Does Agilent X3000 series use Linear or sin x/x interpolation?

[alm]

With 2MS (all channels) then zooming in a long way might result in well under one point per division but for the zooming case sinc(x) isn't valid.

Why not? sinc(x) interpolation should result in a good reconstruction for a signal bandwidth limited to below the Nyquist frequency. This is a function of sample rate and signal bandwidth. You can zoom in however you like on a signal with 1 MHz bandwidth that was sampled at 10 MS/s, but the reconstruction should still be correct. There are no details beyond 1 MHz in this signal. Zooming does not affect the bandwidth of either the signal or the scope.

[jpb]

With 2MS (all channels) then zooming in a long way might result in well under one point per division but for the zooming case sinc(x) isn't valid.

Why not? sinc(x) interpolation should result in a good reconstruction for a signal bandwidth limited to below the Nyquist frequency. This is a function of sample rate and signal bandwidth. You can zoom in however you like on a signal with 1 MHz bandwidth that was sampled at 10 MS/s, but the reconstruction should still be correct. There are no details beyond 1 MHz in this signal. Zooming does not affect the bandwidth of either the signal or the scope.

The point is that the signal bandwidth is only limited by the bandwidth of the scope so you can't know that the signal is limited to 1MHz and it is dangerous to make this assumption as would be required for sinc(x) interpolation. Of course the signal may be externally limited but if you're measuring it with a scope presumably you don't know this. Even if the signal is nominally limited you may be zooming in to look at some high frequency noise.

[Wuerstchenhund]

Because of the discussion I tried the same on my scope (LeCroy Waverunner LT 224) yesterday. The scope does linear interpolation and sin(x)/x, and both can be switched on and off independent of the timebase setting.

The signal is a 5MHz sine wave at 300mVpp. Source is a Siglent SDG1020, the line is 50 Ohms fully terminated.

The screenshots below show a non-interpolated sine wave on the top grid and the sin(x)/x interpolation on the bottom grid at same rates from 10MSa/s to 10GSa/s.

[marmad]

This may be considered ugly, but it's a clear warning that there are insufficient samples to reconstruct a true representation of the incoming waveform.

Could you explain why I need a 'warning' from my DSO? I don't need my hammer to beep when I lift it by the head instead of the handle to warn me that it's not the correct way to use it. What I need is good documentation - with explanations of features pros and cons - and then user-selectable menu options to turn those features on and off. I thought one of the points of using sin(x)/x was that it could accurately reconstruct the waveform, assuming a sample rate at least 2.5 times the highest frequency component - as opposed to linear interpolation, which requires a sample rate at least 10 times higher. Let me, the user, chose when and how to use each respective tool.

With regard to some of the example waveforms, it seems that many modern DSOs don't announce the fact that they have shifted acquisition mode from repeated single shot mode to Random Interleaved Sampling.

I'm not sure if you're implying that the Rigol is doing this - but if that's the case, you're incorrect.

[alm]

The point is that the signal bandwidth is only limited by the bandwidth of the scope so you can't know that the signal is limited to 1MHz and it is dangerous to make this assumption as would be required for sinc(x) interpolation. Of course the signal may be externally limited but if you're measuring it with a scope presumably you don't know this. Even if the signal is nominally limited you may be zooming in to look at some high frequency noise.

Sure, there may be components beyond 5 MHz, but the zoom level has no effect on this. Aliasing can easily show up at much lower zoom levels.

[kg4arn]

......   What I need is good documentation - with explanations of features pros and cons - and then user-selectable menu options to turn those features on and off. I thought one of the points of using sin(x)/x was that it could accurately reconstruct the waveform, assuming a sample rate at least 2.5 times the highest frequency component - as opposed to linear interpolation, which requires a sample rate at least 10 times higher. Let me, the user, chose when and how to use each respective tool.

I agree.  Yet, I concede that it is Agilent's right to decide the scope's operation and feature set. I respect that. 

However, I am miffed that the User Guide for the scope spends page space explaining rudimentary sampling theory and says absolutely nothing about how the scope actually presents the sampled data.  As is plain from the preceding discussion, that information is crucial to understanding how to apply the scope properly.  The information was in a separate app note.  Why???

And this isn't really an entry level scope (my opinion).  Fully optioned, at the highest bandwidth, this scope is $20,000+ US
I do expect the technical documentation to have more depth and relevance.

[AndyC_772]

I agree that 'entry level' isn't really the proper label. Maybe 'general purpose' would be better, as it's certainly a very good range of models for a design engineer's bench, and way above what a production technician or hobbyist would ever need.

