DSD Has Better Dynamic Rage = Misleading

[mansr]

What he fails to realise is that to calculate the dynamic range of a DSD recording, it must first be converted to PCM. That alone invalidates any conclusions of his.

[mansr]

2 minutes ago, elcorso said:

That means there isn't any tools to measure DR from DSD directly?

It is mathematically meaningless to do so. With 1-bit resolution, you have by definition maximum loudness all the time. Only by filtering out the ultrasonic noise can you get a meaningful signal to analyse, and that necessarily means going to a multi-bit PCM format (although the sample rate can remain high if you wish).

[mansr]

46 minutes ago, crenca said:

No possible way to get a meaningful range in the analogue domain (that is, of the signal after the filter/conversion)? I realize this would not be quite apples to apples, but could (is?) this done in a way that is meaningful for listeners/consumers?

How do you propose to measure the analogue signal?

[mansr]

8 hours ago, tailspn said:

As formats, DSD has +6dB greater dynamic range than PCM.

 

DSD and PCM are digitally storable formats to record and transmit analog signals, mostly audio for our interest. 0dB is a definition in recording to signify a maximum level not to be exceeded. Below 0dB, both PCM and DSD are capable of the same signal level range, better known as dynamic range. Both can express an infinitely small signal, far below the practical minimal signal transferable by practical analog electronic circuits.

 

In the case of PCM, 0dB represents the maximum binary range that the the format can represent; there's no bits left. It's a 2's compliment binary word for each sample that's either all 1's, or all 0's at 0dB (full scale). It's 2's compliment to support both positive and negative values.

 

In DSD, there are no values represented. It's the density modulation of a bit clock, who's percent of modulation is proportional to the signal level, not a numerical value of a signal level (at an instant in time). 

 

All of that is background to the fact that from the lowest signal level deliverable to a  A/D converter to the maximum that produces 0dB, the same dynamic range is expressible in both a PCM or DSD format up to 0dB. The DSD format however has an additional +6dB of headroom above 0dB that is not achievable with PCM. That's because DSD 0dB is specified as 50% modulation, allowing an additional 6dB of signal level to be represented. 

DSD requires the extra headroom to prevent the sigma-delta modulators destabilising, so it's not actually available to encode the signal. Moreover, to compare dynamic range of formats, you need to look at both the high and low end. With PCM, the range between the highest and lowest level representable is trivial to calculate, and it increases with 6 dB for every added bit. Since the quantization noise in PCM is evenly distributed over all frequencies, doubling the sample rate also lowers the noise floor by 6 dB. With DSD it's not so simple. The noise level in the audio band depends primarily not on the digital format but on the quality of the noise shaping filter, and no matter how good it is, there will always be some residual noise as no filter has infinite stop band rejection.

 

In practice, both PCM and DSD are capable of representing the full signal range between the analogue noise floor and the maximum analogue level. The 6 dB headroom of DSD is an implementation detail and should be ignored for the purposes of this discussion.