Is PCM to DSD conversion a lossless process

I think the other question is Why?
If music exists in your Library as PCM then play it as PCM, if it exists as DSD and you have a player that supports native DSD playback then play it as DSD.
Upsampling or native format conversion prior to playback is not going to add any further detail than doesn’t already exist.

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‘Upsampling’ isn’t about ‘adding extra information’. We all know that’s not possible.
Any sonic changes or improvements from upsampling come from shifting audible ‘nasties’ up into higher frequencies, and then using ‘better’ filters to curtail them.
I must admit to not being too technical on this matter myself, but I’m sure that other, more tech-savvy contributors may help me out here.

But at the risk of data loss in the process and then to use filters.

Think the Vinyl approach is appropriate here - find a better pressing/recording.

You have understand modern D/A converters except multi bit ladder D/A, convert PCM to DSD internally using sigma delta modulator with noise shaping. This process happens at very frequency, we are talking at least 256x of 44.1kHz (DSD256 or 11.289Mbps). Some high-end D/A will do higher.
If one argue that PCM to DSD conversion process is lossy, then all modern D/A converters using Sigma Delta architecture is seriously flawed.

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When describing what happens to PCM inside some popular modern DAC chips, you will sometimes find people like @jussi_laako are careful describing it as ‘DSD-like’… because it is not strictly DSD (1-bit SDM) but the data is ‘like’ DSD…

You are right it may be not strictly 1 bit SDM architecture, some uses multi level SDM; i.e, some uses ‘4 to 8 bit’ with up to 64 multi-levels and are summed together to improved SNR when compared a single SDM.
The main function of SDM is to convert PCM to single bit pulse at very high frequency, so it can use a single bit converter to analog signal. That single bit pulse to analog signals can use any form of architecture, such as PDM (Pulse Density Modulation) which used in SACD/DSD, PWM (Pulse Width Modulation) or even PEM (Pulse Edge Modulation). All these required bitstream to work, not multi-bit. Of course all these requires aggressive noise shaping because multi bit is now converted to 1 bit.

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Well maybe Naim have it right with use of the Brown Burr PCM1704U-K

Filters are not a choice. Filters are a necessary part of digital to analog conversion. The choice is about what characteristics or trade offs to make with filters.

This post by Jussi Laako remains the best description I have read of how a typical Delta Sigma chip DAC works. FIR means “Finite Impulse Response” which is a type of digital filter. “Taps” is a way of describing the length of a filter. Longer filters require more computation. The filters Jussi is describing within the typical DAC chip are comparatively very short due to processing constraints, which in turn imposes a constraint on how “sharp” their cutoff can be (bandwidth of the transition zone).

Exactly, multi bit ladder type DAC (PCM1704) is best suite for converting PCM into analog signals. This is because no conversion is required and it doesn’t use noise shaping at all. It always work in ‘native’ mode. For DSD to work at it’s very best, it shouldn’t undergo SDM at all, it should in fact goes directly to bitstream converter; in this case directly to a PDM (Pulse Density Modulator) converter. Some DAC converter like Holo Spring have two different architectures for handing PCM and DSD signals.

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What kind of DAC do you have? In most cases, playing “PCM as PCM” means immediate conversion to something non-PCM at the DAC side. And typically the implementation of this inside DAC chips leave a lot to hope for.

No, but it may help you hear more of that detail, instead of it getting lost in poor DSP algorithm inside a DAC…

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No, this is not the case, because of lot of physical problems and challenges it has. It is actually pretty poor way to do it.

That’s one reason why it performs so badly…

You cannot have DSD data existing in first place at all without SDM…

Yeah, I have both Spring 1 and Spring 2. And always run it in DSD mode. But the PCM side can be helped a lot by choosing correct number of output bits (16 - 20) and using noise shaping.

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One major problem is that due to clocking and other resource limitations, they have limited rate conversion factor. Typically only 8x. They then just copy the same sample 16 or more times to increase rate further (S/H aka ZOH), but doing so produces images at the 8x digital filter output rate which are also apparent in the DAC output, because the analog reconstruction filter is not steep enough.

What I do instead is to run digital filters straight to 256x or 512x rate, so no images left.

This is before going to design of modulators, which have also notable impact on the performance/sonics.

So there are four important stages in design of D/A conversion chain.

  1. Design of oversampling digital filters
  2. Design of modulators
  3. Design of the D/A conversion stage
  4. Design of the analog reconstruction filter

Steps (1) and (2) can be run on a computer, before passing data to the DAC.

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There are many techniques to solve the shortcoming of multi-bit DAC. Zero crossing can be eliminated by using sign magnitude and linearity can be improved by linear compensation (using two sets like in Holo Spring and PCM1704). If I’m not wrong Holo Spring R2R linearity is on par or better than most SDM in the market. Because multi-bit architecture like R2R works on open loop, the slew rates are extremely fast. This means, transients response is greatly improved. On the other hand, SDM required a closed loop in order to work, the feedback which constantly correcting itself from errors, therefore, it is not as fast as multi-bit design. There are many DAC manufacturers like MSB, Schiit and Holo Spring, etc still stick with multi-bit design for PCM and offer a separate 1bit SDM for handling DSD.

Signal to noise ratio for multi-bit converter is extremely low across a wide range of frequencies, not just the audio range. That’s why they don’t need noise shaping like 1bit SDM. They are inherently more ‘quieter’ than SDM converter.

