Choosing between entry-level 12-bit DSOs

[gf]

170 MHz folds back to 142 MHz in the first Nyquist zone. So it looks like you had sampled a 142 MHz sine wave.

if you really try to probe 170MHz fundamentals at 312 MSa/s really you have something wrong within you, not the scope,

There is nothing wrong with bandpass samling if the frequency plan permits it. An ADC can act as a mixer. But you need to know what you are doing. 312 MSa/s is indeed suboptimal for 170 MHz. Better use 156 MSa/s. Then you get 14 MHz and for sample_rate/11, sinc interpolation is expected to work (it's not expected to work for 142 MHz @312 MSa/s).

Edit: Admittedly, bandpass sampling is more interesting in conjunction with frequency domain analysis than with time domain analysis. But it also works in the time domain for periodic non-sinewave signals with a fundamental frequency close to an integral multiple of the sample rate (for example f = N*SR +-0.01*SR).

[Mechatrommer]

1) to be precise, anything more or equal to Sample rate / 2 will not be reconstructed correctly, i havent found literature saying exactly 2.5

Anything equal to sample rate/2 can NOT be reconstructed.

thank you for re-emphasizing my statement and hence Nyquist Theorem.

Now work from there to something a tiny bit below that ... you'll go between zero crossings and peaks over time, and get an AM effect as seen in that video.
...
2.5 isn't a mathematically derived number, it's what works in practice.

yes 2.5 is not derived from theory, its probably from empirical testing of imperfect sampling mechanism (presence of jitter/harmonics/hi-freq more than nyquist limit)...

[gf]

yes 2.5 is not derived from theory, its probably from empirical testing of imperfect sampling mechanism (presence of jitter/harmonics/hi-freq more than nyquist limit)...

It is primarily a compromise with the computational complexity of the interpolation filter (and consequently, the number of extra samples which need to be acquired in order that the settling phase of the filter can be discarded). For example, the frequency response of a sinc function, truncated to a length of 20 sample intervals, and then windowed with a Kaiser window, happens to start rolling off at approx. 0.4 * sample_rate (or sample_rate / 2.5), see figure3.

Amendment [without figure]: And if I truncate to a length of only 10 sample intervals (which reduces the computational complexity by ~50%), then the roll-off starts at approx. 0.3 * sample_rate (or sample_rate / 3.3).

[Fungus]

FWIW you'll get the same with a hardware filter, too.

eg. I've seen the "2.5x rule" appear when sending a PWM signal into an RC filter.

My PWM frequency was 31.25kHz and the "AM" effect appeared right around 12.5kHz  (31.25/2.5=12.5). 

This image shows where it comes from - the amplitude changes depending on the phase difference between the samples and the signal:


Edit: The effect vanishes very quickly below 2.5x. I'm not sure why...

You can see it in that video: The "AM" effect starts around 2.6x (120MHz)

[Mechatrommer]

This image shows where it comes from - the amplitude changes depending on the phase difference between the samples and the signal:

by theory, Sinc should be able to reconstruct grey wave (original wave) from blue dots (sampled points) but since we saw AM modulated reconstruction by Sinc interpolation earlier meaning its not perfect according to theory. or possibly nyquist limit was already violated due to presence of harmonics (imperfect BW limited scope). ymmv.

[Fungus]

since we saw AM modulated reconstruction by Sinc interpolation earlier meaning its not perfect according to theory. or possibly nyquist limit was already violated due to presence of harmonics (imperfect BW limited scope). ymmv.

The thing is: I've seen the same effect in a synthesizer, not a sampler, and with a hardware filter.

[Fungus]

by theory, Sinc should be able to reconstruct grey wave (original wave) from blue dots (sampled points)

Riddle me this:

Signal theory also says there's only one curve that fits a set of sampled points in a bandwidth limited signal.

The "AM" signal fits perfectly so how can we say it's possible to reconstruct the original sine wave? It contradicts theory.

[gf]

Riddle me this:
Signal theory also says there's only one curve that fits a set of sampled points in a bandwidth limited signal.
The "AM" signal fits perfectly so how can we say it's possible to reconstruct the original sine wave? It contradicts theory.

Perfect reconstruction requires an ideal brickwall interpolation filter (-> infinte length).

With a realizable interpolation filter, the reconstructible bandwidth becomes lower.
For example samle_rate / 2.5. The actual denominator depends on the frequency response of the filter, see my previous message.
The point where the filter starts rolling off is basically the the reconstructability limit.

[awakephd]

Friends, again I thank you for filling in some of the gaps in my ignorance. I probably will not attempt to keep up in this thread, as the discussion has left me behind - I sorta kinda understand some of what is being discussed, but it is way beyond my current needs and abilities. This is not a complaint - it is the nature of open discussions to go where they will. I just don't want anyone to ask a question to the OP (me), get no response, and think I have taken my marble (only one, and it is cracked!) and gone home. I may start a new thread when I am about to pull the trigger on a purchase - only about a month away, now - can't wait!

