You don't have to re-read them if you have already. But some folks might enjoy reading them in the order that I posted them (I took my time to make the link's order as comprehensible as I can). > I did my research too, and I also read them all. ...Plus much more; but them seven links were the ones I picked @ the end.
Hi Bob. I read a ton of articles about audio yet you manage to unearth links I have not seen
. So I read the first one and unfortunately it is completely wrong. It has this common graph:
What he shows about digital is just flat our wrong. Take a 1 Khz sine wave, convert it to digital, and playing on a CD player. The look at the output from the analog jack on the CD player. It will look just like the original waveform on the left. It never, ever looks like what he is showing. If it did, you would think someone, some place, would have measured a CD player outputting such, rather than a graphic created in a paint program.
The reason what he shows is impossible is not because of anything related to audio. It is the nature of signals. That sine wave he shows with steps in it indicates at those increments, the signal immediately jumped from one value to the other. For a signal to go from one value in zero time to another value, you must, let me repeat, must, have infinite energy. And of course no real signal does.
A signal that is similar to that is a square wave. A symmetrical square wave at 1 Khz has harmonics going to infinity at odd multiples of 1 KHz, i.e. 3 Khz, 5 KHz, 7 Khz, etc. Those harmonics based on above, must go into infinity or else, you don't have a square wave. You can choose to truncate that signal at any point, and if you do, then your signal deviates from square wave. The more you truncate those harmonics, the more it will not look like a square wave.
Turns out that is exactly what every CD player/DAC does. They have a filter on the output of the DAC whose job is to eliminate all of those extra harmonics. It is called a reconstruction filter. Apply that filter and 1 Khz now looks just like 1 Khz and that is that. It cannot have steps in it because there are no harmonics to generate them.
We can see this effect if we create a square wave using a computer, record it and then play it on a CD player. Stereophile does this in their CD player tests. Here is a random example:
The CD player was instructed to play a pure, square wave. The numbers were computed to be completely accurate. Yet what comes out of the CD player are those wavy corners. The corners get wavy because the CD player's DAC is filtering the high frequencies. When it does that, the math, not anything to do with digital or analog, says that it cannot be square wave.
Now, the reproduction is not perfect because it is limited to the resolution we have determined for our system. There are errors that can be measured but they don't show up like his made up graph. Here is stereophile again, feeding a DAC a sinewave at -90 dbFS:
Yes, it doesn't look like a perfect sine wave. The reason is that we are feeding the DAC such faint signals. No analog system can even reproduce such a clean signal as it will be overwhelmed by noise. A tape deck would be doing good at -80 db. The little jumps in there also is due to lack of dither. If we tolerate a bit of noise, they can look like analog noise just the same.
Cutting out all the technical bits, he is attempting to explain away theory of relativity from knowledge level of elementary school kid. It is junk marketing material. Not any kind of technical article. The person is unqualified to write such things.
Digital audio concepts unfortunately are complicated. They immediately involve a ton of math and signal processing. They are not approachable as a topic so I wish people would not. They can say they have a preference against it which is fine. But don't try to get technical and mislead when a simple measurement would invalidate everything you just wrote.
The man even gets the analog side wrong. Analog by definition has noise and lots of it. There is no way what you feed it, is what comes out, putting aside all kinds of other distortions it also piles in for good measure. Waveform comparisons of real devices would paint a horrific picture of analog against digital. It just happens that we either like the distortion, or it gets masked.