@Thad
The red wave is not the output but the input and the pic only shows how the digitization traces it.
The measured output wave when zoomed into could show aberrations like this.
This is the measurement of TEAC's "reference" series DAC doing its duty at its best, but without any digital filtering.
Even with
digital filtering, you could see it is still not smooth but jaggered to a fine degree.
@Joshua
Yes they are quantization errors. But what do errors mean?
When I see this pic, it makes me believe that errors are nothing but "deviations" from the original signal.
Now how well it is taken care by the DAC is beyond the scope of the discussion but errors do exist and have to be dealt with meticulously to achieve best possible output. I also think not all DACs deal with errors with same efficiency.
By loss of music, I do not mean loss of frequency. It is loss of detail. When we say DAC 'A' has more detail than DAC 'B', what do we actually mean here. It likely means that DAC 'A' is able to perform better in reconstruction of the original wave and thereby retaining the finer details of music.
The theories are guiding principles to program the semiconductors but the output as you have mentioned in your own post, depends on how well we are able to implement it. It guarantees the process not necessarily the output. If merely applying the theorem is all it takes for recovering the original waveform 'perfectly', then all DAC's would sound the same isn't it? The theorem is in the DAC chip while the quality of output depends on various other components apart from the chip itself. They do help to a great extent in overcoming the limitations of reconstructing the original signal through technologies like oversampling, noise cancellations, jitter management, over clocking, digital filtering etc.
Not sure if I got it clear but if errors are minimized how that will not result in improvement in sound?
Ofcourse I will be the last man on earth to conclude that digital is inferior to analog because it has to deal with the "approximations" but I am merely reiterating that analog does not face this challenge.