A "valid but not absolutely" claim? Hey, what are you talking about?

=== update on 12 May 2024 ===

Some of the links to Head-Fi are broken now as the moderator of the Audio Science forum there decided to delete all the evidences/facts in the thread that support my view point.

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If an expert (e.g. a MIT graduate in Electrical Engineering) claim the following:

"The analog signal can be reconstructed losslessly, smoothly, and with the exact timing of the original analog signal [by using CD format]" (the claim)

What would you think about such claim?

I bet most people would understand the claim as the following:

"Using 44.1kHz / 16 bit digital source (i.e. CD format) would allow us to reconstruct the original analogy signal perfectly. "

Is it your understanding too?

You may said, "Yes, of couse. That's what the claim means. They are talking the same thing. Are you that stupid to ask such simple question?"

I thought the same too. But I think going forward when I discuss something in any audio science forum, I may need to ask them, is it "absolutely valid" or just "valid but not absolutely".

The answer I got from many members in audio sciecne forum is "no, they are not the same" (they may not use the exact wordings but that's what they meant). More details is here.

Why they said so? 

Reconstructed losslessly, smoothly, and with the exact timing of the original analog signal?

Let's have a look of the following simulation of the analog signal reconstruction. (note: the following are simulation)

The following graph shows an original analog signal (i.e. a perfect analog sine wave input)

Figuare 1: A perfect sharp sine wave analog input signal

By digitizing the analog signal to 44.1k Hz / 16 bit and then reconstructing an analog signal from the digitized source via a DAC with perfect reconstruction filter, the output would be something like the following:

Figure 2: the simulated output from a DAC with perfect reconstruction filter

The reconstructed output would look like a "smooth" sine wave but with a smeared line (sorry for my hand-drawing, the above graph should look like a "smooth" sine wave with a smeared line. The level of the smearing may not be in scale with the actual ouput from a DAC as the above graph is for indicating the effect of various artifacts in the reconstruction process.) 

The smearing of the output analog signal is due to vaious artifacts introduced in the ADC and DAC processes. For example, dithering is one of the source of such artifacts. (Note: dithering is a technique used to make the quantization errors of the final reconstructed analog signal looks "smooth" rather than "rough")

Ok, back to the claim, i.e. "The analog signal can be reconstructed losslessly, smoothly, and with the exact timing of the original analog signal [by using CD format]"

Would you describe a perfectly reconstructed analog output with smeared signal as "losslessly, smoothly, and with the exact timing of the original analog signal?

Is the signal shown on Figure 2 same as the one shown on Figure 1 above?

Most members of audio science forums would say "Yes, they are the same" as they truely believe in the claim.

How this interesting belief of most audio science forum members is related to the "Monty's video"? Well... this "valid but not absolutely" claim is one of the claims in his article he referred to in the video.

You are still confused if they are the same?

Think about the question.... "Is 1.001 same as 1.000?"

If your answer to the question is "No, 1.001 is different than 1.000", then you would have no way to understand why those people would consider Figure 1 and Figure 2 are the same.

If your answer to the question is "Yes, 1.001 is same as 1.000", then I bet you would agree Figure 1 and Figure 2 are the same. Correct?

It is no kidding, many people in the Sound Science forum in Head-Fi truely believe they are the same. They told me in our discussion in Head-Fi about it (but they had removed our discussion so I cannot show you any evidences to you). However, you can go there and just ask yourself, you would get the same (pun indeed) response.

Another example they used is that 0.63 micro pascal pressure does not exist... Well... what do you think? Is it possible to have 0.63 micro pascal? I bet anyone with high school level Physics knowledge would know about the Ideal Gas Law. In that case, they should know the answer. 

Do they have another "correct but not absolutely" version of the Ideal Gas Law? For that, I am not sure. 

==== Thank you ====

I am having a great fun in discussing the "Monty's video" on head-fi.org. I would like to say a big thank you to the moderator there as he can bare with me and allow me to have an open discussion with other members there. 

On other Audio Science forum, the moderators there would just simply ban me or remove my account and my old writings (due to the banning culture) as they found the facts I bring to them are incompatible with their firm beliefs in audio science.

Thanks for your reading. See you next time!

p.s.: How to form a scientific argument: