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John Siau

Losses in 1-bit DSD vs multi-bit PCM

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Modern PCM sigma-delta converters produce much lower error signals than1-bit sigma-delta DSD converters. The errors in the DSD system are due to the1-bit quantization that occurs in 1-bit sigma-delta DSD converters. Multi-bit PCMsigma-delta converters can be fully dithered and do not suffer from this un-dithered truncation. Plus, every added bit reduces the noise signal by 6 dB. A 4-bit sigma-delta converter is 24 dB quieter than a 1-bit sigma-delta DSD converter. Right from the start, 1-bit DSD signals have much higher losses than multi-bit PCM signals.

Conversion from 1-bit DSD to multi-bit PCM is a lossless process inside the audio band. The only thing that is removed is the out-of-band noise above the Nyquist limit of the PCM system. Nothing else is lost. Don't believe the DSD marketing hype.

In contrast, conversion from multi-bit PCM to 1-bit DSD is always a lossy process.The loss is due to the 1-bit truncation. This truncation introduces a very large ultrasonic error signal that makes the ultrasonic region unusable for audio. But remember the ultrasonic region of DSD is always unusable for audio because of the high noise levels. This ultrasonic noise produced by 1-bit DSD systems must always be removed before reaching power amplifiers and tweeters. When the noise is removed, the ultrasonic audio content is also removed.

Processing a 1-bit signal to create a 1-bit signal is also always alossy process. A volume control is one of the simplest processes in a multi-bit PCM system, but it creates a large error signal when applied in a 1-bit DSD system.The same is true for any other 1-bit to 1-bit DSP process. The lossy part of these DSP processes is the quantization back to 1-bit. Cascaded 1-bit truncation processes can rapidly degrade the audio quality. For this reason, DSD is almost always processed as multi-bit PCM.

Any DSP process applied to a 1-bit DSD signal produces a multi-bit PCM signal. No loss of information occurs until this multi-bit signal is quantized back to a 1-bit signal. Why incur the loss by going back to a 1-bit signal after the processing inherently produces a multi-bit PCM signal?

All practical DSD systems require some sort of DSP processing (gain control, mixing, filtering, etc.) and all of these processes produce multi-bit PCM results. Taking these lossless multi-bit results and adding loss by truncating them back to a 1-bit DSD signal makes absolutely no sense. DSD complicates the signal processing and adds unnecessary losses in several places along the signal path. DSD does not simplify the signal path.

There is absolutely no truth to the marketing hype that claims that 1-bit DSD is a simpler system than multi-bit PCM. The exact opposite is true. 1-bit DSD is a lossy system.

John Siau, VP Benchmark Media Systems, Inc.
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Updated 05-22-2015 at 06:08 PM by John Siau (typo)

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  1. Miska's Avatar
    Most of the losses happen in on-chip conversion from ADC's SDM format to PCM and then on-chip conversion from PCM back to DAC's SDM format. Why not stick to the SDM format and skip the intermediate PCM format with back-and-forth conversions altogether? So use whatever is the native format of the actual conversion section at native sampling rate.

    The conversions built into ADC and DAC chips are systematically resource constrained and not as good as technically possible.

    When you add two 24-bit sample values, result is 25-bit. If you multiply two 24-bit values, result is 48-bit. Following your logic, why not produce arbitrarily long PCM. With a bit of processing you would easily end up with 512-bit samples. When you go back to 24-bit for output, the PCM process also becomes lossy. Processing PCM and SDM is equally lossy or non-lossy. Number of bits is just an arbitrary number without meaning in itself when not connected to a correct context.

    Functionality inside ESS Sabre you use is closer to DSD than you seem to realize...

    What matters in the end is what you get out of the converter in analog domain. If you want to be in control of your converters, you need to build the converter sections, digital filters and modulators yourself. I prefer not to use resource constrained DSP stuff implemented on COTS chips.
  2. mkrzych's Avatar
    Interesting stuff, especially, that DSD is the hottest topic now and many recording labels go for it. My personal feeling is the technology is there for sure and doesn't matter if it's PCM or DSD, but what is more important is how the final product was done - recorded, mixed and mastered finally for the target medium. This chain I believe is the most important thing. How good are the recordings from the analogue era (Living Stereo), where nobody was even dreamt of DSD?
  3. Jud's Avatar
    I like precision in explanations, because they promote clear thinking and easier learning, and that is the primary thing I'm here for - to learn. Conversely, when explanations confuse/conflate two separate ideas, this inhibits learning, which bothers me greatly. I think there is at least one instance of such confusion/conflation here, possibly two. (If I'm wrong about this, I would as always appreciate corrections.)

    "Lossless" - The precise meaning I've seen is that the conversion is entirely reversible by algorithmic operations. Thus "lossless" compression (e.g., WAV to FLAC) or format conversion (e.g., WAV to AIFF). The blog post tries to elide this with the idea of "lossless" as "any information lost is not audible." Even those who claim that mp3 of some quality is audibly indistinguishable from WAV, AIFF, FLAC, ALAC, etc., do not then go so far as to call mp3 "lossless." Or to put it very simply: Once you see that information is lost, by definition the conversion is not lossless.

    "PCM sigma-delta converters" - The precise name for the output of a sigma-delta converter that I'm aware of is "PDM," pulse density modulation. PCM is pulse code modulation. These are two different forms of modulation. The former represents amplitude (loudness) of a wave by the density of 1s versus 0s in the bitstream. More 1s in a given bitstream, greater amplitude. In the latter, the position of the 1s and 0s matters. Thus in a PCM bitstream "100" would equal 4 in binary, while "011" would equal 3. If those examples were PDM rather than PCM bitstreams, the fact that the second bitstream had two 1s while the first had only a single 1 would mean the amplitude of the second bitstream was greater, the opposite of the result with PCM. (This is a little oversimplified - in PDM the greater number of 1s would mean the direction of the amplitude was headed up. You could think of it as 1s "steering" the signal in the direction of greater amplitude, 0s steering it lower.) Thus "PCM sigma-delta" is contradictory nonsense, since mathematically the two types of modulation give entirely different results.

    DSD is a type of PDM bitstream. The post appears to be claiming any operation that requires multiple element processing is by definition PCM. For reference to a physical proof that this is not the case, see http://www.computeraudiophile.com/f6...tml#post435091.