Aha! I can't use the zoom?! Really? I mean, when using a scope with an ADC of 1GS/s at max I assume that you understand that the time between two samples is 1ns, right? So you're zoom can't resolve more than showing you samples in a distance of 1ns, what happens between is not displayed, but interpolated if not switched off. An analog scope using 1ns can show any value between because there's no sampling but a continous steering of the beam. Disadvantage: you can't store it. Think about it.
That's only true for single shot signals. Even cheap Chinese are able to determine the timing relation between the sampling clock and the trigger to a resolution of 25ps, which gives you a timing resolution of 25ps when acquiring long enough.
No it's generally valid even for cheap Chinese scopes and it doesn't depend on single shot.
- ADC with a sample rate of 1GS/s enables 1ns time interval between two samples - as given in my example
- ADC with a sample rate of 4GS/s enables 25ps time interval between two samples - as you mentioned.
But it doesn't influence the fact that a screen of limited pixels for example 800 pixels on the abscissa cannot display more than 800 pixels at once. Either the scope displays only each - lets assume - 10th sample of the sample memory on screen by transferring it to the display buffer or you have to zoom in until you see the samples in the distance of your 25ps, in this case your timebase is very small.
That's how all digital scope work, cheap Chinese ones as well as expensive Agilents, Teks or whatever.
In REFRESH mode digital scopes use double buffering, where one part of the memory is filled up with samples whilst the other part is displayed, which leads to the famous wfm/s limitation. Manufacturers as Agilent use special ASICs for generating high wfm/s with parallel processing where cheap scopes for hobby purposes use simple FPGAs which result in lower wfm/s.
In SINGLE SHOT mode the scope fills up the complete memory with samples and stops. Depending on the chosen timebase the ADC might work with its highest sample rate, in my example I assumed an 1GS/s ADC, so the memory is filled with samples in a distance of 1ns - you can't fill it up with a higher sample rate than the physical limits of the ADC offers - even not with cheap Chinese scopes. And you can easely check that by switching off the interpolation & zoom in until you see the samples. Measure the time interval between two subsequent samples, just that simple. Done a few times.
And we're not talking about random sampling, that's another construction and works for periodical signals only.