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?
BW = sample rate / 2so for 200MSps, the upper limit is/should be up to 100MHz. for 1GSps sampler, the sensical upper limit is 500MHz.
bin count = number of samples / 2
RBW = upper limit / bin count, hence...for example 200MSps @ 4MSamples... upper limit = 100MHz, RBW = 50Hz ... or if 1GSps @ 1MSamples... full span (upper limit) = DC to 500MHz, RBW = 1KHz.
RBW = (sample rate / 2) / (number of samples / 2), hence...
RBW = sample rate / number of samples
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?
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. 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.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.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.
This thread is a very clever application of equivalent time sampling:i think you are confusing between equivalent time sampling (https://www.tek.com/document/application-note/real-time-versus-equivalent-time-sampling) and down sampling (http://electronicmusic.wikia.com/wiki/Downsampling). 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...
https://www.eevblog.com/forum/testgear/how-to-quickly-determine-your-dso-timebase-accuracy/msg1748363/#msg1748363 (https://www.eevblog.com/forum/testgear/how-to-quickly-determine-your-dso-timebase-accuracy/msg1748363/#msg1748363)
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.
The whole point of ETS is to under sample a repetitive signal from DC to <bandwidth> without aliasing problems.
Any signal which is BW limited is by definition repetitive.
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?
But the sum of two sine waves of different frequencies is another sine wave. This is basic trigonometry.
ROFL!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.
Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.
Good luck!
Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.
ROFL!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.
Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.
Good luck!
sin(w1*t)+sin(w2*t)=sin(w1-w2*t)*sin((w1+w2)/2*t) and that's not a pure sinewave.
JS
ROFL!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.
Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.
Good luck!
sin(w1*t)+sin(w2*t)=sin(w1-w2*t)*sin((w1+w2)/2*t) and that's not a pure sinewave.
JS
That's exactly correct. And that amplitude modulated signal is a periodic sine wave. It's called a beat note both in radio and in music. I'm sure the latter is the older usage. The motivation for the 12 tone scale was to minimize dissonance. Hence "The Well Tempered Clavier".
My statement was that a BW limited signal is periodic. I thought it sufficiently obvious it did not require a rigorous proof. After a long series of "ex cathedra" pronunciations, I don't think a rigorous proof would have made any difference.
But the sum of two sine waves of different frequencies is another sine wav...no. square wave is summation of several sine waves with different freq (and phases). square wave is not sine wave... period. if you BW limit the 10MHz square, fair enough you'll get 10MHz sine (loosing all the higher order sine harmonics), but when you have non repetitive 10MHz square, BW limit it, you'll get 10MHz sine, but still non repetitive. so i dont know what you are talking about when you say
ROFL!
Obviously you've never learned to play a musical instrument, nor learned trigonometry or physics.
Good luck!
Any signal which is BW limited is by definition repetitive.if a 10MHz square (100ns period, 50ns HI pulse) is happening non-repetitively on non integral of period (say happening in 100.3 period later), no practical BP filter will be able to cope with that (the signal will still pass) unless you capture 100+ period of signal and do SW processing on it all at once.
Read Shannon's paper if you want further explanation.i guess you read it wrongly. i have a suspicion from the way you are describing things..
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"....any FT derivatives are originating from the Original Fourier Transform (DFT or FFT is a "crippled" version of the OFT). if you are deluded from the original FT purpose, then i think something went wrong.
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...reading theories is good, but when it separate us until we dont know what is real and what is abstract, then its no good. theories developed to fulfill reality requirements, but if its to delude reality, its off the chart.
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.ETS does not sample at MULTIPLE PERIOD + some fractions. ETS samples from TRIGGER POINT + some fractions. for non-integral period pulses, ETS still works, but your Shannon theory collapsed. not that Shannon is incorrect in his theory, its just the theory is not applicable here. do not confuse infinitesimal time (mathematical or non-causal) with real time (reality or causal) sampling.
