There is an audiophile argument stating that analog audio "sounds better" than digital, due to inherent limitations of digital audio, which would always cause "staircasing".
Well now. Except for live performances, analog audio is reproduced by electronic systems. By definition, the smallest signal that can be carried by such a system is one electron. Since all analog audio must be represented by a discrete number of electrons, analog audio, too, is subject to this staircasing issue.
To determine what the quality of recorded digital audio would have to be to match analog audio, let's have a look at the physical limits of audio.
Under most circumstances, it's fair to say that audio is a longitudinal air pressure wave. The minimum pressure possible is pure vacuum; anything louder and the analog audio would suffer hard clipping, which is not acceptable for any self-respecting audiophile.
As it turns out, the upper limit on undistorted loudness is roughly 194.094 dB [1].
In terms of frequency, the upper limit on sound in air is ~ 5GHz [2] but it would not carry very far - Frequencies of 1 MHz won't carry further than 10cm, while 10MHz won't go further than 0.1 mm [3] which isn't far enough to travel even from headphones to your eardrums. As such, to capture the entire physical audio spectrum, we can safely use an upper frequency limit of 10MHz since nobody has ever been close enough to a sound source to hear frequencies this high (disregarding limitations of the human ear). This means that a sample rate of 20 million samples per second will suffice for any purpose.
What bit depth do we need? For each bit we get about 6dB worth of dynamic range. The full physical dynamic range of audio is limited to 194 dB, so encoding audio at 33 bits per sample captures the entire physical audio range.
I don't care if you're human, dog, or bat. Digital audio encoded at 20 million samples per second, 33 bits is superior to analog.
[1] http://physics.stackexchange.com/questions/2523/is-there-a-limit-to-loudness?rq=1 [2] http://physics.stackexchange.com/questions/23418/is-there-an-upper-frequency-limit-to-ultrasound An additional problem is created by the strong absorption of ultrasound in air, at least for frequencies higher than 250 kHz. As a consequence, ultrasound of e.g. 1 or 2 MHz can propagate in air over a distance of not more than a few centimeter "The mean free path in air is 68nm, and the mean inter-atomic spacing is some tens of nms about 30, while the speed of sound in air is 300 m/s, so that the absolute maximum frequency is about 5 Ghz. This is much less than 100 Ghz. " [3] http://www.physicsforums.com/showthread.php?t=144509 " http://www.kayelaby.npl.co.uk/genera...2_4/2_4_1.html gives a general account of attenuation. At 100kHz we have about 1800dB/km in fairly dry air. Attenuation on a simple model goes up as f^2. Range of 1000kHz therefore bein of the order of 10m (1.8dB/m). At 1MHz we have 10cm. At 10MHz 100 microns. In my book 100MHz+ can't really exist in air."