Schiit Yggdrasil -- 21 bit?

Rounding and truncation are similar, but with rounding being a broader function over truncation in this use. The idea behind rounding in the case of the Yiggy was that either method would increase quant noise, rounding would result a potentially less quant error and they decided it was low enough in level not to address it in by using a dithering filter. Adding dither would have added cost and complexity to the design and did so knowingly it would not measure in an ideal manner. In the test, it had shown that the rounded method used produced the exact result as truncating. No surprise in that part as rounding can produce the exact same figure. Rounding will in some cases, produce a slightly different result over truncation and have an very minor difference in quant error in comparison to truncation.

In large, this won't present much of an issue to most of recorded music. To the ones that it may have, will be quite low in level.

Mike Moffat knows a thing or two about DACs  since his theta digital dac in 1988  and MoFi Gain system. Introducing dither to Yggdrasil is a software change. He chose not to do so because with the 20 bit chips there is no significant difference between rounding and dither. Last but not least  let's not forget that there are hundreds of milions of digital tracks in 16 bit in distribution and only thousands in higher resolution. 

Shadorne’s technical points and the statements in the video he linked to all make sense to me, at least theoretically, as does the response by Mmeysarosh.

FWIW, though, I took a close look at Figures 6 and 7 in JA’s measurements of the Yggdrasil, which show the responses to undithered 16 bit and 24 bit signals at very low levels of 90.31 db below full scale. The bottom line is that the response to 24 bits looks vastly better than the response to 16 bits, and looks quite good aside from glitches occurring at the zero-crossings. And for that matter a comparison of the 24 bit response shown in Figure 7 with the corresponding Figure 12 for the comparably priced Mytek Brooklyn DAC (and its 32 bit converter!) shows the Yggy looking at least as good and probably better, aside from the zero-crossing glitches. Even though JA described that output of the Mytek as being "a well-formed sinewave," and its overall measured performance as being "superb."

And regarding the zero-crossing glitches, those likely reflect what we’ve previously presumed to be the switchover between the two DAC chips that are used on each channel, that would occur at the zero-crossing, and they would therefore be unrelated to truncation error or rounding error. And given that the glitches are more than 100 db below full scale and are very short in duration they would seem likely to be audibly insignificant.

FWIW. Regards,
-- Al

The video from Nigel Redmon is all clear and right on truncating /rounding, especially with the examples of going from 24 bits to 16. To get his whole message it’s worth going to his site and read about dithering. When and where to use it to make recordings sound better. Surprisingly he advises against dithering at many stages of production.

@almarg



As always I agree with pretty much all your comments.

I would add that the 24 bit will always look much better because at the same -90dbfs you have more bits to characterize the signal. The 16 bit looks square because there are only 2 bits to describe the signal. Even with a 20 bit DAC there are 6 bits available to characterize the sinewave at 24bit (so it looks smooth).

The zero crossing errors are the most alarming in those particular measurements.

"Audibly insignificant" depends so much on the frequencies. Low level noise distributed evenly and randomly across the spectrum is harmless. Rounding or Truncation can lead to high frequency noise of distinct tones which is harmful even at low levels which is why studios go to lengths to dither digital when reducing bit depth.

JA notes the jitter performance is less than desirable also. There has been much importance given to jitter even though it is very very low level noise - and this is because non-random jitter creates distinct tones that are not harmonically related to the music. 

What is actually audible as distortion is very much related to tone and frequency rather than purely a signal level.