Quote:
Originally Posted by
arnyk 
Amir, the myth relates to the stairstepping, and its removal, about which you have been shown to be totally wrong about in a number of ways, and which you still seem to be denial about.
I appreciate you not wanting to discuss the topic anymore

. But as you say, we still have a disagreement as you confirm here so we should sort it out. After all, when it comes to math and science, there should only be one answer and not two. So let's review again what you said:
Quote:
Originally Posted by
arnyk 
Amir recites yet another Audiophile Myth like it was revealed truth - the myth that "...when digital systems use
fixed bit depth, you create distortion since analog waveforms do not have such steps".
It is clear that you are saying that having fixed levels does not create distortion. Otherwise, why would it be a myth?
If it is a myth that the steps add distortion, how about this. Why do we have 16 bits in our CD format? Why not 1 bit at the same sampling rate? If the steps by magic go away as you have been saying, there should be nothing wrong with that. Who wants to raise their hand and agree with Arny that it matters not that we have steps in our amplitude?
Quote:
This other issue is just another one of your red herrings. As soon as you admit your errors in this area, we may talk about other issues.
Red herring? Other issues? I am only asking you what you meant by the myth.
As I said yesterday, my sense is that you confused time domain quantization with amplitude quantization. That is evidenced by the fact that you keep thinking the distortion is only created at multiples of sampling rate rather than in band. From your original post:
Quote:
Originally Posted by
arnyk 
For example, check out Figure 3 on page 3 of
http://www.ti.com/lit/an/slea048/slea048.pdf which shows the output of a DAC chip running at a 48 KHz sample rate. If there were steps present in its output, we might expect to see spikes at 48 KHz, 96 KHz, etc. Instead we see no deviations from a normal random noise floor.
Yet simulation and measurements posted in this thread including that of Ethan's show that amplitude steps create distortions in the audible band, well below the sampling rate which is 2X higher than our highest frequency. Here they are again:

And

Clearly we have distortion in the audible range below half the sampling rate. And we see visible distortion created due to fixed amplitude steps below the resolution of our original signal. Since the first chart is generated using analog measurements post DAC, then we know that noting in our digital system removed them.
The "audiophile myth" as I stated in whatsbestforum is about fixed samples in time being problematic. That myth we can bust using sampling theorem. And the solution is the band limiting of our system.
There is NO myth related to fixed steps causing distortion. Mathematics this time *guarantee* that it will be there rather than the other way around. There is an entire science around quantifying it, and how to deal with it using dither.
Bottom line, you are dabbling in audio alchemy, imagining solutions to problems that mathematically can be shown to be false. If you still think this is a myth and that you can recover our signal using "reconstruction filter," you may want to note this line from the Wiki:
http://en.wikipedia.org/wiki/Quantiz...nal_processing)
"Because quantization is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible in general to recover the exact input value when given only the output value)."
Saying otherwise amounts to believing in unicorns and such.

Who said only one camp is guilty of that?
As I said earlier, your arguments in this area is the best reason to deliver 24 bits to the consumer. If you can't figure out the science behind this, what hope there is for some creative type trying to produce music?