A very good ENGINEERING explanation of why analog can not be as good as digital..

audioengr

Digital is sampled, not continuous. The reproduction accuracy with digital is a function of the sample-rate and filtering to "smooth" those steps.

The Fourier Transform proves otherwise, and the transform really has more than one proof. One is in the video, but there's mathematical proof, too, if you really want to dive deep into it.

The Nyquist theorem is true and often cited, however, it makes some assumptions such as the waveform is continuous and not transient.

It relies on the Fourier math.

Transient waveforms cause the Nyquist theorem to break-down ... the sample rate required to get an accurate transient reproduced is much higher that Nyquist would predict.

If you could disprove the Nyquist Theorem, you'd be famous. It's already been proven. That's why it's a theorem.

It is not matter of disproving, but rather knowing limitations (understanding it).  This theorem only states that you can recover continuous signal by sampling at least two times per period.  It does not say you can do that when waveform constantly changes.

And to all vinylistas, who highlight the "shortcomings" of sampling, do you think that the small groove of a record is large enough to be able to store all frequencies from 20 - 20 khz, not to mention the relative intensities, ie the dynamic range.  You think all that information is FAITHFULLY written into 20 - 25 micro meters (typical width of a groove for 33rpm vinyl).  No way, since it is limited by PHYSICAL SPACE.

With digital, there is no limit, all you need is a bigger disk.  One can sample at higher frequencies as well as amplitudes.  The typical 16 bit deep CD can store 65k different ranges.  Increase that to 32 bits, and it will be 4 billion.

As I said before, I also DO like listening (I should say looking at) to vinyl but not because it sounds better but because it LOOKS better :-)

On a more practical level, vinylistas don’t seem to care that most current lp issuues Of Classic albums use digital masters, due to the sticky tape phenomenon.  Vinyl bigots like Fremer and Dudley were embarrassingly silent on this after touting many of these releases only to have the remastering engineers spill the beans.  So if they prefer lps made from corrupt digital discontnous sampled waveforms, that preference must be based upon something completely unrelated to that waveform 

kijanki

This theorem only states that you can recover continuous signal by sampling at least two times per period. It does not say you can do that when waveform constantly changes

Actually, that’s exactly what the Fourier Transform addresses and proves - the transient need only to fall within the bandwidth of the system. It’s why digital audio works.

Again, I’m very much an analog guy. But to claim the digital audio isn’t continuous like analog is misunderstanding how digital audio works. It has problems, but non-existent stairsteps aren’t part of them.