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> Nyquist-Shannon means a 44.1kHz-sampled signal can perfectly capture an reconstruct a signal up to 22.5kHz freqs, and it's not like it's a flat cut off after that.

Not sure what you mean by "it's not like it's a flat cut off after that". Any spectral content above 22.05 kHz is aliased to frequencies below 22.05 kHz -- that is mathematically inescapable.

Maybe you're referring to the low-pass filters used to prevent this aliasing and for reconstruction -- these do have gradual rolloffs, but their center frequency is necessarily chosen to be somewhat below the Nyquist point, to ensure there is no noticeable spectral content above the Nyquist point.

Notably, because it's much cheaper implement filters with steep rolloff in the digital domain, ADCs and DACs often operate at much higher bitrates (e.g. 384 kHz) to allow for simple analog filters for antialiasing/reconstruction, and then digital filters are used for down/upsampling to/from 48 kHz or what-have-you.

But even in the digital domain, 20--22.05 kHz (or actually, 20--24.1 kHz) is a very tight transition band. 20--24 kHz (actually, 20--28 kHz) provided by 48 kHz sampling allows a much less complex filter to be used. And remember that the cutoff point for filters, 20 kHz in this case, is already at -3 dB (typically), meaning it's lost some fidelity.

> Not sure what you mean by "it's not like it's a flat cut off after that". Any spectral content above 22.05 kHz is aliased to frequencies below 22.05 kHz -- that is mathematically inescapable.

Yes, that's what I mean. If you encode a 23kHz sound you don't get a flat signal as you'd get with a (-inf low pass filter) but an aliased one approximating the original; and as freq goes up, the errors introduced by aliasing (kind of) increase. You are also correct about mentioning the reconstruction filters and internal oversampling.

In practice these errors don't matter, as we humans are, at the very best, barely able to hear anything up there (as in, is there a 23kHz sine vs is there nothing at all), let alone discern any difference between two different sounds (as in, is the sound emitted a 23kHz square or a 23kHz sine or a 23.5kHz sine), and even less when drowned by any signal in the human ear highly sensitive range.

(Not even mentioning that getting into these areas start needing so much pressure to be perceived that it can become painful/damaging)

So theory is all fun and games, because I guess ultimately my point is that in practice anything above 22kHz flat out doesn't matter. Admittedly I'm taking many many shortcuts and possible lies here and there, but I don't thing going "why doesn't Feynman fall through his chair" really helps.

Let's all get out and enjoy some love and music already.

There was a study in the late 2000s that suggested kids (later end of the millennials or younger) tended to prefer the sound of music encrusted with MP3 artifacts over a straight digital reproduction, which suggested that what you grew up with is what you like to hear and the criteria for a "good sound" are slipperily subjective.

Try running that by a Gen-X music enthusiast, though, and watch them make a Wojak face and cry "NOOOOOO! Digital can't possibly capture the warm guitars and fat synths of my analog-mastered vinyl Zeppelin album! It HAS to be 100% analog from the studio to my earholes!"

The difference being that depending on the bitrate MP3 artifacts are hearable, whereas digital pure mathematically is not.

You're missing the analogy; it's the artifacts introduced by an AAA[1] mastering process that are audible.

1: https://en.wikipedia.org/wiki/SPARS_code

> Not "you". Not most. None.

Maybe not "none", but certainly it's only the very, very rare individual. And likely those aren't in the set of people that care about these things. And the intersection set are people who don't even care so much about the music as they do the sound.

I'm older now so I just mentally roll my eyes at these folks, but I used to rage at the people who insisted on 320bps MP3's or would faux outrage at any non-lossy media, then play it in their car.

> Maybe not "none", but certainly it's only the very, very rare individual.

Maybe not none, but to my knowledge we have not found one single individual is the world who actually have these "golden ears".

At some point absense of evidence is actually evidence of absense.

> I used to rage at the people who insisted on 320bps MP3's

bps and compression is a separate issue. Lossy formats don't represent the audible spectrum (up to 22050Hz or 24kHz) literally 100% accurately, but non-lossy do.

Edit:

Oh, and keep in mind that now that you (as you say) are older, not only are you maybe less passionate about the issue, but also your ears aren't what they used to be.