[wasedadoc]

by theory, Sinc should be able to reconstruct grey wave (original wave) from blue dots (sampled points)

Riddle me this:

Signal theory also says there's only one curve that fits a set of sampled points in a bandwidth limited signal.

The "AM" signal fits perfectly so how can we say it's possible to reconstruct the original sine wave? It contradicts theory.

The theory applies if the reconstruction filter is a perfect low pass filter with regard to the highest frequency component that was present in the original continuous version.  (And that the sampling rate was at least twice that of the highest frequency component in the original.)  A perfect low pass has a sinc impulse response and that has infinitely long pre and post tails.  No practical implementation can achieve that.  The '/x' part of sin(x)/x diminishes only slowly as x increases.  Truncating or windowing the sinc introduces discrepancies which become more significant as one approaches half sample rate.

That wave which passes through the sample points yet has undulations does contain frequencies above half sample rate.  Hint:  AM sidebands.

[shapirus]

Latest firmware update was 5 days ago on the TinySA Ultra. I wonder if they fixed that bug. There's been significant updates apparently since the version I had. I was using 1.4-120, now they're at 1.4-159.

Nope, same exact thing with 1.4-159.

Here's a demonstration with increased persistence (to see the glitches) and the lowest memory length for the max waveform update rate.

First, there's a 20 sec-long frequency sweep from 20 MHz to 120 MHz, then (00:30) frequency is changed manually in +100 kHz steps and finally (01:25) amplitude is changed manually.

As we can see, on any change in frequency or amplitude it has a brief period during which it outputs all sorts of crap. Frequency sweep output is the easiest way of catching it.

It's not the scope: it displays frequency sweeps from a different generator just fine, nice and clean.

[KungFuJosh]

Latest firmware update was 5 days ago on the TinySA Ultra. I wonder if they fixed that bug. There's been significant updates apparently since the version I had. I was using 1.4-120, now they're at 1.4-159.

We should probably continue this discussion in the TinySA thread, and report the bug to them as well. I'll try recreating it also when I have some time.

[shapirus]

We should probably continue this discussion in the TinySA thread, and report the bug to them as well. I'll try recreating it also when I have some time.

Makes sense.
Moved it here: https://www.eevblog.com/forum/testgear/tinysa-ultra-launched/msg5470555/#msg5470555

[Mechatrommer]

Riddle me this:
Signal theory also says there's only one curve that fits a set of sampled points in a bandwidth limited signal.
The "AM" signal fits perfectly so how can we say it's possible to reconstruct the original sine wave? It contradicts theory.

the possibility is i already mentioned...

1) oscilloscope is not properly BW limited, so Sinc filter is unable to reconstruct perfectly, instead of nice sine, it creates AM sine.
2) the filter probably assumes (algorithm used is for) "uniform sampling distance" where in reality is not.
3) or simply, DHO900 is not using proper Sinc filter? (if shapirus can provide me with CSV data of the sampled 142MHz @ 312.5MSps that produced the AM shape on DSO, i may try to replot it in my VisaDSO with its latest implementation of Sinc (internet open source copy pasted implementation) so we can see if same AM shape is produced)

https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

maybe we can look the same test made by shapirus on SDS800X if scope can produce the same AM shaped signal very near to (but not reaching) Sr / 2. if SDS800X is properly BW limited and Sinc filter/interpolation is implemented correctly i suspect it will not create such AM shape, it should be nice 142MHz sine (constant amplitude on each cycle) unlike the picture you linked earlier (on Rigol DHO900) if sampled at slightly higher than 284MSps (such as 312.5MSps). ymmv.

[Fungus]

1) oscilloscope is not properly BW limited, so Sinc filter is unable to reconstruct perfectly, instead of nice sine, it creates AM sine.

140MHz is below Nyquist.

[2N3055]

All 4 channels on.

[wasedadoc]

1) oscilloscope is not properly BW limited, so Sinc filter is unable to reconstruct perfectly, instead of nice sine, it creates AM sine.

140MHz is below Nyquist.

Referring to the photo in post #436, one cycle of the undulation frequency occurs every 5 cycles of the  varying amplitude 136.17 MHz which makes the undulation 27.234MHz.  So one sideband is 136.17 + 23.234 which is 163.40 MHz. That is more than half the 312.5 MHz sample rate.

[egonotto]

Hello,

The problem here is that the conditions of the Nyquist-Shannon sampling theorem are not fulfilled and therefore it cannot be used. We do not have the required infinite number of sampling points. The infinite number of sampling points is essential in the proof of the Nyquist-Shannon sampling theorem.

Does anyone know a sampling theorem that only requires a finite number of sampling points?

Best regards
egonotto

[gf]

1) oscilloscope is not properly BW limited, so Sinc filter is unable to reconstruct perfectly, instead of nice sine, it creates AM sine.

140MHz is below Nyquist.

Referring to the photo in post #436, one cycle of the undulation frequency occurs every 5 cycles of the  varying amplitude 136.17 MHz which makes the undulation 27.234MHz.  So one sideband is 136.17 + 23.234 which is 163.40 MHz. That is more than half the 312.5 MHz sample rate.

