Again off the rails...
Back to the topic. Reg KNOWS his DSP. I argue with him when he confuses seismography equipment with a 1 GHz (input bandwidth) scope.
Reg properly said that by choosing proper input filter you will get perfect impulse response.
He properly said that that filtering can be done partially in analog and partially in digital domain.
He properly said that using DSP you can "idealize" (shaping it to achieve proper calibrated response) scope pulse response.
He properly said that by using proper reconstruction filter you can fully reconstruct sinewave with more than 2,5 samples per period. Make note that reconstruction filter is not simply low pass filter.
He properly said that even if scope doesn't have Gaussian frequency response, by choosing reconstruction filter appropriate for it's response, you get the scope to reconstruct signal properly.
He properly said that FFT on most scopes is far from being optimal, not to mention easy to use, or giving directly usable results similar to SA.
He properly said that decimation by simple throwing away samples is wasteful. Data can be downsampled by filter and gain additional dynamic range and lower noise in usable bandwidth. That also filters out all higher frequency components (low pass filter) so it takes care of aliasing . If that is what you want to accomplish. (edit:that is important if want to further process data, if you simply show it on the screen it's not important)
Things he gets wrong are connected with not knowing how other people use scope, and generally having limited insight into oscilloscope use cases by industry.
Also we are getting back to people again saying " we need at least 10x oversampling". No you don't. If band limiting and reconstruction is done correctly, you don't. Because, if you do that correctly, there is nothing in the signal reaching the A/D converter in between those samples that doesn't fit perfectly on top of interpolated sine segment. On a 1 GHz scope, looking at a 1 GHz square wave, you have to see perfect sinewave on the screen.
Reason why Keysight itself used to recommend 5x oversampling (which I find good compromise) is that input filtering is not ideal...
On most 1GHz scopes and up nowadays they use brickwall (sharp rolloff) filtering and sampling factor of 2.5 with all channels on.
That brickwall filter takes care of aliasing. But pulse response of that filter is not the same as Gaussian response filter. It has pros and cons. Pulse response is worse, it overshoots. But, same 1GHz scope will have 15% more accurate rise/falltime measurements. Additionally, it's frequency response will be essentially flat, gaining excellent amplitude accuracy, all the way up to the cuttof. In practice, that means that on 900 MHz you get less than 5 % amplitude error, compared to almost 30% on Gaussian response scope.
Also that distorted pulse response? Well, it isn't there if you don't feed scope stuff over 1.2 GHz, in amplitude that is high enough to show on screen. That overshoot shows only when you feed it signal with components in gigahertz range. You need to buy (or make) special pulser to even be able to create pulse that fast, and connect pulser directly on scope input. Even a foot of coax cable will make things very different.
In practice that is pretty much not going to happen. There are no 40 ps pulses in Raspberry Pi, Arduino, switching and analog PSUs, and pretty much 90% of all electronics. Unless you are working on multigigabit data links, picosecond lasers, or designing MRI machines or such, no worry. And if you do, your employer bought you the fancy stuff. That is no small business or hobby territory.
People who work on 40ps pulses need 20GHz+ scopes and equipment. DUH.
Stuff is, of course, more serious when same things happens on a 100 MHz scope. That bandwidth is pretty much easily pushed into aliasing with anything on your desk.
So question here is how to make it to not alias. Again it is simple. Cheaper scopes are being made with 1x1GS/s A/D for 4 Ch (those that will get in trouble), and those that have 2x1GS/s (those that will be doing better). Also if aliasing and pulse response is more important than maximum bandwidth, you can always opt NOT to buy highest bandwith machine.
It is quite obvious really. You don't get Keysight MSOX3104T, but deliberately get MSOX3054T or even better MSOX3034T. Those will still sample at 5 GS/s but with maximum 350/500 MHz frequency are guaranteed not to alias. And step response will be perfect. Really, just buy Rigol DS1054Z and DON'T hack it to 100MHz. Take a look at that pulse response...It will be slow, but perfectly behaved.