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This is a conversation that will go nowhere because I cannot provide the measurements or data to support Chord's / Rob Watts' claims.
I am also not saying I know that it does what he says. I am merely saying that something is happening that results in a sound that I prefer and I am accepting his explanation in lieu of any other reasonable one. If someone could demonstrate negative traits like added harmonics, I'd accept that happily - it's not about it having to prove or disprove Rob's claims.
There's been no clarity provided about how the theory/hypothesis that the WTA filters are built on (i.e. the benefits of extending the sinc function as close as possible to its infinite products) is wrong. Instead we have this circular argument about how it can't be possible because it isn't possible.
Let's take this to a slightly different, but related topic for a moment. Is the takeaway from all of this that upsampling in general does nothing? Does software like HQ Player offer no benefit to the sound quality?
Thanks again for sticking with this conversation. I agree it is likely to end in an impasse, but at the same time I do think some points of disagreement are coming into sharper focus, and that in and of itself can be a good and useful thing.
You don't improve the sound by upsampling. Once again, the reason you don't improve the sound by upsampling is not because I can't hear any improvement or someone else can't hear any improvement. The reason is that upsampling simply, and literally, just duplicates samples. So if you upsample from 44.1kHz to 176.4kHz, that's 4x oversampling, which means every original sample is replicated three more times - it's copy-pasted three times so that every original sample is now four samples. All four samples are identical - there is no "interpolation" like you might get with a TV that increases the frame rate by creating new frames that are combinations of the frames before and after them. That's not how upsampling works - it just copies the existing sample exactly.
It might be helpful or useful to ask, Why not create a digital upsampling system that DOES interpolate samples, that looks at Sample 1 and Sample 2 and creates a new Sample 1.5 in between them that is a combination of them, to "smooth" the transition from Sample 1 to Sample 2 just like video frame interpolation on a TV smooths the perceived motion of the moving video?
The answer is that digital audio doesn't work that way: there is only one way to get from Sample 1 to Sample 2. There is no need for interpolation in the digital domain, and in fact the idea of synthesizing such an interpolated new sample doesn't even make any sense. The reconstruction filter does the smoothing during the digital-to-analogue conversion step. It doesn't - and can't - happen within the digital domain.
The only scenario in which there is more than one way to get from Sample 1 to Sample 2 is if the original audio signal contains frequencies higher than 1/2 the sample rate of the digital recording device. That's why analogue signals going into an ADC (analogue to digital converter aka a digital recorder) have to be (or at least should be!) band-limited so that they contain no frequencies higher than 1/2 the sample rate.
This is the same principle that dictates that any frequency needs to be sampled only twice - and that sampling it more than that does nothing and changes nothing.
So no, HQ Player's upsampling does nothing - or more precisely, increasing the sample rate does not change or refine the sound, and it doesn't enhance time accuracy because sample rate has nothing to do with time accuracy - it has to do with which frequencies can be accurately encoded. If you try to record a 15kHz signal using a 20kHz sample rate, then there will be a "time inaccuracy" because a 20kHz sample rate can only encode frequencies up to 10kHz. So it will encode that 15kHz signal as 5kHz (10kHz minus 5kHz instead of the original and proper 10kHz + 5kHz = 15kHz). So the "time inaccuracy" will be that the frequency - the speed, the timing - of the signal will be aliased; reproduced at 5000 cycles per second instead of the original 15000 cycles per second. But as I'm sure you can see, that "timing inaccuracy" would not be subtle (to say the least!) and would be an indication of a fundamental operational error rather than a subtle change or improvement in the "refinement," "pacing," or "precision" of the sound.
As has been explained by folks with far more knowledge than I have, increasing the sample rate does allow the reconstruction filter to operate in a larger frequency range above the limit of human hearing but below the Nyquist limit of 1/2 the sample rate. However, as those with more knowledge than me - including Amir - have shown, Chord products do not need to take advantage of that extra "wiggle room" - instead they use their gazillion taps to create a very well-implemented reconstruction filter that has tons of ultrasonic attenuation and does its work in a very small/narrow frequency band (Amir has repeatedly acknowledged that Chord products have great reconstruction filters). So with Chord products, to the best of my knowledge even this one potential implementation benefit of oversampling is not necessary or taken advantage of.
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