switch to linear interpolation in such a scenario which I think is a sane default. At the very least it gives you an immediate visual cue that you are sub-sampling. I guess the only mathematically correct option would be dot mode?

EDIT: I am not sure if the Siglent behaviour is a Lecroy-ism or if this is actually more widespread. It seems strange to me.

On first image, scope is set for 500 us/div (7 ms total on screen) and 2kS/s. That is only 14 points on the screen, although scope shows memory setting of 14 kpoints.
On other images timebase and memory depth is show the same but sample rate is different?
How was variable sample rate with fixed memory length and same timebase achieved? SDS1104X-E has manual sample rate setting? I don't have it, so I'm asking for clarification and manual is not saying...

Sample screen shown are certainly not how scope would behave by default.
Scope is by default trying to keep sample rate as high as it can. Also that is smallest memory settings, only 14kpoints of 14Mpoints available, so 1000 times worse than possible.
Also it has both linear and sin(X)/X interpolation, and point mode that does no interpolation whatsoever. And would probably show this signal nicely.

I can demonstrate wrong signals with any scope if I deliberately set it wrong...

I understand that post was meant to demonstrate sampling, but this is not scope normal behaviour. Robert had to specifically set it to show these effects.

[Fungus]

On first image, scope is set for 500 us/div (7 ms total on screen) and 2kS/s. That is only 14 points on the screen, although scope shows memory setting of 14 kpoints.

Does that mean it could zoom out a bit? 

[2N3055]

On first image, scope is set for 500 us/div (7 ms total on screen) and 2kS/s. That is only 14 points on the screen, although scope shows memory setting of 14 kpoints.

Does that mean it could zoom out a bit? 

No it probably means he captured this at extremely long timebases like 1sec/div and then changed timebase back to 500us/div with stopped acquisition to provoke this effect. Like I said, definitely not how you would use the scope..
While i understand he did it to explain sampling, without explaining what was done, people here started discussing how scope is performing poorly. Any scope would do this even Keysights mentioned if driven this way..

[switchabl]

IMHO switching to linear interpolation isn't a good solution either. It is entirely possible that the signal you are looking at still meets Nyquist at a lower sampling rate. The oscilloscope simply doesn't know that. This is a typical case where the user needs to know what he/she is doing.

It is not ideal but I think it makes sense as a default. The oscillscope can't know, so it shouldn't guess but instead use the safest option. I am not saying you shouldn't be able to override it if you want to. If you have a large touch-screen, it might be nice to have a little warning symbol pop up that you can tap to change the setting or something. I don't know if anyone actually has that.

I mean if you actually forced a super low sample-rate manually, I guess you had it coming and are probably getting what you wanted. But if just did a single-shot at a long timebase, the sample-rate dropped automatically and then you zoom in, chances are you didn't want to see massive ringing that isn't actually there.

While i understand he did it to explain sampling, without explaining what was done, people here started discussing how scope is performing poorly. Any scope would do this even Keysights mentioned if driven this way..

No, I realize what he did. I was just surprised it doesn't turn off sinc-interpolation when you do that (I am sure you could do that manually). With the Keysights this actually happens more often because they don't have a lot of sample memory, so I know they switch to linear interpolation and don't do this.

[Fungus]

No, I realize what he did.

To be fair: There was a caption that said "2000 sps (2x frequency)" above the image.

[robert.rozee]

No it probably means he captured this at extremely long timebases like 1sec/div and then changed timebase back to 500us/div with stopped acquisition to provoke this effect.

exactly: use timebase to set acquisition rate (2x frequency, 5x, 10x, 20x, 50x, 100x, 200x), allow buffer to fill, stop, then adjust timebase to set 500us/div. in all cases 14kpts of buffer was more than sufficient.

this simulated a DSO measuring a 100MHz (as specified by original poster) square wave, with a maximum sample rate of 20Gsps, and unencumbered by any bandwidth limitations on the analog front-end.

i would have used an actual 100MHz signal and my 20Gsps DSO, but it is currently in at the shop having the oil changed and the fluffy dice re-calibrated...



cheers,
rob   :-)

(image from: https://en.wikipedia.org/wiki/Fuzzy_dice#/media/File:1958_Ambassador_4-d_hardtop_fuzzy_dice.jpg)

[2N3055]

IMHO switching to linear interpolation isn't a good solution either. It is entirely possible that the signal you are looking at still meets Nyquist at a lower sampling rate. The oscilloscope simply doesn't know that. This is a typical case where the user needs to know what he/she is doing.

