Help me understand FFT Span on Digital Storage Oscilloscopes

[TK]

I have both the Agilent 54622D (100MHz, 200MSa/s) and the Keysight DSOX1102G (70MHz, 2GSa/s) and there is something I need to understand.  On both scopes, the FFT function has a SPAN of 100GHz, and the center Frequency setting goes up to 25GHz.  How are these values possible and is there any way these devices can show signals on these ranges?

[rhb]

The short answer is they can't.

The maximum span is controlled by the sample rate.  The resolution bandwidth is controlled by the length of the FFT.  It is *highly* unlikely that either scope has the analog BW to go that high.

Shannon showed that the sample rate controlled the *bandwidth*  which does not have to start at DC.  But woe unto the user if they feed a signal with wider bandwidth than Nyquist with the anti-alias filters turned off using what  is called "equivalent time" sampling.

In short, they can't because it's not possible.  I find it very distressing that what's left of HP is doing this sort of thing.  The MSOX3104T is supposed to have a 1 GHz BW, which it does.  But at the price of a 7% overshoot on a step response and only a 450 pS rise time instead of the 350 pS rise time and 2-3% overshoot one would expect from a high quality analog scope.

How do you tell when a computer salesman is lying?

His lips move.

Unfortunately, this malady now afflicts the A list T&M companies.

[TK]

The maximum span is controlled by the sample rate.  The resolution bandwidth is controlled by the length of the FFT.  It is *highly* unlikely that either scope has the analog BW to go that high.

That is what I understood, but the 54622D has a sample rate of 200MSa/s and the DSOX1102G 2GSa/s and in both scopes, the SPAN goes to 100GHz.  There must be something else.  If they want to lie, why  not use a figure like 10GHz which is also a high figure?

[Mechatrommer]

the upper limit FFT bandwidth is using formula:

BW = sample rate / 2

so for 200MSps, the upper limit is/should be up to 100MHz. for 1GSps sampler, the sensical upper limit is 500MHz.

otoh FFT bin count is:

bin count = number of samples / 2

FFT resolution bandwidth however will be according to formula:

RBW = upper limit / bin count, hence...
RBW = (sample rate / 2) / (number of samples / 2), hence...
RBW = sample rate / number of samples

for example 200MSps @ 4MSamples... upper limit = 100MHz, RBW = 50Hz ... or if 1GSps @ 1MSamples... full span (upper limit) = DC to 500MHz, RBW = 1KHz.

[TurboTom]

That is what I understood, but the 54622D has a sample rate of 200MSa/s and the DSOX1102G 2GSa/s and in both scopes, the SPAN goes to 100GHz.  There must be something else.  If they want to lie, why  not use a figure like 10GHz which is also a high figure?

I guess the answer is rather simple: The manufacturer uses a single software module to implement the FFT functionality into all his scopes and simply forgot to include configurable limits to match the different scopes's physical capabilities...

[Berni]

Technically its possible to get a higher sample rate in equivalent time sampling mode, but you can't really get anything useful out of that.

[rhb]

Technically its possible to get a higher sample rate in equivalent time sampling mode, but you can't really get anything useful out of that.

No!  It is *not* a higher sample rate.  Equivalent time sampling works by bandpass filtering the signal so it meets the Shannon-Nyquist criterion.  If you are band limited to 950-1050 MHz you can examine a 1 GHz signal by sampling at 200 MSa/S.

There are radar band sampling scopes which are *very* useful.  Those are what was used designing radar systems for many years.   But the analog section has to be able to handle the BW of the signal.  DSOs generally don't have the BW in the AFE to make equivalent time sampling usable even if they have a menu option for it.

In summary, equivalent time sampling uses an alias of the signal to examine the signal.

[nctnico]

Technically its possible to get a higher sample rate in equivalent time sampling mode, but you can't really get anything useful out of that.

No!  It is *not* a higher sample rate.  Equivalent time sampling works by bandpass filtering the signal so it meets the Shannon-Nyquist criterion.  If you are band limited to 950-1050 MHz you can examine a 1 GHz signal by sampling at 200 MSa/S.

No. Equivalent time sampling works by sampling a repetitive signal at random (known) intervals which are then used to reconstruct the original signal. The bandwidth is DC to whatever the analog front-end and ADC supports.

[Z80]

FFTs on scopes seem to be universally shitty and badly implemented to the point of being a useless gimmick on some.  You can't get any accurate measurements without knowing the response of the front end so you can apply corrections for the roll off.  It is possible to collect data up to approx sample rate / 2 but without corrections it's just a novelty rather that a useful tool.  Obviously 100GHz is a joke!

