Scope Wars

[rhb]

So, I sat down in front of the scope and tried the 100Hz modulation of a 20MHz signal - nothing like a real example, right?

It seems to me that the digital scope behaves pretty much like an analog scope in this case.  The slow sweep speed does not seem to detract from the ability to display an outline of the 20MHz signal (even without Peak Detection enabled).

Obviously, filtering out the 20MHz would destroy the information as displayed here.

(note: normal mode, not peak detect)
(Attachment Link)

Thank you for a very nice example.  As you correctly note, it's obvious that you cannot sensibly filter out the carrier and not kill the side bands.

If the signal were down converted to DC - 500 Hz with the carrier at 250 Hz followed by a 500 Hz LP filter it would be very accurately displayed in the frequency domain provided the programmer took the frequency translation into account.  A mere change in the carrier frequency would not change the picture unless the ratio of carrier and the modulation were very small. And that would only be in the time domain.

Have Fun!
Reg

[bdunham7]

If you properly downsample with low pass filtering rather than decimating by throwing away samples you will *always* have a band limited spike.  It will *not* disappear.  However, it *will* make "peak detection" moot.

Won't its amplitude change?  And why would it 'disappear' using decimation provided its bandwidth is under Nyquist?  EDIT:  To be clear, I mean the Nyquist limit of the new, lower sample rate.

[Fungus]

Won't its amplitude change?

Nothing in the passband will change amplitude.

And why would it 'disappear' using decimation provided its bandwidth is under Nyquist?

When you throw away samples you're doing very bad things in the frequency domain.

[SilverSolder]

So, I sat down in front of the scope and tried the 100Hz modulation of a 20MHz signal - nothing like a real example, right?

It seems to me that the digital scope behaves pretty much like an analog scope in this case.  The slow sweep speed does not seem to detract from the ability to display an outline of the 20MHz signal (even without Peak Detection enabled).

Obviously, filtering out the 20MHz would destroy the information as displayed here.

(note: normal mode, not peak detect)
(Attachment Link)

Thank you for a very nice example.  As you correctly note, it's obvious that you cannot sensibly filter out the carrier and not kill the side bands.

If the signal were down converted to DC - 500 Hz with the carrier at 250 Hz followed by a 500 Hz LP filter it would be very accurately displayed in the frequency domain provided the programmer took the frequency translation into account.  A mere change in the carrier frequency would not change the picture unless the ratio of carrier and the modulation were very small. And that would only be in the time domain.

Have Fun!
Reg

I can see how the down-conversion won't damage the frequency domain display, but the time domain looks terrible...

Below, I used a 250Hz carrier modulated by 100Hz to demonstrate the downconverted case. 




It doesn't really look good in the time domain.  To make it look similar to the 20MHz image,  I had to lower the frequency of the modulation and increase the sweep time.

Using my limited math skills -

The first example with the 20MHz carrier could have been sampled at 40MHz for a sweep of 50ms, so would consist of 2,000,000 samples.

The downconverted 250Hz carrier is samled at 500Hz for 4,000 seconds, with a modulation of 0.0015Hz.  This also has 2,000,000 samples and looks exactly the same.

It seems to me that to display this waveform, we end up with the same number of data points needing to be plotted even after downconversion?

Example with 250Hz carrier, but 0.5Hz modulation (scope cannot sweep slow enough to show 0.0015Hz)

[bdunham7]

Won't its amplitude change?

Nothing in the passband will change amplitude.

And why would it 'disappear' using decimation provided its bandwidth is under Nyquist?

When you throw away samples you're doing very bad things in the frequency domain.

Some numbers in an example would help.  Unless I'm missing something, throwing away samples only does bad things if the remainder is insufficient to meet the Nyquist criterion, plus a margin for the practical limits of reconstruction.  And if  you use LP filter on a pulse with a bandwidth within Nyquist before decimation but beyond it after, it will be smeared or spread out and have a lower amplitude.  This is what peak detection prevents. 

[SilverSolder]

Won't its amplitude change?

Nothing in the passband will change amplitude.

And why would it 'disappear' using decimation provided its bandwidth is under Nyquist?

When you throw away samples you're doing very bad things in the frequency domain.

