So why do they not quote dsd512 at 20 kHz or do they ?

Thatās not audible, and you can do better than that with a higher order modulator. Also, with DSD, the noise is always correlated.

Yes, it can be uncorrelatedā¦

Or do you need to Jussi to tell you differently again:

Because the noise is no longer present at 20KHz. It has been moved much higher in the frequency range.

Does that mean negative infinity dB at 20kHz?

Well, that, or the fact that generally āhighly resolvingā means ācanāt output a sinewave when fed a pure sinewave on inputāā¦

I find the idea that one canāt perceive, in any way, a certain frequency blasting in their ear for a long time, but add the same frequency, at a lower level at that, to a music signal, and suddenly thereās a veil-lifting, audible difference to beā¦ rather preposterous really.

-110 dB is insignificant already so it cannot go much lower anyway.

Your problem is that you are thinking in frequency-domain, stationary terms when much of what happens in hearing is a lot more transient dependent. Donāt take my word for it https://www.cambridge.org/core/books/human-and-machine-hearing/3660166B40020EE587D94BB7A309FC12#.

Which ever (HQPlayer) modulator is used, the dynamic range way exceeds that of 24-bit PCM. With my newer developments at DSD512 it is over 180 dB for 100 kHz bandwidth (and over 144 dB over 200 kHz bandwidth). Idea is that for 22 kHz bandwidth it exceeds dynamic range of 32-bit PCM with good margin for mixing and such (over 200 dB).

With the better DSD DACs, ultrasonic noise doesnāt exceed -100 dB at any frequency. In best cases it doesnāt appear at all from the analog noise floor.

Just want to point out that there is nothing āstationaryā about the frequency domain, since time-domain and frequency-domain representations of a signal are 100% equivalent. Whether one or the other is useful/required for DSP depends on the DSP.

I do ALL of my listening with a fully and properly calibrated set of audio testing equipment. That way I can see, as well as hear, jitter and quantization noise, regardless of its level. Think of it has having turbocharged golden ears!

I do love the way audiophiles and especially the high end audio press (print and online) play the numbers game:

With respect to tubes and analog playback, where the ānumbersā are often terrible they say itās not about the numbers, itās about the sound.

With respect to digital itās all about the numbers!

You are again making up your own theories based on over simplified assumptionsā¦

Can you offer more details about the over-simplifying assumptions? We can get highly technical in the other thread.

Sigh, not about to discuss the fine-print in the equivalence, which makes all the difference to practical application in biophysics. Next Iāll be reading about the physical reality of a Dirac delta.

(Call me pedantic, but a digital delta signal is perfectly realizable.)

Yes, there is a āfine printā, and thatās exactly why we have ABX testing, to see how well theories hold up to reality. So far, I think theyāre doing quite well.

Quod erat demonstrandum

No, Iāve already spent way too much time repeatedly explaining same things over past 25+ years that it gets a bit too boring to do it every six months you (or someone else) pop up on the same matter. And Iām not going to tell all the technical details of the nice things Iāve developed over the past 25+ years.

No problem. For whoever is interested: Iāve provided a mathematical proof; I expect a mathematical rebuttal.

As I said, you have roughly proven that ROT-13 is bad encryption. Not that same would apply to AES.

Your āproofā is practically missing the modulator altogether.

P.S. With PCM it is very easy to calculate mathematical correlation of error signal from the DAC analog output. And it is obvious also from spectrum analysis.