Usually claims like this fall into two buckets: (1) crazy, (2) existing idea spun as something new. (Like airless tires, which have been around for a hundred years.)
This is quite clearly (2).
> Effectively they can replace the anti-aliasing hardware with software that operates on the digital side after the sampling step
Sampling with filtering in the digital domain after sampling is absolutely old hat, found in everyday tech.
Let's look at audio. We can sample audio at 48 kHz, and use a very complicated analog "brick wall" filter at 20 kHz.
There is another way: use a less aggressive, simple filter, which lets through plenty of ultrasonic material past 20 kHz. Sample at a much higher frequency, say 384 kHz or whatever. Then reduce the resolution of the resulting data digitally to 48 kHz. There we go: digital side after sampling step.
This is cheaper and better than building an analog filter which requires multiple stages/poles that have to be carefully tuned, requiring precision components.
First sentence from the original article: „A team from Columbia University led by Ken Shepard and Rafa Yuste claims to beat the 100 year old Sampling Theorem“
> (2) existing idea spun as something new
The existing idea is oversampling and is often spun as beating the sampling theorem. But this is unlike the airless tires example, because, while oversampling works, it isn‘t beating the sampling theorem but rather based on it.
You can filter after sampling, but that filter is not a replacement for the analog ant-aliasing filter. To avoid aliasing you have to somehow limit the bandwidth of your input.
Right; it's not a replacement. But you can then pretend (due to naivete or dishonesty) that the analog one doesn't exist and claim you've beaten the sampling theory. Why: because the input stage before the sampler naturally has a limited frequency response and you happen sample well above that. Thus a filter is de facto there but wasn't formally designed in.
This is quite clearly (2).
> Effectively they can replace the anti-aliasing hardware with software that operates on the digital side after the sampling step
Sampling with filtering in the digital domain after sampling is absolutely old hat, found in everyday tech.
Let's look at audio. We can sample audio at 48 kHz, and use a very complicated analog "brick wall" filter at 20 kHz.
There is another way: use a less aggressive, simple filter, which lets through plenty of ultrasonic material past 20 kHz. Sample at a much higher frequency, say 384 kHz or whatever. Then reduce the resolution of the resulting data digitally to 48 kHz. There we go: digital side after sampling step.
This is cheaper and better than building an analog filter which requires multiple stages/poles that have to be carefully tuned, requiring precision components.