phase resolution between two digitized signals

[NiHaoMike]

The page about the DIY speaker kit had a number of reviews including one by a pro audio tech. I was curious so I checked out her other videos and came across this:

She makes the argument that although 48kHz should be able to represent the entire audio spectrum, where it starts to lose out is when it comes to representing the phase differences at high frequencies.

Stepping away from the controversial world of HD audio, is there a general formula for the phase resolution between two digitized signals given a signal frequency and sample rate?

[ataradov]

The notion of moving sample time around  to find maximums of the sine wave is plain wrong. This just shows complete misunderstanding of how Nyquist theorem works. It "feels" like if you sample sine wave on its side slopes, you won't be able to recreate it back. But math does not go by "feeling". And everything else that follows from that assumption is nonsense.

[tooki]

He doesn’t understand digital sampling at all — he’s relying on the common misunderstanding of how it works, as opposed to how it actually works. Cf https://xiph.org/video/vid2.shtml

As long as the DACs are processing the left and right samples at the same time (the first CD player actually did not!!), then they will be in perfect phase, because it does not matter where in the wave the samples are taken, they still reproduce the original waveform perfectly.

[Domagoj T]

how it actually works. Cf https://xiph.org/video/vid2.shtml

I love this video! Clear, concise and supported by actual tests and demos on scopes.

[vk6zgo]

I haven't spent the time to watch the video, but if they are talking about channel to channel phase, ears are not at all good in determining phase at high frequencies
 Perhaps there may be some degree of cancellation if you are listening to mono, but even that is a bit problematical.

PS :- By the way, sorry Domagoj T, but I didn't really thank your posting .
Dunno how that happened-----Safari strikes again?

[Domagoj T]

PS :- By the way, sorry Domagoj T, but I didn't really thank your posting .
Dunno how that happened-----Safari strikes again?

Why would you apologize? Here, have a "Thank" yourself, it's Christmas after all  .

[Rerouter]

For the actual phase deviation between 2 signals, that's not hard to calculate out, you have your sample rate of 48KHz, so lets take top of average joes hearing, 20KHz,

1 sample time is     0.00002083 seconds,

1 Cycle of 20KHz is 0.00005 seconds

0.00002083 / 0.00005 * 360 = ~150 degrees Phase Shift,

Now lets try down in the middle of human hearing,
1 Cycle of 4KHz is 0.00025 seconds

0.00002083 / 0.00025 * 360 = ~30 degrees Phase Shift

Now personally seeing as our hearing has to normally account for 625 µs of delay from ear to ear, Its not likely to affect your listening experience, but a fixed delay from one ear to another will make your brain derive direction information from the sounds, e.g. you would perceive it arriving from an angle, not straight above your head as inphase audio normally does.

So to put it to the test yourself, you can easily use something like audacity to insert a fixed delay of 1 cycle time between 2 audio channels and see if it sounds any different, At a guess you would hear it from an angle, I know some songs have used this effect for multiple singers so you end up perceiving them to your left and right,

[dmills]

Except that the way the maths (specifically the reconstruction filter) works is such that provided the signal was correctly band limited before being digitised the accuracy with which you can determine phase in the digital (or reconstructed analogue domain) domain is limited only by the system noise (just the same as it would be in the analogue domain)!

I really wish the 'audio education' books would stop with the silly stairstep diagrams of quantisers, that is NOT the reality of a correctly dithered system (And any quantiser which is not correctly dithered is non linear and thus broken by definition). 

Similarly the fact that the sampling theorem requires Fs to be **STRICTLY GREATER** then twice the bandwidth could use some emphasis, it eliminates that silly 'thought' experiment where you have a sine at 24kHz sampled at 48kHz, so beloved of the hard of thinking 'audiophile'.

[Rerouter]

Not sure if that comment was pointed at me, but to my understanding, there could still be a lag between channels, so while I ignore the video I still like the Concept.

Say using 1 interleaved ADC for sampling both channels, where the phase would be reconstructed faithfully as the signal was sampled correctly for that half offset, but when played back on a DAC that handled both channels simultaneously it would have a half sample time lag versus what the input captured,

Then trying to relate that back to "resolution of phase" vs "reproduction of phase delta" I can see where some noises might be pointed, Still doubt it would ever be an annoyance, otherwise recording companies would have a lot more marketing budget around phase syncing of stereo signals to deliberately remove any positional information in the songs.

[Kleinstein]

For audio frequencies it would be rather unusual to use a single ADC and interleaving. The more typical would be to also use some kind of oversampling during recording and only than reduce the sampling rate. For the DAC side oversampling is pretty standard.  The idea with oversampling is to use a rather moderate analog filter (e.g. 50 kHz corner frequency) and do the sharp fine filtering at some 22 kHz in the digital domain. This was used in CD players from the very beginning.  The digital filter can be very accurate and with little phase shift even up to 18 kHz.

SD DACs use oversampling to the extreme.

[soldar]

https://xiph.org/video/vid2.shtml

That is a most excellent video! Perfect information perfectly presented! That guy knows his stuff!  Thank you!