Some numbers in an example would help.  Unless I'm missing something, throwing away samples only does bad things if the remainder is insufficient to meet the Nyquist criterion, plus a margin for the practical limits of reconstruction.  And if  you use LP filter on a pulse with a bandwidth within Nyquist before decimation but beyond it after, it will be smeared or spread out and have a lower amplitude.  This is what peak detection prevents.

Say we have a sampled waveform in a buffer with 10,000,000 samples that we want to display on our screen, which has a width of 1,000 pixels.

The sampled waveform is a 20MHz carrier, modulated by 100 Hz, sample length 50ms.    The sample rate is 200MHz.

Can we get from 10,000,000 samples to the 1,000 pixel available width on the screen without throwing anything away...  ?

[gf]

Below, I used a 250Hz carrier to demonstrate the downconverted case.  But here's the crunch - I also had to lower the frequency of the modulation and increase the sweep time to make the waveform look like the first example...

Using my limited math skills -

The first example with the 20MHz carrier could have been sampled at 40MHz for a sweep of 50ms, so would consist of 2,000,000 samples.

The downconverted 250Hz carrier is samled at 500Hz for 4,000 seconds, with a modulation of 0.0015Hz.  This also has 2,000,000 samples and looks exactly the same.

Down-conversion (down-mixing) does not preserve the overall time-domain waveform shape. For the given AM signal it only preserves the envelope. I would not use an IF of of only 250 Hz, though, but rather say 10 kHz (->leading to still 100 carrier cycles per envelope period then). Down-conversion is not generally useful, but only for particular signals. You need some a priori knowledge about the signal in order to decide whether it can be used at all, and to establish a suitable frequency plan.

On the other hand, if you would decimate to a samling rate < 4.99995 39.9998 MSPS with ideal boxcar AA-filtering, then you lose the signal completely.

Decimation with peak detector instead of AA filter still remains a very useful alternative to get what you want to see.

EDIT: Just noticed that the given carrier was 20MHz.

[gf]

Can we get from 10,000,000 samples to the 1,000 pixel available width on the screen without throwing anything away...  ?

When you decimate for sceen display, you are not limited to a 1-dimensional destination signal vector, but you have more opportinuties. E.g. you can light up multiple pixels in the same column, and you can assign different intensity and/or color to the pixels.

You could, for instance, map the first 10,000 samples to colum 0, and set all pixels in this column which correspond to the 10,000 values, then map the next 10,000 samples to column 1, etc. The pixel brightness/color could depend on the number of values which hit the pixel. Just be creative

[gf]

Please do not raise issues which are amply addressed by references I provide. If you are not willing to read the references,..

Well, it's possibly rather the missing willingness to buy a dozen of (printed) books, just in order to read one chapter then. If you could provide references as web links to (freely) downloadable documents (which focus on one particular subject, and not the whole DSP world in hundreds or thousands of pages), then I guess that more people were willing to read them

[2N3055]

Won't its amplitude change?

Nothing in the passband will change amplitude.

And why would it 'disappear' using decimation provided its bandwidth is under Nyquist?

When you throw away samples you're doing very bad things in the frequency domain.

No, I have to correct you there. Decimation (by throwing away samples, periodically) will have absolutely same effect as sampling with lower frequency. Samples are not integrated voltage between intervals, but discrete point in time voltages, points, not little lines. Dot mode on scope is showing exactly what is being sampled. So at any sample frequency, you get same samples (in theory) only more or less dense or sparse.
Actually, faster A/D will have closer to ideal (shorter) sample window and in theory be more mathematically "correct".

So sampling at 5 GS/s and keeping every 5th sample, and sampling at 1 GS/s and keeping every single one is SAME.

By applying averaging (as in Hires), you can get signal with less noise, so converting from 5 to 1 GS/s by filter will be more beneficial that simply decimating.
But sample per sample decimation gives same result as lower sample rate (if we exclude fact that slower A/D sampling on REAL A/D will probably have better ENOB by virtue of lower operating frequency).

[rf-loop]

Can we get from 10,000,000 samples to the 1,000 pixel available width on the screen without throwing anything away...  ?

Of course.
Try even one time (example Siglent) so that you capture (example) 14ms long capture to 14M memory and so that whole captured length is displayed. Because there is 14 div time scale 1ms/div. Just single sho, exmple with wideband high level noise and then scope stopped. You have there every single sample mapped to screen. Trace length is 700 pixel. So first displayed signal area column have 20000 samples. After capture done then  start zooming in and look carefully what all kind of things you can see.