If the signal frequency is 136.17 MHz (according to the frequency counter -- don't know if it can be trusted here), then its image in the 2nd Nyquist zone is 176.33 MHz. Ideally, the image should be eliminated by the interpolation filter. But if the interpolation filter does not provide sufficient attenuation at 176.33 MHz, then we see the interference between the two frequencies as "AM". The result is as expected when a Nyquist filter is used as the interpolation filter.

The problem here is that the conditions of the Nyquist-Shannon sampling theorem are not fulfilled and therefore it cannot be used. We do not have the required infinite number of sampling points. The infinite number of sampling points is essential in the proof of the Nyquist-Shannon sampling theorem.

Does anyone know a sampling theorem that only requires a finite number of sampling points?

A realizable reconstruction filter (with finite length) just lowers the highest frequency which can be reconstructed (almost) exactly.
Instead of sampe_rate / 2, the limit decreases to say samle_rate / 2.5 or samle_rate / 3,... (depending on the filter).
Frequencies beyond this reconstructability imit are either attenuated, or reconstructed with the observed "AM effect" (again, depending on the filter).

[Mechatrommer]

1) oscilloscope is not properly BW limited, so Sinc filter is unable to reconstruct perfectly, instead of nice sine, it creates AM sine.

140MHz is below Nyquist.

right! and i know. instead of reinforcing my earlier points with "strawman" argument kind of thing, let me do some simulation (i cant operate my DHO800 right now and i dont have pure 142MHz sine source) i simulated 3 signal channel CH1 only fundamentals at 142MHz, CH2 with 2nd harmonics, CH3 including 3rd harmonics, sample rate is 312.5MSps (see attached xlsx and produced CSV file from it for peer checking) and then my VisaDSO Line vs Sinc (Lanczos Resampler) plot. it seems even with pure fundamentals (CH1) can create AM shape, by sampling theory, it should be perfect sine. not sure where's the variables now, probably imperfect Sinc implementation in Lanczos? or conversion/digitization to 8bits values from real values that my App only supports. i wont speculate further, but since it contradicts with theory (CH1 should be able to be reconstructed properly with Sinc to 142MHz pure sine) that means there has to be some imperfection here and there, what exactly? i'm not sure. ymmv.

[Mechatrommer]

All 4 channels on.

this is what i meant... perfect sine reconstruction.. i tuned my sim files to this setup, 220MHz sampled at 500MSps (f = Sr / 2.27), here is what i come up with. so it seems Rigol and VisaDSO got broken implementation.

[KungFuJosh]

All 4 channels on.

this is what i meant... perfect sine reconstruction.. i tuned my sim files to this setup, 220MHz sampled at 500MSps (f = Sr / 2.27), here is what i come up with. so it seems Rigol and VisaDSO got broken implementation.

Well, it looks pretty cool anyway! 😉

[ebastler]

i tuned my sim files to this setup, 220MHz sampled at 500MSps (f = Sr / 2.27), here is what i come up with. so it seems Rigol and VisaDSO got broken implementation.

That interpolation looks broken indeed. It seems to assume that the sampled data points are alway the extrema of the curve. Why would that be the case? Whatever that "smooth" interpolation is, it's not sin(x)/x, I would say.

Edit: Did you ask for a sin(x)/x interpolation through all the linearly interpolated datapoints, by any chance? That might explain the strange results. Of course only the actual sampled points must be fed to the interpolation.

[Mechatrommer]

i tuned my sim files to this setup, 220MHz sampled at 500MSps (f = Sr / 2.27), here is what i come up with. so it seems Rigol and VisaDSO got broken implementation.

That interpolation looks broken indeed. It seems to assume that the sampled data points are alway the extrema of the curve. Why would that be the case? Whatever that "smooth" interpolation is, it's not sin(x)/x, I would say.

Edit: Did you ask for a sin(x)/x interpolation through all the linearly interpolated datapoints, by any chance? That might explain the strange results. Of course only the actual sampled points must be fed to the interpolation.

i just copied lanczos resampler code lying around in the internet somewhere, i dont have skill to code real Sinc filter nor i know how lanczos resampler is coded/works, assume its a black box functions. and yes i feed it with sampled points visible on screen and it returned like 10X points (sampled + interpolated points) and then plot on screen. i can guarantee those curve will pass through real sampled points... open source code like this... https://gist.github.com/kode54/6338299

[gf]

All 4 channels on.

this is what i meant... perfect sine reconstruction.. i tuned my sim files to this setup, 220MHz sampled at 500MSps (f = Sr / 2.27), here is what i come up with. so it seems Rigol and VisaDSO got broken implementation.

What is the length of your Lanczos filter?
For example, lanczos3 has a reconstructability imit of sample_rate / 3.57, and for lanczos5 it is sample_rate / 2.72.
In order to achieve 2.27, you rather need lanczos10 or lanczos11.

EDIT: Added frequency response plots.