Next time, before you tell others they don't know what they're talking about, I recommend you get a at least a basic Yes, a 1GHz burst requires a higher sample rate than 2.5GSa/s (or 5GSa/s, for that matter), as due to its non-continuous properties it will contain frequency components that are much higher than f0. But it also requires an analog bandwidth of a lot more than 1GHz, so the 7904 is utterly useless for such signals. You might see something, but it won't have much to do with how the input signal really looks like.
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A burst does not necessarily contain "
much higher frequency components" than a CW signal of the same frequency.
It is all dependent upon the envelope shape of the burst.
For instance,the 4.433MHz colour burst in PAL TV contains very little harmonic energy--line & field rate sidebands,yes,harmonics no.
OK,that is a specially "tailored" envelope,but naturally occurring intermittent bursts of oscillation tend to build up over time,rather than just suddenly appear full amplitude,with the result that the envelope rise is also fairly gradual.
Add to this,the frequency limitations of the circuit the problem appears in,& those "much higher frequency" components will be well attenuated before you go anywhere near it with an Oscilloscope.