It must not decimate! Do you know why. Because it is for analyzing signals and not for make entertainment images or lottery. 

Yes old time there was once mistake and there was "accidentally" some decimation before display mapping... perhaps some peoples who are still angry to Siglent remember this quite short time case before it was corrected...

[Fungus]

No, I have to correct you there. Decimation (by throwing away samples, periodically) will have absolutely same effect as sampling with lower frequency. Samples are not integrated voltage between intervals, but discrete point in time voltages, points, not little lines. Dot mode on scope is showing exactly what is being sampled. So at any sample frequency, you get same samples (in theory) only more or less dense or sparse.

OK, let's sample a sine wave at 2x frequency. We might get values [0, 1, 0, -1, 0, 1, 0, -1, ....]

Now let's throw away half the samples. Depending on where we start we might get 0,0,0,0 or we might get 1,-1, 1,-1. It's not the same thing at all.

If we apply a very simple low pass filter to those same numbers we might get [0.5,-0.5,0.5,-0.5, ...] and that will always work no matter where we start in the sequence.

[gf]

By applying averaging (as in Hires), you can get signal with less noise, so converting from 5 to 1 GS/s by filter will be more beneficial that simply decimating.

In fact it is a digital low-pass filter, applied before the decimation, usually having a boxcar pulse response. This filter kernel has a -3dB point in the frequency domain is at ~0.9 * Nyquist (of the decimated rate). As long as the resulting roll-off in the pass-band does not matter, one could use it generally instead of plain decimation. Still it is by far not a suitable replacement for a proper AA filter, in case AA filtering is desired.

OK, let's sample a sine wave at 2x frequency....

2x frequency is not enough. It still violates the sampling theorem. It must be greater than 2x frequency.

Now let's throw away half the samples.

This violates the sampling theorem even more.
In order that you don't suffer from aliasing, the signal frequency must be < half of the decimated sampling rate.

[2N3055]

For those who think scope manufacturers are stupid and don't know about DSP some material:

http://cdn.teledynelecroy.com/files/whitepapers/dsp_in_oscilloscopes.pdf
https://www.edn.com/advantages-and-disadvantages-of-using-dsp-filtering-on-oscilloscope-waveforms/

Also a document on methods of establishing GUM for dynamic signals..

[2N3055]

No, I have to correct you there. Decimation (by throwing away samples, periodically) will have absolutely same effect as sampling with lower frequency. Samples are not integrated voltage between intervals, but discrete point in time voltages, points, not little lines. Dot mode on scope is showing exactly what is being sampled. So at any sample frequency, you get same samples (in theory) only more or less dense or sparse.

OK, let's sample a sine wave at 2x frequency. We might get values [0, 1, 0, -1, 0, 1, 0, -1, ....]

Now let's throw away half the samples. Depending on where we start we might get 0,0,0,0 or we might get 1,-1, 1,-1. It's not the same thing at all.

If we apply a very simple low pass filter to those same numbers we might get [0.5,-0.5,0.5,-0.5, ...] and that will always work no matter where we start in the sequence.

Read again. Decimation is same as decreasing sampling frequency. If you sample at 100 MS/S, and take every 100th sample, it is same as if you were sampling at 1 MS/s. Off course it will be different than original. Statement is that if you sample at higher clock and decimate it is same as slower sample rate..

And that is what scopes are doing most of the time when timebases get long.  They don't switch to Hires mode without asking. Which  is what you get when filtering. 

This is what I do manually. If I'm looking at something fast I sample normaly. If I'm looking at slow signals, where sample rate drops, I manually switch to Hires mode because efective sample rate will be the same, and Hires will be less noisy.

[gf]

If we apply a very simple low pass filter to those same numbers we might get [0.5,-0.5,0.5,-0.5, ...] and that will always work no matter where we start in the sequence.

Yes, you have just invented the basic principle of an anti-aliasing filter
(As said above, your example signal is too fast and suffers from aliasing.)

EDIT:

[A perfect AA filter would have cut-off your signal completely, though, so that the sampled signal were 0,0,0,0... and the decimate signal were 0,0,... too.]

If you retry your example with a sine wave signal having e.g. 5x 1/5 the frequency of the initial samping rate then you'll be able to reconstruct the sine wave exactly with sinc interpolation, even after decimation by a factor 2 (granted that you capture either an infinte number of samples, or an exact integral number of signal periods).

