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# Converting PCM to single bit DSD rates

I read this old Q&A with Thorsten Loesch about PCM vs DSD

"If we convert from 24-Bit at 352.8KHz (DXD-PCM) to 1-Bit at 2.822MHz (DSD) – we need to throw away around 99.96% of the amplitude information the PCM format is capable off, while we are only having 12.5% of the time domain information that the DSD system is capable of. If we convert to DSD to DXD, that is 1-Bit at 2.822MHz to 24-Bit at 352.8kHz – we need to throw away 87.5% of the time domain information of DSD, though we can theoretically remap all of this into the amplitude domain. So in effect we get the worst of both formats, rather than the best of one."

Q1a) Regarding the bold above (PCM353kHz to DSD64 conversion ), how significant are these points about throwing away amplitude information and having only 12.5% time domain info capacity? Is it correct?

Q1b) Is this improved or worsened when up-sampling to 20 x DSD rates (like the DS does), rather than the DSD64 mentioned above?

PS: I’m just ‘playing the ball, not the man’ here. So it’s not so much asking about Thorsten, more just about the technical theory/figures he’s mentioning

There are “lies, damned lies and statistics.” The numbers he gives aren’t correct for DSD as a process. Noise shaping allows trading higher resolution in one range of frequencies for lower resolution in other ranges: PCM is stuck using the same resolution for all frequencies, even those not picked up by mics, those that are masked by ambient noise, etc. When he talks about throwing away amplitude information he’s basically comparing 1 bit PCM against 24 bit PCM, not DSD against 24 bit PCM.

Noise shaping means that over the audio band DSD64 can have at least 120dB S/N, tho 24 bit PCM theoretically has 24 bits/144dB across the audio band, 20 bits is near the limit of what’s practical for a whole system (how accurate are typical speakers?) Also, for example: Using any significant amount of the S/N in 24 bit PCM at say, 50k will likely destroy your speakers and possibly harm your amp or (probably less likely) your preamp. (And certainly your ears if your system survives.)

In the real world the amount of power for sounds in nature, recording… goes down as the frequency goes up, otherwise each new octave would double the power that the ears (and your system) need to be able to handle.

Double rate DSD can easily have more than 24 bits or accuracy across the audio band and significant S/N (> 100dB) to above roughly 100k.

The DS ends up with DSD256 which has much more resolution than 24 bit PCM significantly higher than the audio band.

Thorsten is a good guy, but I have no desire to debate people about DSD vs PCM - we might as well discuss current politics.

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Thanks Ted. I don’t think that article is talking about DSD versus PCM, but more-so converting from one to the other. Don’t think he has anything against DSD (he has products with DSD in the product name).

What about " while we are only having 12.5% of the time domain information that the DSD system is capable of" (converting from DXD to DSD64)

Is that related to the amplitude information you talk about or is amplitude information something different to time domain information?

Cheers!

He’s just saying that 352.8k is 1/8 of 2.8224M and that 1 is less than 24 But that’s like saying a 2L water bag is only 1/4 thick so it can’t hold more an cup. Noise shaping allows trading frequency range for amplitude range, just like a water bag can get fuller but as it does so it gets shorter - it’s the total volume that matters in both cases.

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If he’s really saying that DXD is a weird compromise, I agree. But thank goodness it’s old news.

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Hi Ted, regarding the quoted:

This is mostly relevant to recording right?

You can’t get higher SNR by converting PCM to single bit DSD rates? I ask because the original quote I posted, is mostly talking about converting between PCM/DSD, not the recording formats. Although I guess some (not all) DSD can go through a PCM stage for editing, so I guess conversion can apply to the recording process too.

Yes, when converting you never gain S/N but when editing it’s often useful to keep extra dynamic range. DSD64 has the rising noise floor close enough to the audio band that doing a lot of editing (either with an analog console or by converting to PCM and back) will slowly pollute the audio. But DSD128 allows a lot of editing passes without affecting the audio band and with DSD256 there no practical limit.

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