Even if you regard all the cheap scopes from Far Eastern manufacturers as toys, there's still the 2000X series to carry the 'entry level' tag.

[Wuerstchenhund]

And this isn't really an entry level scope (my opinion).  Fully optioned, at the highest bandwidth, this scope is $20,000+ US

I know $20k is a lot of money for an individual (who rare ly would spend even 1/10th on a scope) but I can tell you in terms of oscilloscopes it's really not much. It's still the very bottom end of the market.

And 'entry level' is the common term for this class of scopes because they provide a basic set of functionality at a modest price and are usually bought as learning devices for schools and universities, as first scopes for ongoing EEs and for smaller elecronic shops, or as basic test device for simpler tasks. It's an adequate label.

I agree that 'entry level' isn't really the proper label. Maybe 'general purpose' would be better, as it's certainly a very good range of models for a design engineer's bench, and way above what a production technician or hobbyist would ever need.

Most scopes are 'general purpose' no matter if it costs $2k, $20k or $200k (in fact, the more expensive scopes are even more 'general purpose' as they offer much more functionality than the entry level scopes).

And many of the options that are required to bring a DSO-X2000 to $20k are specifically *NOT* 'general purpose' but in fact only certain purpose.

[kg4arn]

I know $20k is a lot of money for an individual (who rare ly would spend even 1/10th on a scope) but I can tell you in terms of oscilloscopes it's really not much. It's still the very bottom end of the market.

    I do to have a big boy oscilloscope.....  I do, I do, I do.... 

Seriously, point taken.

[Wuerstchenhund]

I did the same tests with a 5MHz square wave. The following screenshots show the true (non-interpolated) signal in the upper grid and the sin(x)/x interpolation in the bottom at sample rates of between 5MSa/s and 10GSa/s.

[Wuerstchenhund]

And last but not least, a comparison between linear interpolation (top grid) and sin(x)/x interpolation (bottom grid) between 10MSa/s (didn't make sense to go much lower) and 10GSa/s. Again, the source is a 5MHz square wave.

I think the images show pretty well that interpolation in general has its limit, and no matter if a scope is cheap or expensive, it should always indicate when interpolation is used and if so, what type of interpolation. Most importantly, interpolation must be optional (i.e. can be switched off by the user).

[marmad]

And last but not least, a comparison between linear interpolation (top grid) and sin(x)/x interpolation (bottom grid) between 10MSa/s (didn't make sense to go much lower) and 10GSa/s. Again, the source is a 5MHz square wave.

Great stuff - very interesting; thanks for your time and effort to do these. Any chance you might repeat this last series using a 5MHz sine wave while comparing the linear and sin(x)/x interpolation?

[Wuerstchenhund]

Any chance you might repeat this last series using a 5MHz sine wave while comparing the linear and sin(x)/x interpolation?

Sure, no problem. The images below show a 5MHz sine wave at 300mVpp, 50 Ohms fully terminated, with linear interpolation in the upper grid and sin(x)/x + linear interpolation in the bottom grid (unfortunately on my scope linear interpolation can only be enabled for all displayed waveforms, unlike sin(x)/x), at sampling rates between 10MSa/s and 10GSa/s.

[marmad]

Sure, no problem. The images below show a 5MHz sine wave at 300mVpp, 50 Ohms fully terminated, with linear interpolation in the upper grid and sin(x)/x + linear interpolation in the bottom grid (unfortunately on my scope linear interpolation can only be enabled for all displayed waveforms, unlike sin(x)/x), at sampling rates between 10MSa/s and 10GSa/s.

Thanks very much! It's clear from these that the Rigol is doing linear interpolation - at least at sampling rates <= 100MSa/s. But the Agilent is either not doing linear interpolation correctly, or the sample points are not symmetrical/equidistant for some reason.

[Wuerstchenhund]

Thanks very much! It's clear from these that the Rigol is doing linear interpolation - at least at sampling rates <= 100MSa/s.

Can you disable interpolation on the Rigol scopes?

But the Agilent is either not doing linear interpolation correctly, or the sample points are not symmetrical for some reason.

It seems DSO-X 2000/3000 Series Agilent did go quite a long way in making various decisions which should be up to the user. The more I hear about this Series the less I like what I hear.

[marmad]

Can you disable interpolation on the Rigol scopes?