As long the DSD data is in ‘raw’ state; no leveling or filter is applied during DSP process, you can actually route this signal to PDM converter (consist of either resistors or switch caps network) which convert to analog signals. For example CS4398 allows ‘Direct DSD’ which actually bypass the SDM internally.

In most application, under Sony/Philips Scarlet book, SACD player will always operate in ‘Direct DSD’ mode.

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Well, when Roon does any signal rate conversion it processes it through the user chosen filter option. So, the converted DSD playback is getting that filter pass and the other is not. Discernible, maybe.

If you run it at 1.5 MHz and 16~20-bit with noise shaping, then it is not that bad. Noise shaping helps correcting some of the linearity problems. Jitter performance cannot reach that of it’s SDM side though.

Analog output slew rates are limited by sampling rate (because highest frequency you can represent is fs/2), and another problem is that increasing sampling rate increases settling time problems. Because it needs to settle to ½LSB within fraction of the sample period. If you use lower sampling rate, you have increased problem of images because analog reconstruction filter is not able to fully reconstruct the analog waveform when sampling rate is too low. So if you improve one aspect of R2R you worsen another aspect.

No, in fact it is much faster and more accurate, because it runs at very high frequency. For example DSD64 has no problem following anything RedBook CD data can contain, by large margin.

This is why all modern DACs are SDM types, because that is much better way to implement such. Even more so for ADCs. Probably like >90% of all PCM music on the market these days has been recorded using SDM ADC. So no matter how much you play it through R2R DAC, it has gone through SDM step already and converted to low rate PCM (which, IMO, is totally unnecessary step).

Multi-bit converters produce high levels of directly correlated out-of-band distortion products. In addition they suffer from settling time and linearity problems.

How do you think DSD data came to be? It was created by delta-sigma modulator…

DSD is just way to pass SDM through, end-to-end, without resorting to intermediate PCM.

Like the one I designed and published as open hardware project, you don’t need a DAC chip for that:
https://www.signalyst.com/hardware.html

Although there is no “PDM converter”. The converter doesn’t understand anything, it is just a dumb device. But essentially it is an analog FIR filter converting PWM (you can also call it PDM or SDM if you like) to analog.

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I think you miss-understood me… of course DSD need to be created by SDM at the ADC side. My argument is there’s no need to undergo another SDM at the DAC side provided the DSD stream is not modified in anyway; such as doing attenuation or and filtering. In this case, it needs to convert to PCM, as the result you need to undergo another SDM (DAC side or software) before converting to analogue signal. SACD/DSD is created to be simple; all it needs only to have a single SDM at the ADC. The DAC side is essentially behaving like a ‘LPF’.

When I refer ‘PDM converter’ essentially referring DSD converter which in fact the working principle of DSD. DSD is encoded using Pulse Density Modulation not PWM (Pulse Width Modulation)

Converting DSD to analog signals is not as simple as passing through an analog FIR (DSC-1 which is designed by you), it requires multi-level bit switches; some goes as high as 64 levels (6 bit) to produce a clean low noise waveforms. This working mechanism is based on PDM.

http://audiodesignguide.com/DSC1/index.html (4 bit, 32 levels?)

It depends, you can play it as is, but I play it upsampled to DSD512. For that purpose I have two separate DSP engines, one for PCM and one for SDM. So I directly process SDM-to-SDM. It takes quite a bit of processing power, so not commonly done. But one of my motivations was that I wanted all the same DSP algorithms available for DSD content that I had for PCM, such as digital room correction. And I didn’t find any of the existing solutions acceptable.

It is not really “PDM” unless you specifically want to call it that way, I don’t mind. In the article you quoted PWM is mentioned.

Yes, further developed / modified version of my design as stated on the page…

Forget those “bits”… “Bits” are not relevant in this context, for SDM converters, number of levels is the correct term. You have number of elements, like in my case 32 elements which means it has 33 output levels. (with one element you get two output levels, with two you get three output levels, etc)

That DAC is a PWM DAC (or to be exact, SDM DAC), not PDM. Difference is that adjacent same values are joined and don’t cause switching to go up or down. If you have let’s say stream “11100”, in this case output stays “1” for period of three samples and then goes “0” for period of two samples. So number of adjacent same bits define width of the output pulse. You can easily make it operate also with other sample lengths than 1-bit.

Believe me I understand how this works, the reason why I designed that DAC (in 2014) is that there was so much misunderstanding and strange claims about DSD/SDM DACs on forums (such as DSD DAC cannot be multi-level) that I wanted to make an understandable no-black-boxes design. And it certainly helped…

But as I stated on my page, that design doesn’t work correctly with DSD64. It can be made work correctly at DSD64, but it needs some DSP pre-processing if you want to run it at DSD64 rates. Or alternatively you can upsample DSD64 to higher rate for it.

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Thank you so much @jussi_laako in your opinion it is possible to built a PDM DAC? My understanding is PDM will convert more ‘1’ as more positive voltage, ‘1010…’ or ‘0101…’ as zero while more ‘0’ results in negative voltage. Those off shelves DACs in the market actually uses PDM or PWM DAC?

Thank you, both @jussi_laako and @MusicFidelity, this was an interesting Q&A, quite insightful. :slight_smile:

You can of course also build a PDM DAC too, but it is more complex. Both operate on the same data, but in a different way. There is no simple reason to favor one way. There are so many small devils in the detail, that combination of all design choices in the end define behavior and performance. Most probably operate like PWM…

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