# Is PCM to DSD conversion a lossless process

On another forum I’m told it’s lossy and am surprised at this.

Specifically…,.

_The problem is the way in which data are contained by DSD and LPCM. The differences are in the way that information is mathematically distributed between the amplitude domain and the time domain. The effect is that there is no direct correspondence of one information pattern and the other. Whenever analogue data are subjected to the entropic process of digitising the data some data are inherently lost as a function of the entropy (e.g. the data in the ‘gaps’ between samples are not encoded in the digital signal for LPCM). This digitisation loss is different from the lossless storage of the data: As both formats are lossless, there’s no subsequent mathematical loss of data by compression (or other processing) of the data. However the data that are lost by the entropic process of digitising the data are different for LPCM and DSD. Since the lost data are different, then when convertin from one to the other the information lost in one format cannot be recreated in the new format, but the data that cannot be stored in the new format are also lost - hence the final result is less than the original before the conversion.

Each may be lossless in their own right, but as they can hold slightly different interpretations of the analogue data, the conversion can still be lossy…

Is this correct?

.sjb

From a 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."

It’s all way over my head but let’s tag the Guru for his thoughts @brian

There is a certain encoding format that specifically tries to address this issue of lossless digital that does not preserve the analogue at the encode or decode stage.
As stated above neither PCM or DSD can win both arguments. Another approach is needed.

I think the bit rates also plays a part here. For example a DSD64 has a bit rate of 2.82Mbps while PCM 16/44.1k has only 1.41Mbps. Obviously, DSD64 carries 2x more information compared to PCM 16/44.1k. Now if one use Roon to upsample PCM 16/44.1k to DSD64, no information is lost, thus the process is lossless. To put in the other way around, DSD64 convert back PCM 16/44.1 will lose information thus the process is lossy.

A PCM 24/88.2k still fall short of a DSD64’s bit rate and PCM 24/176.4k is over killed. The exact match will be PCM 16/176.4k but this is unorthodox. Another problem is ultrasonic noise when DSD64 is converted to Hi-Res PCM, the PCM must applied a very steep filter around 30kHz to cut off ultrasonic noise from DSD.

As long the bit rate of the format you want to convert must be less or equal to the final format of conversion, then no information is lost, thus the process is lossless.

Lossless/lossy is a concept from information theory. The important test for whether a process is lossless is: is it reversible? I.e. for a given PCM → DSD conversion scheme, can I construct a DSD → PCM scheme that reverses it and recovers the original bits?

I’m not aware of any DSD → PCM or PCM → DSD conversion that meets the criteria for lossless–they all lose information.

Not all information loss is harmful to audio quality–most DSP and all analog domain audio processing is lossy. Speaker wire is lossy. Lossy isn’t always bad–have to take the effect level into account.

The more important question is: is the conversion transparent–in other words–does the conversion produce audible differences when tested to a scientific standard? This is a much more useful word than lossy when talking about processes like this.

DSD is not PCM–it is a fundamentally different encoding scheme that requires noise shaping. A 1-bit high-rate PCM signal with no noise shaping is not DSD.

And that’s the problem with these two paragraphs–they seem to be talking about DSD as if it were just 1-bit, high-sample-rate PCM.

DSD cannot in fact represent a step transition 8x faster than DXD. It is only slightly faster. Nor does it have 24x less dynamic range. That implies a huge degree of information loss/“throwing away”, not the relatively minor information loss that happens in these conversions in reality. Again, really important to consider effect size here.

Disagree. The important criteria is not bitrate, it’s reversibility of the processes involved.

Upsampling 2x using zero-order-hold is lossless/reversible. Upsampling using a high quality 2x FIR filter is lossy. The second one sounds a lot better . This is why it’s important to think about transparency with audio, not just information-preservation.

MP3 is bad as an archival format because it’s information-lossy, but it’s bad for sound quality because it is not transparent.

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The reversibility process of PCM to DSD and DSD to PCM can never be bit perfect but it can be lossless(No loss of information) as long when a ‘small is converted to big’ or simply a lower bit rate is converted to higher bit rate on a lossless format. Take for instance, a PCM 24/176.4k can carried all the information of DSD64 plus more in DoP without any loss of information. Yeah, I may missing the point here, but I’m comparing the bandwidth of 24/176.4k capability. As long a format has enough bandwidth(bit rate) to accommodate the conversion process, no information is lost.

Re-sampling either in PCM and DSD can be lossless(No loss of information) but not bit perfect. As long the re-sampling is equally or higher than the original sampling rate.

The problem with this is that “information” has a precise definition, and a whole domain of study attached to it.

Non-reversible processes can’t be information-preserving. It’s not about bit rate or resolution or quality or audio. It’s just math…

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Thanks @brian

It is interesting to see the matching bitrate(bandwidth) for DSD to PCM and vice-versa are mathematically as followed…

DSD64 to PCM 16/176.4k exact match at 2.822Mbps
DSD128 to PCM 16/352.8k exact match to 5.644Mbps
DSD256 to PCM 16/705.6k exact match to 11.289Mbps
DSD512 to PCM 16/1411.2k exact match to 22.579Mbps

Bitrate is not a sufficient metric to measure information content.