It is not ideal but I think it makes sense as a default. The oscillscope can't know, so it shouldn't guess but instead use the safest option. I am not saying you shouldn't be able to override it if you want to. If you have a large touch-screen, it might be nice to have a little warning symbol pop up that you can tap to change the setting or something. I don't know if anyone actually has that.

I mean if you actually forced a super low sample-rate manually, I guess you had it coming and are probably getting what you wanted. But if just did a single-shot at a long timebase, the sample-rate dropped automatically and then you zoom in, chances are you didn't want to see massive ringing that isn't actually there.

While i understand he did it to explain sampling, without explaining what was done, people here started discussing how scope is performing poorly. Any scope would do this even Keysights mentioned if driven this way..

No, I realize what he did. I was just surprised it doesn't turn off sinc-interpolation when you do that (I am sure you could do that manually). With the Keysights this actually happens more often because they don't have a lot of sample memory, so I know they switch to linear interpolation and don't do this.

If you are doing long single capture you don't  set scope for smallest memory setting.... He could have set scope for 14MPts and have 1000X better sampling rate. If you want to capture all possible glitches use peak detect mode.. For single captures like that I set scopes for all it has (200-250 Mpts, would use more if available, although it gets to the point of diminishing returns after a while) and I can get lots of data at full sample rate...

As for linear/sinc interpolation, that is a matter of visual aesthetics in this case.. Both are showing nonsense...

And as I said, you could set Siglent for dot mode and get "sort of" ETS and it would actually show signal correctly (if signal is repetitive, of course) ..  Or it would show single dots and give you info on sparsity of data. So you know that you should up the sampling rate...

[The Electrician]

I figured out what robert.rozee was doing a couple of hours ago, and did the same thing on my Agilent DSO5054 scope.  I set the timebase to 50 seconds/division and used the probe cal signal as input.  I went back to watching the Queens last trip to London while wating for the buffer to fill up.  I then switched the timebase to 500 uS/div and set the display to dot mode.  Here's what that looks like; the dots are really hard to see, but they're there:

]

Here it is with Agilent's linear interpolation turned on:



If you can see sharp corners in linear interpolation mode where there should be smooth curves, the signal is probably sub-sampled.  Of course, some sharp corners should be there, such as the corners of a square wave, but if a sine wave looks like it's made of only a few straight lines, that's what I'm referring to.

[nctnico]

The signal isn't sub-sampled. Just turn sin x/x reconstruction on and you'll see the actual waveform. Linear (vector) display is one of the most useless features of a DSO IMHO.

As for linear/sinc interpolation, that is a matter of visual aesthetics in this case.. Both are showing nonsense...

No, not at all. Both methods will show a waveform that connects all the sample points by definition. Remember an oscilloscope is there to visualise a waveform. It makes little sense to turn sin x/x off when there are few sample points to work with; it is there to help your brains to see and interpret the signal. However the assumption is that the oscilloscope is setup in a way the signal is sampled correctly (either through a high enough samplerate or using ETS on a periodic signal).

[The Electrician]

The signal isn't sub-sampled. Just turn sin x/x reconstruction on and you'll see the actual waveform. Linear (vector) display is one of the most useless features of a DSO IMHO.

As for linear/sinc interpolation, that is a matter of visual aesthetics in this case.. Both are showing nonsense...

No, not at all. Both methods will show a waveform that connects all the sample points by definition. Remember an oscilloscope is there to visualise a waveform. It makes little sense to turn sin x/x off when there are few sample points to work with; it is there to help your brains to see and interpret the signal. However the assumption is that the oscilloscope is setup in a way the signal is sampled correctly (either through a high enough samplerate or using ETS on a periodic signal).

