There was an oscilloscope article written by Steven B. Warntjes about
sustained sample rate in digital oscilloscopes. I wanted to get a
verification from the experienced users on this group. Let's say I have
an oscilloscope with 25000 sample memory depth and a real time sampling
of 1 gigaSamples / sec with 200 MHz bandwidth (-3dB).

If I had an FM carrier at 100 MHz with a 1000 Hz (1 mS period) test
signal modulating it, does that mean that a digital oscilloscope with
the specs above will not be able to capture the waveform properly?

I was thinking that if the capture window (in seconds unit) is equal to
the memory depth (in samples unit) divided by the sample rate (in
samples / sec unit), then the maximum capture window that I can use and
still maintain the rated sampling rate would be 25 uS (micro-seconds).

So that means that if my carrier signal is deviating between 100MHz +/-
1kHz, then my capture window would at least have to be 1ms/div to
capture the deviation properly (?). With a capture window of 1ms/div,
my sample rate would decrease to 25 mega-samples/sec, which is not
enough to sample the 100MHz carrier frequency.

Is that right?

I know that I can just use a spectrum analyzer, but I wanted to capture
the waveform and duplicate the time-domain plot of frequency modulation
(amplitude vs. time) that I've seen in the books.

Thanks!