In any case, for regular sampling, Shannon-Nyquist applies and ETS for a signal consisting of 10 & 120 MHz tones sampled at 200 MSa/S, one must BP filter to preclude aliasing. The discussion wandered off into the weeds from there as a consequence of ex cathedra pronouncements without proof.Again: ETS isn't regular sampling because the sampling interval is varied. Your really are confusing naming conventions here.
Assume a stable, periodic trigger point and samples at evenly spaced delays from the trigger point and compute the Fourier transform of the sampling function. Then compute the transform of a signal which exceeds the Shannon-Nyquist BW limit. Then do the convolution of the two.and then we get what?
In the case of random delays from the trigger point, there is no aliasing. But if the delays are at regular intervals there is. There is a nice demonstration of this with a Keysight X3104 in the thread I linked about measuring timebase accuracy.so? the random decimation need to be turned off anyway if FFT is activated.
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.
JS
Thank you. Very neat proof by counter example. However, there are an infinite number of rational approximations to an irrational number. So I shall amend my assertion to "all BW limited signals are quasi-periodic". I'd gotten rather weary of this thread, but your proof made it worthwhile.
I pay close attention to the fine print in mathematics. While it generally doesn't matter, I have been bitten. Most notably by the general failure of writers to note that the discrete Fourier transform is defined on the semi-closed interval [-pi,pi). That nicety cost me considerable distress once while implementing code to do arbitrary resampling by Fourier transform. I'd done it routinely for years, but encountered an edge case. I had long series with missing data and was resampling the segments and reassembling them. I ran into a phase error at the end of a test case which took me over a week to resolve.
In any case, for regular sampling, Shannon-Nyquist applies and ETS for a signal consisting of 10 & 120 MHz tones sampled at 200 MSa/S, one must BP filter to preclude aliasing. The discussion wandered off into the weeds from there as a consequence of ex cathedra pronouncements without proof.
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?
Horizontal SPAN CENTER FFT Resolution AcquisitionComment
(sec/div) (Hz) (Hz) (Hz) (Sample/sec) Samples
2.00E-09 16.00E+09 8.00E+09 15.60E+06 2.00E+09Looks messy, can’t test 40
5.00E-09 6.40E+09 3.20E+09 6.25E+06 2.00E+09Looks messy, can’t test 100
10.00E-09 3.20E+09 1.60E+09 3.13E+06 2.00E+09Looks messy, can’t test 200
20.00E-09 1.60E+09 800.00E+06 1.56E+06 2.00E+09Looks messy, can’t test 400
50.00E-09 1.00E+09 500.00E+06 977.00E+03 2.00E+09 1,000
100.00E-09 1.00E+09 500.00E+06 488.00E+03 2.00E+09 2,000
200.00E-09 1.00E+09 500.00E+06 244.00E+03 2.00E+09 4,000
500.00E-09 1.00E+09 500.00E+06 61.00E+03 2.00E+09 10,000
1.00E-06 1.00E+09 500.00E+06 30.50E+03 2.00E+09 20,000
2.00E-06 1.00E+09 500.00E+06 15.30E+03 2.00E+09 40,000
5.00E-06 500.00E+06 250.00E+06 7.63E+03 2.00E+09 100,000
10.00E-06 250.00E+06 125.00E+06 3.81E+03 2.00E+09 200,000
20.00E-06 125.00E+06 62.50E+06 1.19E+03 2.00E+09 400,000
50.00E-06 62.50E+06 31.30E+06 954.00E+00 1.00E+09 500,000
100.00E-06 31.30E+06 15.70E+06 477.00E+00 500.00E+06 500,000
200.00E-06 15.60E+06 7.80E+06 238.00E+00 250.00E+06 500,000
500.00E-06 6.25E+06 3.13E+06 95.40E+00 100.00E+06 500,000
1.00E-03 3.13E+06 1.57E+06 47.70E+00 50.00E+06 500,000
2.00E-03 1.57E+06 780.00E+03 23.80E+00 25.00E+06 500,000
5.00E-03 625.00E+03 313.00E+03 9.54E+00 10.00E+06 500,000