In theory you should be able to capture the waveform and demodulate it using software on a PC.
Nah. Get RTL-SDR dongle and consider it done. For those who work with wider than 1MHz bandwidth signals scope with downconverter won't do any good anyway.
Why do you say that?
There are very few 1MHz bandwidth oscilloscopes around these days.
There is no reason why a "chunk" of spectrum equal to the bandwidth of the associated 'scope cannot be downconverted.
Such tricks were not uncommon in the days of quite low bandwidth oscilloscopes.
Just such a device was described many years ago in an ARRL Handbook.
The idea was so you could look at AM, SSB, & Morse code to check modulation percentage with the former, & the shape of the keyed signal with the latter.
This still could be useful with, say, a UHF transmitter & a low-ish bandwidth 'scope.
With the improvement in bandwidth of 'scopes, & the advent of, first, analog sampling oscilloscopes with bandwidths into the GHz region, followed by normal DSOs & GHz versions of them, the requirement (which was never mainstream) went away.
All in all there are plenty of interesting time-domain properties of an RF signal.
Sure. Please share your experience - tell how do you do RF work using scope.
Certainly, on one occasion, an oscilloscope found a problem in an FM Broadcast transmitter which appeared to be quite mystifying.
The FET Driver PA drove the grid of a Tetrode output tube, with a meter showing the output of the former.
The normal tuning method was to tune the tube grid circuit for a maximum on this meter, till in passing, we discovered that the Transmitter output increased when we detuned from that "grid peak", instead of falling.
I looked at a monitor point associated with the meter & tuned as normal, displaying 3 or 4 cycles of the 100MHZ signal on a IWATSU 200MHz Oscilloscope.
The problem was immediately obvious, from the shape of the waveform.
When "peaked" the driver amplifier produced a large amount of 2nd harmonic distortion, which gave the waveform a "peakier" shape, with the narrower peaks higher in amplitude.
The meter, being a "peak & hold" circuit, happily interpreted that as a higher output.
The PA stage tuned circuits rejected the harmonics, so the output power dropped.
A Spectrum Analyser would have shown the problem up, too, but the 'scope was there to hand, with a minimum of setup required, & the time domain result of a waveform change was probably easier to associate with the high meter reading than a bunch of extra carriers.
This obviously wouldn't have been an application for the original idea we were discussion, but it is a real example of the use of an oscilloscope for RF work.