Lossy, or not lossy, THAT is the question.

Now that I‘ve learned how to extract ISO / DSF from my SACDs thanks to another thread of this forum, I‘m looking for a way to convert the resulting files into a format my Rotel PreAmp can process when that tiny Daphile server sends the data. The Rotel RC-1570 is not capable of processing DSD, only PCM up to 192 kHz / 24 bit.

I‘m still rather new to this topic. When reading articles or posts about it, one claim appears to be popping up frequently: ‚Conversion from DSD to PCM is (always) a lossy process.

But is that really correct? I did a little bit of primary school math:

Sample rates.JPG

At 2822.4 kHz @ 1 bit, an SACD delivers a data stream of 2,822,400 bps. (To the DJs around: this is bits per second, not beats per second 😉 )

Resampled to 88.2 kHz @ 24 bit, which is often suggested for an SACD, our target files should deliver 2,116,800 bps. Well, this is lossy.

Choosing 176.4 kHz @ 16 bit instead would deliver an output stream of 2,822,400 bps, exactly like our SACD source. From a naive point of view, I would not consider this lossy.

If we now encapsulate our PCM file into a FLAC container, compressing it by lossless algorithms, where should losses of the original audio quality appear?

Looking at the topic this way, theoretically a resampling to 88.2 kHz @ 32 bit should also be lossless, only my Rotel cannot process this, and it seems to be rather uncommon. So 176.4 kHz @ 16 bit should be my format of choice, at least until I do not have a DAC that can process DSD directly.

Are these considerations correct or am I missing something?

Some sources suggest to choose always the highest quality the DAC in use can handle if converting from DSD to PCM. In my case, choosing 192 kHz @ 24 bit would increase the resulting file sizes by 63 %. Do I get some audio quality in return?
 
The reasoning for 88.2/24 is explained very well in this article.
You're absolutely right - that article is really excellent. Thanks a lot for the link! Already made a mental note to look for more articles of this particular author.

Some quotes from this article discussed in short:

DSD, typically has a small role to play in that because each conversion of another Digital Audio format INTO DSD is a source of potential quality loss.
Well, that really hit me by surprise - quite the contrary that is stated so often in the (eternal?) DSD vs PCM discussion.

Again I refer you back to the historical discussion above: DSD was DESIGNED to be converted to other Digital Audio formats -- particularly LPCM!
Looking at the original purpose of DSD as a digital archiving format for historical analog tapes and taking in account that DSD cannot be processed digitally by design, this statement is absolutely comprehensible.

DSD64, the original DSD format and the only one found on SACD discs, has an effective dynamic range of 20-bits of LPCM. So as long as you are converting to LPCM of 24-bits per sample or higher, you are fine.
...
The commonly accepted limit for perceivable dynamic range -- i.e., the limits of human hearing when trying to distinguish between the softest and loudest sounds -- is also around 20-bits.
Check! 24 bits make sense for my purpose!

So, the PRACTICAL limit of frequency for DSD64 is something below 50kHz. You don't WANT DSD64 to retain frequencies above that because, "Here There be Exaggerated Noise!"
...
And the most convenient way to do this is to take advantage of the Nyquist Limit mentioned above! So for example, if you convert DSD64 to LPCM at an 88.2 kHz sample rate, the frequencies captured in that LPCM stream will be limited, automatically to no higher than 44.1 kHz -- 1/2 the sample rate.
Quantization noise - didn't really think of that! Will have to do some more research in relevant literature to really understand the topic, though!

So the sweet spot for conversion of DSD64 to LPCM is to use LPCM 88.2 kHz 24-bit.
The necessity to avoid resampling that leads to rational numbers as frequency factors to be on safe ground when it comes to potential rounding errors was clear to me from the beginning. So 96 kHz was never really part of my practical considerations.

So: my DSD64 material will be converted to 88.2 kHz / 24 bit PCM format in the near future to make it accessible for my PreAmp's DAC.

And the article @NSBulk pointed me to is highly recommended reading for anybody interested in this topic!
 


I think this pic demonstrate the differences between DSD and PCM nicely.
DSD has a higher dynamic range and a higher frequency range
In principle even 24 bit PCM cannot cover the dynamic range of DSD but in practice it is almost impossible to make anything audible below -120 dBFS.
Likewise even recordings made with very low noise gear can’t do better than 20/21 bits.

The frequency range is another story
In case of DSD64 (SACD) you see a strong rise of the quantization noise getting really loud at 22 kHz.
One might wonder if this is beneficial. I do think it likely it exceed the breakup point of the tweeters.
DSD gear does have a filter at 50 kHz
If you convert to 88 kHz PCM, you must filter out anything above 44 kHz.
However you might consider even 44 kHz or use 88 with a stronger lowpass filter as anything above 22 is plain noise.
 
Doesn't the Nyquist-Shannon-Theorem automatically take care of this?
No, Shannon-Nyquist says you can reconstruct the analog signal if there are no frequencies above 1/2 fs.
Means you are the one to see to it that there are no frequencies above 1/2 fs in the signal you feed to the AD converter or the downsampler.
 
Means you are the one to see to it that there are no frequencies above 1/2 fs in the signal you feed to the AD converter or the downsampler.
Allright. So possibly my next step would be to look for an appropriate lowpass filter to process the FLAC files after conversion?
 
No.
If you convert DSD to e.g. 88 kHz PCM any frequency > 1/2 fs hence 44 kHz should be removed before the conversion takes place.
 
If you convert DSD to e.g. 88 kHz PCM any frequency > 1/2 fs hence 44 kHz should be removed before the conversion takes place.
Since DSD (at least as far as I know) cannot be processed, does this mean that I should

1 - convert DSD to PCM at a high sampling rate, e.g. 352.8 kHz
2 - apply a not too steep low pass filter somewhere above 15 kHz
3 - downsample this one to 88.2 kHz

If this is correct, which filter types would be appropriate?
 
Well designed software for converting DSD to PCM allows you to choose a desired sample rate.
The software will do the filtering for you.
Have a look at dBpoweramp, it has a free trial

 
Have a look at dBpoweramp, it has a free trial
Thanks, I will!

I think this pic demonstrate the differences between DSD and PCM nicely.
The graphs are discussed in a little more detail by former Sony engineer Andreas Koch. Maybe he is the original author.

On the other hand, Alexej C. Ogorek claims to have found 7 faults in Koch's paper (this is only in German, though). An English language overview of Ogorek's articles can be found here.

For now I'll leave this as a short note for further studies.
 
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