Thanks for your response. I visited England once. I saw the Buckingham palace from outside.
I see what you are saying. That's a concept that's given me pause too. We have signals that are already beyond the threshhold of audibility and even if they aren't can impact the ear very little. So if the signals are below audbilty what does it matter. For me that's a strong argument. However even very cheap gear can reach this level. So even though I can't prove it, it's never proved true for me that things sounded the same.
I'm willing to venture something that contradicts what I usually say about audbility. That is technically the two signals aren't the same. They are different. It's hard for me to imagine that would make a difference though due to audibility.
But the standard measurements we make tend to be measuring single tones. Except perhaps the IMD test. Perhaps something changes during music playback. I know the DACs/preamp impedance also can matter. The Yggy first generation didn't do too well with 600 ohm impedance. A lot of dacs now are used as preamps to power amps as well.
I don't see a whole lot about timing in standard measurements. I think maybe we see impulse response.
I had a question since you seem to have been involved in record players. I notice that LP's do not have ringing or a digital filter they have to go through while (most) digital audio does. The LP players do have an RIAA filter and other distortions but they don't have a digital filter and ringing. Also unlike DS DACs they don't have things like taps and ways to approximate the waveform produced. What are your thoughts on that?
What two signals aren't the same?
In a linear system, which is what we are trying to achieve, testing with standard tones should be fine, as long as Fourier is right. Such tests may fall down a bit testing something non-linear, but that is junk anyway.
RIAA is an equalisation curve rather than a filter (though the 1976 curve does sensibly include a high pass filter to remove overload due to spurious subsonic cartridge output).
The standard RIAA equalisation curve was made available in 1954 (IIRC), up until then different recording companies used (slightly) different equalisations to each other.
I don't know if the ringing seen from standard reconstruction filters is a problem/audible but I doubt it based on its frequency and duration. The Shannon Theorem shows that the digital system precisely reproduces the waveform, not approximately, as long as the frequency content doesn't exceed half the sampling frequency, which is easily achieved.
LPs have MUCH bigger shortcomings than that which are well and truly in the audible frequency range and duration!
They have been well understood for decades but are conveniently ignored or glossed over frequently nowadays. Several of the shortcomings are because of the compromises necessary to manufacture the disc, which means even if you could make a perfect record player some shortcomings would still be there from the LP itself.
All 4 of my record players do sound very nice (if different to each other) but when I had a range of DACs to listen to here a few years ago any difference between them was vanishingly small and inconsequential or non-existant and they were all from well known makers and the most expensive was 10x the price of the least.
In terms of listening to things I would say that anybody who makes sound recordings will know that digital is audibly more accurate than analogue. I started with a valve mono reel to reel recorder in the 1960s and worked up to a Revox B77, which I still have, but however carefully I set levels I could always tell the off-tape sound from the microphone feed. The first digital recorder I used (StellaDAT) produced recordings indistinguishable to the microphone feed in comparison.
Mind you, a bit of tape saturation sounds quite nice and a plugin simulating it is popular with some recording engineers today, which is a bit of a laugh!