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Well, what other factors contribute other than bitrate(Bandwidth)? Take for instance, if you have a 100Mbps vs 1Gbps internet speed, which one can carry more information?

I can send a flat signal down a 1Gbps connection and a movie down a 100 Mbps. Which stream has more information in this example?

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That is because you are sending a signal that does not exceed the 100Mbps transmission bandwidth thus sending over a 1Gbps doesn’t make the difference. However if the signal bitrate exceeded the 100Mbps transmission bandwidth, you going to have dropouts. So having a higher bandwidth, your signal bitrate can stretch further thus able to carry more information. Here is a good reading…

The point is you’re stuck in the digital domain and thinking only about the maximum bit rate instead of thinking of the actual information content of the signal that is getting encoded in the bitstream. Of course a higher bitrate has the potential for more information but the bitrate by itself won’t guarantee information content…that depends on the original signal and the encoding scheme.

The point the OP and @brian were making is even if PCM and DSD bit rates are the same the encoding scheme for each is different and that impacts the actual information captured in the signal.

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I agreed bitrate is just one of factor, assuming encoding and decoding scheme are lossless, such as PCM and DSD, one can still achieve virtually lossless (no information is lost) when converting them in pure digital domains(PCM<->DSD). The only place one will lose minimal information are at A/D and D/A converters; once analog get digitilized and digital get converted to analog.

I believe PCM to DSD conversion is virtually lossless while DSD to PCM may not perfectly lossless because of the ‘ultrasonic noise’ get into PCM domain.

None of this means anything. It’s one of those arguments/discussions audiophiles like to have that doesn’t have much to do with reality.

All that matters is how do conversions from hi res PCM to DSD or DSD to hi res PCM sound?

The simple truth is they can each sound excellent if done well.

Does the conversion sound slightly different from the original? Yes.

Is there any actual audible loss of resolution, etc? No.

It’s just a slightly different presentation with each format. Each has a bit of a characteristic “sound”. Which you prefer is due to personal taste, the system you are listening to, and the characteristics of the music/recording itself.

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Any geeks in the crowd may want to take a look at Wikipedia.

DSD is to PCM like FM is to AM in terms of what is happening. The DSD converter compares the signal to be encoded with a repeating ramp wave form. Each time the signal crosses the sawtooth, the converter emits a narrow pulse. The encoded signal varies in pulse density proportional to the signal amplitude. This is the analogy.

The article describes both the encoding and decoding mathematics and gives block diagrams for realizations of each. Please read the editor’s description of the article’s limitations. It needs work but it does give some useful insight into how these puppies work. There is also an extensive list of references, many device maker application notes but some diving deeper into the theory. Most of the theoretical articles are senior year EE stuff.

I did not wade through the entire discussion to write this article but would like to offer this caution about any conversion process. The mathematics describe an ideal theoretical process that we have to approximate with real world parts. Some aspects of the mathematics, for instance an ideal lowpass filter, can’t be built. This is where the engineering art comes in, knowing how to make realizable approximations of the math and understanding how good they must be for acceptable reproduction and an engaging listening experience. Some engineers will do this well and others not so well. Real world DACS succeed or fail based on the quality of the reconstruction filters and output line stages. These have the biggest effect on what you hear during playback.

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Please excuse my amateur question, but, if we are concerned about transparency, can a human with ordinary hearing and a decent sound system tell the difference between a 16/44 FLAC file and a DSD file converted by Roon to the highest sample/bit rate? If, for example, one has a hybrid SACD ripped in 16/44 (Redbook layer) and DSD, will it sound different when played over Roon to a Bluesound Node 2 (with Roon’s conversion of the DSD to PCM), assuming the same mastering?

If it is an amateur question, imo it’s a very appropriate one.

I haven’t got files that I would be confident were the same mastering or the exact hardware in order to definitively check this, but given my own track record I doubt very much that I could distinguish between those cases in a blind test.

It may be that there are audio engineers or others with trained ears who can hear a difference. I would expect that difference to be associated with a reduced “attack” on transients.

A couple of times I’ve left my favourites playlist on shuffle while doing other things, listening in a rather relaxed and stress free state (compared with A/B blind testing which I’ve always found a bit stressful).

And every now and then a great recording would come up in this shuffle mode and I don’t have any idea what version it is (Roon or other software player is minimised on the Mac) but I think ‘this has GOT to be the Qobuz/HDTracks purchased version’… only to bring up Roon (or other software player) and find it’s ‘just’ the CD quality version… this has happened with what I thought was my Acoustic Sounds purchased DSD version of ‘Thriller’ too, only to find it was RBCD playing.

That’s always a humbling experience

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Since the Bluesounds can handle 24/192, any DSD rip will downsample to 24/176.4 when destined for a Bluesound unit.
If that’s what you are comparing to a rip of the CD layer, playing back at 16/44.1, then i’d wager you will hear the difference. I know i do!
Is it significant? No, even minute, but it’s still obvious.
But it’s not possible to claim the masters for the different layers are identical. Besides, on the Bluesounds, letting Roon upsample Red Book material to 24/176.4 creates a very similar experience as when listening to DSD adapted to PCM!
All in my personal opinion, of course.