[Berni]

Yes, exactly why i said you can't get anything useful out of that. You can get enough points to do a FFT to 100GHz but the spectrum there will be nothing but noise.

[rhb]

Technically its possible to get a higher sample rate in equivalent time sampling mode, but you can't really get anything useful out of that.

No!  It is *not* a higher sample rate.  Equivalent time sampling works by bandpass filtering the signal so it meets the Shannon-Nyquist criterion.  If you are band limited to 950-1050 MHz you can examine a 1 GHz signal by sampling at 200 MSa/S.

No. Equivalent time sampling works by sampling a repetitive signal at random (known) intervals which are then used to reconstruct the original signal. The bandwidth is DC to whatever the analog front-end and ADC supports.

They did make random sampling scopes, but equivalent time sampling is most often regular sampling at less than 2 samples per cycle, perhaps as little as a sample every N cycles.   Any signal which is BW limited is by definition repetitive.  In fact, the FFT of *any and all* sampled signals are repetitive over a period equal to the length of the series.  Except in the case of mathematical abstractions like a Dirac functional, *all* signals are BW limited, and hence repetitive.

You really do have to have the BP filter to limit the BW, otherwise you will have a mixture of signals which does not accurately describe the signal of interest.  Shannon proved this long ago.  I've not played with a sampling scope, but I suspect that many presume the user has sense enough to BP filter the input externally.  But woe unto any who attempt to defy Shannon using regular sampling.  Truly random sampling is different in that there is no aliasing in that case.

This thread is a very clever application of equivalent time sampling:

https://www.eevblog.com/forum/testgear/how-to-quickly-determine-your-dso-timebase-accuracy/msg1748363/#msg1748363

As for the FFTs on DSOs, it all depends. Instek has a very nice FFT based spectrum analyzer in their MDO-2000E line, but they won't allow using it on the GDS or MSO versions.  The FFT function supplied on the latter two works, but is *really* clunky to use because the interface is so poor.  But they will give a span of 500 MHz and an RBW of 50 Hz.  But you're limited to an RBW of 500 Hz in zoom mode.  Up to FW 1.32 you can break out of the demo app for the MDO and use the SA function app on the MSO if it's got the AWG installed.  I mentioned it to them, so in 1.34 they made sure you couldn't do that anymore :-(

[Mechatrommer]

This thread is a very clever application of equivalent time sampling:
https://www.eevblog.com/forum/testgear/how-to-quickly-determine-your-dso-timebase-accuracy/msg1748363/#msg1748363

i think you are confusing between equivalent time sampling and down sampling. the purpose of ETS is to perceptually increase sampling rate from limited ADC. down sampling is the other way (it can be done easily by increasing time base of DSO hence reducing sampling rate). or in other word, you are confusing between trying to observe or predict or reconstruct original signal (higher BW) and trying to capture lower BW from unnecessary high BW components. or as in the thread in your link, is to observe jitter correlation between 2 clocks or alignment (from my quick reading) its some nice trick, sort of signal mixing/superposition/addition technique, but its not to reconstruct the original signal. original signal is 10MHz, and as the OP stated, the signal sampled from 2.5MSps is aliased. in other word, its garbage, not the 10MHz signal. we are not doing that here...

[rhb]

Well, from a mathematical perspective the equations are *exactly*  the same.  If you want to make up new names that's your business.  I don't see a lot of use in it.  10 MHz sampled at 1/8th of Nyquist is no different mathematically from 10 GHz sampled at 1/8th Nyquist except for 3 zeros tacked on the ends of the values.  If that makes a difference to you it's your problem. I can't help you.

[Mechatrommer]

making new name is something, but misguiding people by telling this name is that name, which is not what it is is something else. you were talking about BW limiting (antialias filter), in ETS, you dont need the filter otherwise you will lose any information of the higher order. here we dont want to see a pure spectral FFT garbage. which is what you will get from the link you provided.

[rhb]

I'll let you work out what happens if you regularly sample  a 10 MHz tone and a 120 MHz tone using  ETS at 200 MSa/S.   You've only got 100 MHz of BW.  Read Shannon's paper if you want further explanation.  To get a valid result you must filter out one of the two tones.  If you don't you'll get two tones 70 MHz apart rather than the correct value of 110 MHz apart.