Yes, but the choices are only 'dots' or 'vectors' - and they don't give any information about what interpolation they're using. But the images I posted here before (at lower sample rates) clearly look like linear interpolation (using your images as comparison). But the following images look like sin(x)/x interpolation by the Rigol, so if it switches between the two types, I'm trying to figure out exactly when/how it does that.

Edit: BTW, the following images are from a completely artificially created waveform file, which was loaded into the DSO to see how it would interpolate it.

[kg4arn]

Thanks very much! It's clear from these that the Rigol is doing linear interpolation - at least at sampling rates <= 100MSa/s. But the Agilent is either not doing linear interpolation correctly, or the sample points are not symmetrical/equidistant for some reason.

Indeed the Agilent sample points do not appear to be symmetric, at least the displayed sample points.

Might this be related to anti aliasing?

I have been unable to get my Agilent to present a classic alias waveform where a high frequency signal at low sample rates looks like a signal at lower frequency.  What I see is a "ghost" alias (I don't know what the proper terminology might be).

The attached trace shows a sine input, 50 ohm terminated.  I show a signal slightly off 10Mhz. But anywhere around 10 MHz the un-zoomed trace shows the "ghost" alias.  The zoomed trace suggests that the displayed data points are not symmetric.

[Wuerstchenhund]

BTW: The link below goes to a document talking about interpolation. It's a bit older and contains the occasional bit of marketing blurb, but it's a very good introduction into linear and Sin(X)/x interpolation, and also contains a section on how to test your scope.

http://teledynelecroy.com/support/techlib/registerpdf.aspx?documentID=578

[Wuerstchenhund]

I have been unable to get my Agilent to present a classic alias waveform where a high frequency signal at low sample rates looks like a signal at lower frequency.  What I see is a "ghost" alias (I don't know what the proper terminology might be).

The attached trace shows a sine input, 50 ohm terminated.  I show a signal slightly off 10Mhz. But anywhere around 10 MHz the un-zoomed trace shows the "ghost" alias.  The zoomed trace suggests that the displayed data points are not symmetric.

The image shows you're only sampling at 5MSa/s (5MHz) which is around 1/4th of the minimum sample rate according to Nyquist required for a 10MHz signal.

What you see is the result of interpolation of an insufficient number of sampling points. As your signal is not exactly 10MHz but slightly below these points will be at different spots on the waveform, resulting in the odd trace you see.

[marmad]

BTW: The link below goes to a document talking about interpolation. It's a bit older and contains the occasional bit of marketing blurb, but it's a very good introduction into linear and Sin(X)/x interpolation, and also contains a section on how to test your scope.

http://teledynelecroy.com/support/techlib/registerpdf.aspx?documentID=578

Interesting. At the end of the document, they reference the problem of the Agilent (and show an image that's almost precisely like kg4arn's):

"Agilent and Tektronix alter the interpolation behavior depending most notably on the time/division setting. Effectively both competitive scopes resist interpolation when the acquisition time duration becomes large. In other words, the sample rate improvement with interpolation diminishes as the acquisition time duration is made larger. Since larger time/division settings tend to diminish a user's view of waveform features, unless a zoom is employed, the fundamental message in this behavior is: There is no need for higher resolution and precision in the waveform acquisition unless the fine features are being viewed. LeCroy takes serious issue with this type of instrument behavior. We believe that the measurement results in your waveform analysis should not depend on what you are currently viewing on the screen."

[Wuerstchenhund]

Can you disable interpolation on the Rigol scopes?

Yes, but the choices are only 'dots' or 'vectors' - and they don't give any information about what interpolation they're using.

That's bad but at least you can disable interpolation, so not all is bad.

I guess Rigol (as Agilent) use a table based on the time base setting to decide if using linear or sin(x)/x. You could do some tests to find out at which setting which interpolation method is used.

[marmad]

I guess Rigol (as Agilent) use a table based on the time base setting to decide if using linear or sin(x)/x. You could do some tests to find out at which setting which interpolation method is used.

Well, I ran some tests - and it seems (although I might be incorrect about this) that the Rigol does not use the timebase setting to determine the interpolation method - but instead uses the sample rate. From what I've discovered so far, it appears that:

Sample rate <= 500MSa/s uses linear interpolation
Sample rate >= 1GSa/s uses sin(x)/x interpolation

Based on math, it seems like it would make more sense the other way around - although I guess the fact that it uses linear interpolation at lower sample rates means that (if you don't pay attention) you're more likely to realize you're undersampling.