I mean, there appear to be people able to discern isolated tones above 22kHz in extremely controlled lab conditions, but that's wildly different from being able to hear anything above 22kHz in the midst of vastly more powerful 100Hz-15kHz sounds in realistic music listening conditions.

>insisted on 320bps MP3's

Why though? Was storage a concern?

Think it was at that mp3 bitrate that basically "at this level even audiophiles couldn't tell difference in double blind test"

> Beauty is as much in the ear of the listener as in the eye of the beholder.

For all the human ear can hear, though, this can be implemented with a digital "nostalgia filter".

For the rest I agree with all you said, except a lingering feeling that there is one exception:

In the end audio is analog. Yes, the digital version literally perfectly contains the analog perfection that's hearable. But that assumes a perfect digital to analog conversion.

In theory a 192kHz digital signal, with a DAC that understands it, may create distortions that add in a subjective pleasant way within the hearable spectrum, whereas a 44.1kHz signal may, in DAC, cables, or headphones, create a different set of distortions.

For high end amp and speaker/headphones this should matter less.

> In theory a 192kHz digital signal, with a DAC that understands it, may create distortions that add in a subjective pleasant way within the hearable spectrum, whereas a 44.1kHz signal may, in DAC, cables, or headphones, create a different set of distortions.

Which you then put into a 32kHz 12-bit ear.

I entirely agree. I'm saying that it's perfectly possible to reproduce this distortion perfectly digitally, and play it through audiophile headphones.

This of it as constructive/destructive interference. The 192kHz master has imperfections, and the DAC and headphones have different (and possibly major) imperfections, creating something that sounds subjectively better.

Obviously it would be better to have a perfectly mastered 44.1kHz source and audiophile headphones, but at least in theory you can get this distortion interference add up to something better.

Just like how maybe you like the classic sound of a worn vinyl. It was not recorded with that distortion, but you like it. In theory the artist intended that sound. But digital obviously they could have just mixed it in manually.

The problem with "digital" is the playback equipment used. Most people assume that their expensive smartphone/tablet/laptop has a great DAC in it and will play music great. Sadly, they don't and they won't.

Additionally, most have got rid of or never owned a good amp and a good set of speakers or headphones. So the music sounds much worse that it ought to and the listeners are frequently completely unaware. Also, that bluetooth speaker that they're using sounds awful and even if it supports LDAC and APTx-HD, because they're likely not sending the data from their streaming device to it using those technologies.

That is very true! I'm quite certain decoders also play a role.

Indeed a friend of mine has a superb high quality audiophile setup. Playing vinyls sounds absolutely glorious. Playing WAV and CD sounds equally glorious. Yet for some reason playing AAC, and, more surprisingly, FLAC and ALAC, sounds terrible, which makes no sense, unless the decoders are borked.

>Nyquist-Shannon means a 44.1kHz-sampled signal can perfectly capture an reconstruct a signal up to 22.5kHz freqs, and it's not like it's a flat cut off after that.

After that you get aliasing artifacts so generally having any input above that frequency to ADC will cause some problems.

Similarly with DAC, to get that 20kHz you need to have nice sharp filter cutting any higher frequencies off.

...which leads to one actual benefit of higher sample rate for ADC/DAC, it's easier to design filters because with say 96k you don't need that sharp of a cut to still not get artifact coz you're "safe" all the way to 48k

Those 16 bits are 65,536 linearly-spaced values, while sound and human hearing are logarithmic. The scaling is, ideally, such that only at the loudest instant will the data reach the maximum instantaneous value, like a cymbal crash. Drop down fifty decibels for a quiet section and there's really not much dynamic range left.

Drop fifty decibels on tape and you will be just hearing noise buddy. Might sound a bit more pleasant noise but noise nonetheless

> Drop down fifty decibels for a quiet section and there's really not much dynamic range left.

yeah "just" like 45dB of dynamic range left. Also nobody would master a 16 bit file like that in the first place.

This has never been a problem in practice. The ~90dB of dynamic range in 16-bit audio is far more than any analog format, and the noise floor after dithering to 16-bits is pretty much always well below the floor of the recording environment.