That signal is quite sub-sampled.  The rise time of the square wave is 180 nS; no details of the rising and falling edges are visible.  The sample rate is 8 Ksa/s and there is substantial frequency content well above 4 kHz.

This scope is old enough that it doesn't have sin x/x interpolation.  As switchabl mentioned the older Agilent scopes typically use linear interpolation, and it isn't at all useless.  If your choices are dot mode and linear interpolation, linear interpolation is just fine.  When your signal is oversampled, you can't tell the difference anyway.  This scope has rated max sample rate of 4 Gsa/s, and analog bandwidth of 500 MHz, so it's 4 times oversampled at rated bandwidth, and much more than that for lower bandwidth signals.

[nctnico]

The signal isn't sub-sampled. Just turn sin x/x reconstruction on and you'll see the actual waveform. Linear (vector) display is one of the most useless features of a DSO IMHO.

As for linear/sinc interpolation, that is a matter of visual aesthetics in this case.. Both are showing nonsense...

No, not at all. Both methods will show a waveform that connects all the sample points by definition. Remember an oscilloscope is there to visualise a waveform. It makes little sense to turn sin x/x off when there are few sample points to work with; it is there to help your brains to see and interpret the signal. However the assumption is that the oscilloscope is setup in a way the signal is sampled correctly (either through a high enough samplerate or using ETS on a periodic signal).

That signal is quite sub-sampled.  The rise time of the square wave is 180 nS; no details of the rising and falling edges are visible.  The sample rate is 8 Ksa/s and there is substantial frequency content well above 4 kHz.

This scope is old enough that it doesn't have sin x/x interpolation.  As switchabl mentioned the older Agilent scopes typically use linear interpolation, and it isn't at all useless.  If your choices are dot mode and linear interpolation, linear interpolation is just fine.  When your signal is oversampled, you can't tell the difference anyway.  This scope has rated max sample rate of 4 Gsa/s, and analog bandwidth of 500 MHz, so it's 4 times oversampled at rated bandwidth, and much more than that for lower bandwidth signals.

First of all, I strongly doubt the older Agilent scopes don't have sin x/x reconstruction. This is a pretty basic functionality for a DSO.  Even my old CRT based Iwatsu DS-8617 DSO had sin x/x interpolation. And for a good reason, with 4 times oversampling you won't get a true representation of a waveform using vectors (linear) reconstruction.

Secondly, feeding a high frequency waveform and then using a too low samplerate is just 'user error'. It proves nothing.

[The Electrician]

The Agilent DSO5054 does not have sin x/x interpolation.

[The Electrician]

The Agilent DSO5054 does not have sin x/x interpolation. It's only at 500 MHz that the oversampling rate is 4x.  At lower frequenies, for example audio and low RF, the oversampling rate is much higher.

[tggzzz]

It is what happens if you just ignore the Nyquist criterion. And then apply sinc-based interpolation anyway. Did you have to turn that on manually or is that actually the default? If so, that would seem to be either a bug or a strange design choice indeed.

the default behavior of a Siglent SDS1204X-E. i'd imagine most other similar modern DSOs would default to the same.

I wonder if the OPs question is well answered here?

he asked a simple question, and in return received a whole jumble of complex technical explanation that went straight over his head - and that was, indeed, irrelevant to the context in which his question sat. i'd imagine he is long gone, and will likely not be seen on the forums again.


to answer the OP's question: as the (broadly speaking) frequency of the signal you're sampling heads towards 1/2 of the scope's sampling rate, the image displayed by your DSO will approach a smooth undulation / sine curve. if you wish to observe fine detail in a complex waveform, you need to ensure that your DSO has a sampling rate at least several times the 'frequency' of that detail - as per the earlier posted screenshots.

That is misleading to the point of being false.

Replace "frequency of the signal" with "the highest component frequency of the signal" and that would be more nearly correct.

if you are just wanting to observe a simple RF signal (such as AM modulation on an RF carrier), then you can get away with a sampling rate that is a tad over 2x the carrier frequency. just be wary that a DSO will 'smooth over' signal features that approach the scope's limits.[/i]

Completely wrong in several important respects, as noted earlier in the thread - and in more detail in standard textbooks.

