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Originally Posted by
tpad
Huh, what reconstructed waveform? There is no "digitally reconstructed" waveform in my DAW. If the metering in my DAW is accurate and it indicates that the highest peak value is just reaching full scale, I can open the corresponding WAV or AIFF data file and look at the sample values and verify that they indeed are just reaching full scale value. Basically, just a bunch of discrete amplitude numbers at discrete sampling time intervals that correspond to what is appearing in the DAW. There's no interpolation and no intersample values or intersample peaks.
This is all absolutely correct!
But as you yourself correctly pointed out, we don't hear the digital sample values. We only hear the audio that comes out of our DACs. To be even more correct we don't hear that either. We only hear the sound pressure waves coming out of our speakers. The analogue voltages in audio cables are themselves merely a representation of what we want to hear. For brevity sake I will from now on only refer to this whole chain of abstractions as "audio".
When building a digital level meter (and many other digital audio processing tools) it is computationally much cheaper to just look at the sample values rather than reconstruct the actual audio for every meter in a DAW. The result is that most digital meters are in fact inaccurate audio level meters. They are not even really audio level meters at all! They are just sample level meters!
We can't really blame the DAW builders though. For most practical purposes the sample level meters are close enough for every day use. And these "short-cuts" allow us to save much resources and therefore allow us to do many more things with the limited computational resources that we have. Without these kind of short-cuts, we wouldn't have all the wonderful tools we have today. At least not at this price and with so much power.
On the other hand, this saving of computer resources has brought us to the unfortunate situation that most people don't understand digital audio and confuse the sample values for the signal itself.
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If I do subsequently feed said data file through my DAC, the reconstructed waveform isn't "digitally" anymore, its analog, and there are no "sample" values or "intersample peaks" for that matter, because it is a continuos time waveform. Or at least it is with my DAC.
Indeed! But those peaks in the signal that was encoded in your DAW were at a time position that did not correspond directly to any sampling point. They were at a position that fell between two sample points. But it was still the same signal! It just happened to be in encoded form.

The fact that your DAW took short-cuts in representing the signal (usually through a "join-the-dots representation") is what stopped you from seeing the Inter Sample Peaks. But they were there all the time!
Here is a screen-shot from a DAW that does show the reconstructed signal:
(Well at least it shows a better approximation than most other DAWs

).
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If you want be argumentative for the sake of argumentation, you probably will have better luck with somebody else - somebody with a spare 36 bucks to blow on the book :-).
The video Fabien linked is entirely free!
PS: I don't think Fabien or flatfinger are being argumentative for the sake of argumentation. This stuff represents a paradigm shift in understanding digital audio. I would even go so far as to say that people that haven't fully realised the implication simply do not understand digital audio.
Alistair