How would you define perfect (inter-sample) interpolation, and is it possible?
To quote Armifinn's prior answer:
"I guess the most important result is that for signals with bandwidth limitation, you can have perfect reconstruction via sinc(⋅)sinc(⋅) convolution; the famous sampling theorem..."
If by perfect interpolation it is meant that an analog band-limited signal is recovered perfectly from digital samples, wouldn't a sinc interpolation lead to some problems? Considering that analog equipment is causal while sinc interpolation is anti-causal, shouldn't a minimum phase low pass filter be used instead?
On the other hand, I understand that the above method would not preserve the phase information of the system. Sampling theorem states that band-limited signals can be captured perfectly. So indeed that would be a contradiction.
Finally, a quick thought experiment: consider an analog dirac delta impulse that is low pass filtered using a perfect causal analog filter so that it satisfies the sampling criterion. The signal is then digitally captured by a DSP engineer. Now, the DSP engineer wants to reconstruct the analog signal in his lab, and after running the perfect sinc interpolation he discovers that the signal in fact started BEFORE the analog dirac delta even occurred, to be more precise an infinite time before the analog signal started. This casts some doubts on how the interpolation should in fact be done, and whether the band-limiting criterion is so easy to satisfy.