Need to use something faster than an Arduino
I'm not sure if this is what HP uses, but besides using multiple interleaved ADCs, there
is a technique called "equivalent time sampling" that can be used if you have a stable
trigger capability and a **repetitive** signal.
Basically, what you do is trigger at the same point in the repetitive waveform multiple
times, up to 20 or so, and with each successive trigger you introduce an increasing
time-delay on when the ADC sampling is started. Then, you reconstruct the original
repetitive waveform by re-ordering the samples from memory to the screen. It's not
difficult.
Some years ago, I did this using a 20-Mhz PIC, which has a max sampling rate of about
50-Ksps, which is normally good for sampling about a 5 Khz sinewave, if you want to
display it [for good display, the signal must be much slower than the Nyquist frequency,
eg about 10 samples per period].
With ETS on the PIC, I was able to get an equivalent sampling rate of 1-Msps. With this
I was able to resolve a 50-Khz sinewave with very good fidelity. Even better, when using
an FFT spectral display on the samples, I was able to follow an aliased sinewave all the way
to about 250-Khz, as I recall. It really is magic, :-).