[jpb]

Well, I ran some tests - and it seems (although I might be incorrect about this) that the Rigol does not use the timebase setting to determine the interpolation method - but instead uses the sample rate. From what I've discovered so far, it appears that:

Sample rate <= 500MSa/s uses linear interpolation
Sample rate >= 1GSa/s uses sin(x)/x interpolation

Based on math, it seems like it would make more sense the other way around - although I guess the fact that it uses linear interpolation at lower sample rates means that (if you don't pay attention) you're more likely to realize you're undersampling.

It makes sense in that sinc(x) interpolation is based on the signal being band limited above the Nyquist rate, for 1GS/s this is 500MHz and above so should be well attenuated by the input circuitry whilst at 500MS/s it is 250MHz which won't be much attenuated if the Band Width is 200MHz or more.

Linear interpolation is just to show where the points are really rather than being an attempt to fill in the missing parts of the waveform - that is linear interpolation won't produce any spurious peaks even if it produces discontinuities in the gradient.

[marmad]

It makes sense in that sinc(x) interpolation is based on the signal being band limited above the Nyquist rate, for 1GS/s this is 500MHz and above so should be well attenuated by the input circuitry whilst at 500MS/s it is 250MHz which won't be much attenuated if the Band Width is 200MHz or more.

Yes, of course... I should have thought of that! Thanks    It makes sense in terms of the 200MHz BW limit of the DS2000 series.

[marmad]

I've been reading all I could find recently about the Agilent X-Series, trying to determine the cause of the behavior evidenced in kg4arn's images - which seems to me might indicate what I would consider a design flaw in the X-Series.

For those new to the thread - it has to do with the difference between the following two images:





Firstly, I'd like to point out that it's quite difficult to know the exact sample lengths used with various combinations of channels, running modes, etc, in the 3000 X-Series given both the very limited information - and the strange presentation of some of it - by Agilent. Through all my digging, I was unable to come up with a single table outlining the exact record lengths - and when they're used.

Given that they publish both this specification:

"Maximum duration of time captured at highest sampling rate (all analog channels) 250us"

...which, with a 4GSa/s rate, equals 1MB of memory - so would tend to indicate that a maximum of 1MB can be used by any single channel in any mode.

and this info:

"When running (versus taking a single acquisition), the memory is divided in half. This lets the acquisition system acquire one record while processing the previous acquisition, dramatically improving the number of waveforms per second processed by the oscilloscope."

...it's difficult to know for sure if one channel has access to the entire memory pool when running on it's own or not. In other words, when in Normal mode and running a single channel, does the scope divide the entire 2MB in half, giving one channel a 1MB record length - or - does it divide the 1MB per channel-pair in half, giving the single channel just a 500kB record length.

I mention all this mainly as a caveat since I'm not completely clear as to whether kg4arn's images represent 1MB or 500kB of sample points - which would affect the percentage of error.

Secondly, as evidenced by the images posted by Wuerstchenhund and myself, I think it's pretty clear that what we see in kg4arn's images is NOT an interpolation problem - since mere interpolation changes from sin(x)/x to linear (or to no interpolation, for that matter) STILL result in a clearly symmetrical wave-shape - with equidistantly spaced sample points. No, I think what is visible are sampling 'errors', if you will, and it seems to me that they must somehow arise from Agilent's practice of decimation.

Since both the Rigol and LeCroy DSOs produce fairly similar symmetrical output to the test waveforms - and both DSOs follow the practice of actually slowing down the clock speed to the ADC to reduce the sampling rate (while maintaining record lengths) - it seems to me that it might be reasonable to assume that Agilent's practice of 'throwing away' samples (decimation) in order to simulate a slower clock rate might be leading to what can only be defined as missing and/or misaligned sample points.

If all of this is true, it seems to me that Agilent's decision to optimize it's MegaZOOM ASIC for the fastest waveform update rates - in exchange for signal fidelity at slower sample 'speeds' (when unable to reduce clock rates, the ASIC decimates) - was a mistake. Any further information which might enlighten this issue - from other X-Series owners or Agilent techs - would be welcome.
 
Edit: I might also point out that in the two test images, the Rigol is actually sampling at half the rate of the Agilent (100MSa/s), making it's errors seem even more severe. If the Agilent record length in the above image is 1MB, than the ASIC is throwing away 39 out of every 40 samples; if it's 500kB, then it's throwing away 79 out of every 80 samples.

Edit2: Thinking about this further, I'm wondering if the anomalies in the Agilent's sampled waveform might be produced via it's practice of swapping banks of acquisition memory while running in Normal mode, then appearing to combine both banks together somehow when Stopped.