[Fungus]

Read again. Decimation is same as decreasing sampling frequency. If you sample at 100 MS/S, and take every 100th sample, it is same as if you were sampling at 1 MS/s. Off course it will be different than original. Statement is that if you sample at higher clock and decimate it is same as slower sample rate..

I thought the statement was that applying a low pass filter is the same as throwing away samples.

[2N3055]

Read again. Decimation is same as decreasing sampling frequency. If you sample at 100 MS/S, and take every 100th sample, it is same as if you were sampling at 1 MS/s. Off course it will be different than original. Statement is that if you sample at higher clock and decimate it is same as slower sample rate..

I thought the statement was that applying a low pass filter is the same as throwing away samples.

No it wasn't. Sorry for confusion.
The OP is constantly shifting what is being discussed, ignoring warnings that despite math is being correct most of the stuff mentioned  is either  not applicable to GP scope, or wouldn't serve much purpose, or would be expensive, or would simply convert scope to some new category of instrument (scopalyzer ?) that is debatable whether it is something users would want.
It reminds me of : "To a man with a hammer everything looks like a nail..." Or however that saying goes...

[rhb]

Mostly I'm ignoring the fact that people are saying things that are so wrong as to be simply silly. 

I did not shift the topic.  I started this as a comparison of DSOs, not a debate about what people *think* a scope should do.  My frame of reference is a good analog scope.  So I am comparing DSOs to good analog scope signals.

The purpose of a DSO is to faithfully represent an *analog* signal.  That requires low pass filtering to prevent aliasing.

Decimation without low pass filtering causes aliasing.  It also causes fast impulses to not be captured at low sweep rates.  With proper low pass filtering there is no need for "peak detection".

There is a vast amount of literature on DSP.  I reference the books I use.  I am not going to search the web *for you*.  Do it yourself.  I'm not interested in teaching DSP 101 to anyone, especially people who claim to understand it and then manifestly demonstrate they have not grasped the contents of the first 10 pages of a basic intro to the subject.

My preferred basic DSP reference:

An Introduction to Digital Signal Processing
John H. Karl
Academic Press 1989

It's the book I reach for first when I want to check something.

Have Fun!
Reg

[2N3055]

Decimation without low pass filtering causes aliasing.  It also causes fast impulses to not be captured at low sweep rates.  With proper low pass filtering there is no need for "peak detection".

Decimation by discarding samples doesn't cause aliasing, it is fact that effective sample rate drops by doing it that does. If you want to give us crap about rigorous math, than be accurate.

But you are correct, doing full speed sampling and then downsampling it by filtering is an effective antialiasing method. And many scopes do it. Even little DS1054Z has it as a setting. Keysight 3000T does it too AFAIK because no aliasing is visible in normal use.

But no need for Peak detect?
Pray tell how does THAT work?  MSOX3104T will show a 250 ps pulse on 1 second/div timebase in Peak detect mode.
If you lowpass filter samples you will filter OUT that peak. What am I missing? It will be gone.
Your solution is to pretend it's not there? Is that what Bendat and Piersol recommend ?

[nctnico]

Mostly I'm ignoring the fact that people are saying things that are so wrong as to be simply silly. 

I did not shift the topic.  I started this as a comparison of DSOs, not a debate about what people *think* a scope should do.  My frame of reference is a good analog scope.  So I am comparing DSOs to good analog scope signals.

The purpose of a DSO is to faithfully represent an *analog* signal.

No. An oscilloscope is there to faithfully represent the shape of a signal. Your statement applies to digitizers which are a different beast compared to an oscilloscope even though at first sight there is a lot of overlap in functionality. On top of that some oscilloscopes are more on the digitizer side (the ones from Lecroy for example).

Your statement about peak detect also isn't true. Peak-detect retains the amplitude of a pulse. Decimation spreads the energy of that peak over a longer sample interval making the amplitude lower and thus distorting the shape of the original signal.

Bottom line: from a signal processing perspective you are right but an oscilloscope is not a device intended to do signal processing.

edit: typo

[rf-loop]

Decimation without low pass filtering causes aliasing.  It also causes fast impulses to not be captured at low sweep rates.  With proper low pass filtering there is no need for "peak detection".