[nctnico]

I'll let you work out what happens if you regularly sample  a 10 MHz tone and a 120 MHz tone using  ETS at 200 MSa/S.   You've only got 100 MHz of BW.  Read Shannon's paper if you want further explanation.  To get a valid result you must filter out one of the two tones.  If you don't you'll get two tones 70 MHz apart rather than the correct value of 110 MHz apart.

The thing is that ETS uses (known) random sample intervals to avoid aliasing. The samplerate in that case is just a given to show how fast the sampling process is. ETS and downsampling are two completely different 'processes'. The whole point of ETS is to under sample a repetitive signal from DC to <bandwidth> without aliasing problems.

[KE5FX]

There is no requirement for ETS to involve random sampling.  Random sampling is one way to implement ETS, but you can also use a vernier technique where the timebase is ramped slowly to fill in the sample record.  The old-school Tek 7000 plugins supported both.

'Downsampling' usually refers to decimation of a conventionally-sampled signal; 'subsampling' is probably a better synonym for ETS.

As for 100 GHz FFT scales, your guess is as good as mine.  I have no clue why Agilent does that.    Maybe Daniel B. will see the thread and make some inquiries, assuming the answer isn't already buried in the docs somewhere.

[rhb]

 The whole point of ETS is to under sample a repetitive signal from DC to <bandwidth> without aliasing problems.

This is true *if and only if* the  sampling is uncorrelated with the signal.  Not all ETS scopes use random sampling. Sampling at a multiple of the signal period plus a fraction that varies in a regular fashion is quite common.  For those you cannot escape Shannon.

[egonotto]

   Any signal which is BW limited is by definition repetitive.

Hello,

I dont believe that.

If f(t) := sin(at) + sin(bt) for all t element IR and if a/b is not rational ?

Best regards
egonotto

[KE5FX]

If f(t) := sin(at) + sin(bt) for all t element IR and if a/b is not rational ?

Best regards
egonotto

If a number can be expressed as a/b, it's rational by definition, isn't it?

[egonotto]

If a number can be expressed as a/b, it's rational by definition, isn't it?

Hello,

rational numbers are those number which have the form a/b where a and b are whole numbers. Whole numbers are (.. -3,-2,-1,0,1,2,3,..)

Best regards
egonotto

[rhb]

If the signal is BW limited, then at some point it repeats.  It might be a very long time, but it repeats.  It's like the beat note between two tones.   The repetition period depends upon how many discrete frequencies are involved and what their harmonic relationships are.  But the sum of two sine waves of different frequencies is another sine wave.  This is basic trigonometry.  So it has to repeat.  The longest repetition period is for the sum of two sine waves which are sin( wt) & sin(w+epsilon)t) for epsilon very small.

In the case of the discrete Fourier transform, it repeats with a period of the length of the sample.

If you're a young engineer or physical scientist, one of the most useful things you can buy is Ronald Bracewell's "The Fourier Transform and its Applications".  It has a graphical dictionary of transform pairs.  If you know those few pages well you can do Fourier transforms of complex signals on a bar napkin.  It's engineering oriented, so it's not a substitute for a proper mathematical treatment of the transform, e.g. "Operational Mathematics" by Churchill.  The problem with Churchill is it's integral transforms in general, not just the Fourier transform.  Despite having probably 3 ft of books on the Fourier transform, when I went and looked  I did not see any volume that really does a comprehensive modern treatment at the graduate  level in mathematics.  Nothing to equal Watson on the Bessel function.  The best I know of to point to is Mallat's "A Wavelet Tour of Signal Processing" , 3rd ed.

My undergraduate degree was English lit for which the math requirement was algebra and trig which I had taught myself in grades 6-8.  Thus when I started taking serious math as a grad student I had the great advantage of only being expected to take a 12 semester hour course load instead of the 15 the engineering undergrads suffered with.  That proved to be a huge advantage.  I had far more time to work problems than the other students in my classes.  Of course, by the time you hit Integral Transforms and Tensor Analysis, everyone is a grad student.

[egonotto]

But the sum of two sine waves of different frequencies is another sine wave.  This is basic trigonometry.

Hello,

no

Best regards
egonotto

[rhb]

ROFL!

Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.

Good luck!

[JS]

ROFL!

Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.

Good luck!

No, you are wrong, check it and come back... Summing two sine waves with different frequency gives an amplitude modulated signal, with the modulation at the difference of the frequencies and the carrier at the average of the frequencies if they are both the same amplitude, if not it shifts towards the higher amplitude one. The modulation index will depend on the ratio of the amplitudes as well.

sin(w1*t)+sin(w2*t)=sin(w1-w2*t)*sin((w1+w2)/2*t) and that's not a pure sinewave.

JS