[nctnico]

The Agilent DSO5054 does not have sin x/x interpolation.

It has. It says in the datasheet but not in the manual. It switches automatically between linear and sin x/x mode when linear interpolation is not going to work to produce a waveform that resembles the signal at the probe tip. BTW: I used to own an MSO7000A which is basically the same hardware platform as your DSO5054 so I have some hands-on experience with these models.

[Someone]

I wonder if the OPs question is well answered here?  I would be good if he could return and try to answer the outstanding issues with his first question.

He may not know the difference between BW and SR.

Yes, the thread title and opening post are vague enough that the usual suspects are making some big argument out of thin air:
"perfect band limited signal in infinite time capture can be perfect"
vs
"real world signal with real world oscilloscope does not work that way"

Even "sin(x)/x" is not a fully specified filter, as many (most?) implementations are truncating/windowing the extents.

2.5x is a magic number associated with "sharp" yet still practical antialiasing filters that has been widely misunderstood. It all depends on the input (antialiasing) and output (reconstruction) filters in the specific implementation/use-case....   remembering that most scopes dont have those sharp filters and use gaussian/bessel filters or something close to that for which the "rule of thumb" is 4x or 5x sample rate to bandwidth (attached below since Keysight have started personalinfo-walling all their documents).

[Someone]

and to be more clear, 2.5x is a figure that provides some non-specific limit to that effect under typical band limiting/anitaliasing/reconstruction and does not ensure errors are avoided.

I don't think you can get major distortions at 2.5x with a band-limited signal, but that's still an "if". How would you know?

Because I do this stuff for a living... you can keep putting out non-specific/vague figures but they are just that, something which might be true in some non-specified situation.

There are easily found examples of 2.5x being inadequate.

Please give us some examples where 2.5x is inadequate. 

Please provide the band limited signal source that has zero energy above the measurement frequency and I'm sure it would be difficult. But real world signals are not perfectly band limited....
This can go around and around as many times as you like. It's an entirely different argument which has derailed the thread immediately into complete nonsense.

What are the errors that you are trying to avoid/limit? what is the accuracy of the measurement (and what is the measurement) you are trying to make? What are the antialiasing and reconstruction filters being used?

With that sort of information you could start to answer what the actual bandwidth to sample rate is required. Its not some simple every situation works at 2.5x or everything is fine once you go past 5x, it depends on the specifics.

[Fungus]

Please give us some examples where 2.5x is inadequate. 

Please provide the band limited signal source that has zero energy above the measurement frequency and I'm sure it would be difficult.

I'll take that as a no.

Its not some simple every situation works at 2.5x or everything is fine

No, but in the real world there are some very simple cases that fail below 2.5x. 2.5x is a good starting point.

FWIW: I was observing the AM modulation effect below 2.5x using a hardware reconstruction filter.

[BillyO]

I wonder if the OPs question is well answered here?  I would be good if he could return and try to answer the outstanding issues with his first question.

He may not know the difference between BW and SR.

Yes, the thread title and opening post are vague enough that the usual suspects are making some big argument out of thin air:
"perfect band limited signal in infinite time capture can be perfect"
vs
"real world signal with real world oscilloscope does not work that way"

Even "sin(x)/x" is not a fully specified filter, as many (most?) implementations are truncating/windowing the extents.

That's what I see too.  If the OP is a newbie to all this and does not even know the difference between BW and SR, how is this discussion gong to help them?  More than likely it will send them away.  There seems to be a certain amount of elitism on this site, and I can understand that, but if you are not willing to address a new members basic questions with patience then maybe go off to the the "I know everything better than you" forum and hash out the nuances there.

We need more people in this field rather than out of it and contemplating f'd up concepts of ignorance such as flat earth and anti-science.  The experts are the ones we need supporting STEM and helping people elevate themselves and not alienating those taking baby steps.  This is something I struggle with too, so..

Sorry for the rant.