What kind of humor is this, I do not recognize. I know parody, irony, satire etc but this I do not recognize.
If someone try tell me that digital scope do not need peak detect... and he try sell me this kind of scope. Just he can keep his scope and I keep my money.  Well I have some experience about real works with oscilloscopes for many kind of purposes tens of years including also analog scopes and later digital ones, in real world in real practice... works with hands and tools. If some theory book writer or reader tell me no need peak mode I can as he go back to his cave reading more theory books and lets others do real practical works. But with 

[SilverSolder]

Can we get from 10,000,000 samples to the 1,000 pixel available width on the screen without throwing anything away...  ?

When you decimate for sceen display, you are not limited to a 1-dimensional destination signal vector, but you have more opportinuties. E.g. you can light up multiple pixels in the same column, and you can assign different intensity and/or color to the pixels.

You could, for instance, map the first 10,000 samples to colum 0, and set all pixels in this column which correspond to the 10,000 values, then map the next 10,000 samples to column 1, etc. The pixel brightness/color could depend on the number of values which hit the pixel. Just be creative

Yes, that looks like exactly what my scope is doing.

Looking at the same 20MHz modulated by 100Hz, this time with vectors turned off (points mode, in other words)...



If we crank up the Y axis gain, the screen turns into a snowstorm, showing that more than one Y point is plotted for each X...




The scope's FFT function shows a blank display...  doesn't seem to work when the buffer has more than one Y value per X coordinate.

[bdunham7]

I started this as a comparison of DSOs, not a debate about what people *think* a scope should do.  My frame of reference is a good analog scope.  So I am comparing DSOs to good analog scope signals.

The purpose of a DSO is to faithfully represent an *analog* signal.  That requires low pass filtering to prevent aliasing.

If you are going to compare or critique products without listening to anyone about how those products are used, your results will be meaningless to most people.  Here, IMO, your premise is entirely wrong.  It is not the purpose of a DSO to replace an analog scope nor to 'faithfully represent an analog signal', whatever that means.  The purpose of a DSO is, like Forrest Gump in boot camp, to do exactly what I tell it to do.  That might be 'faithfully represent an analog signal' if it is your scope and that is what you want.  I'll agree that a typical entry level DSO should be able to be configured to do so.  But the show doesn't stop there. DSOs are capable of much, much more and that is why we have them.

Also, since you are comparing and critiquing existing products, your statements on decimation and aliasing need to be reckoned with what the existing scopes actually do.  Can you show us an example of one of those scopes showing aliasing on the screen due to decimation of a signal that was within Nyquist at the native sample rate but is now aliased because of decimation?  Is that happening?  If so, I'll grant that to be an undesirable result. 

Decimation without low pass filtering causes aliasing.  It also causes fast impulses to not be captured at low sweep rates.  With proper low pass filtering there is no need for "peak detection".

Only if the signal wasn't already aliased and has a content above the new, lower Nyquist limit.  That is what peak detect is for.  On the last point, I think I can devise an experiment to prove you wrong. 

There is a vast amount of literature on DSP.  I reference the books I use.  I am not going to search the web *for you*.  Do it yourself.  I'm not interested in teaching DSP 101 to anyone, especially people who claim to understand it and then manifestly demonstrate they have not grasped the contents of the first 10 pages of a basic intro to the subject.

Perhaps you could answer one simple question. I did look up 'folded LP filter' and I'm not finding much that I can access and understand.  From your description, it is a clever, fast implementation that combines FIR, LP and downsampling all in one.  Is that correct?  Can I assume the the actual effect on a signal of your folded LP filter will be similar to any other LP filter?  Or are there special characteristics that make it perform as you say, specifically eliminating the need for peak detection?

[Elasia]

Perhaps you could answer one simple question. I did look up 'folded LP filter' and I'm not finding much that I can access and understand.  From your description, it is a clever, fast implementation that combines FIR, LP and downsampling all in one.  Is that correct?  Can I assume the the actual effect on a signal of your folded LP filter will be similar to any other LP filter?  Or are there special characteristics that make it perform as you say, specifically eliminating the need for peak detection?

It's folded FIR filtering, a specific technique of removing the number of taps / implementation complexity in exchange for adders.. this might help you

https://www.embedded.com/dsp-tricks-an-odd-way-to-build-a-simplified-fir-filter-structure/