It's easy to see that sigma delta systems and/or DSD lose information. Consider "canonical DSD" as a purely 1-bit system (which is not actually how the encoders and decoders work, but still describes the datastream well).
At Fs, the standard sampling rate frequency (44.1kHz I believe, or perhaps it's 48kHz), a 16 bit system has 65536 "states." A 1 bit system operating at 64Fs has 2 states per bit times 64 or 128 states--thus it has 65536 / 128 or 1/512 as many possible states. Now that is huge information loss! (Quad DSD has 1/128 as many states as 16 bit digital. The new PS Audio DAC has 10x the DSD rate or 1/51 as many states as 16 bit digital.)
But what information is lost? DSD with noise shifting has standard specifications superior to 16 bit digital in almost every way. It has higher frequency response, lower midband noise, etc. So how can information be lost? And given this huge information loss, how come so few audiophiles notice it and so many audiophiles strongly believe, nevertheless, that DSD is a superior system to 16 bit PCM--and even high resolution PCM (which has far more states than 16 bit digital)? Surely DSD is not a "lossy compression" system like MP3, which has issues which are far clearer on a technical or listening basis. Strangely, DSD is a "lossy expansion" system which uses more bits to encode less information about amplitude, and it's very hard to see what is actually being lost.
The reason the limitations of DSD systems go unnoticed is that human hearing and most technical measurements don't actually deal with small changes in amplitude that do not cause detectable differences in continuous waveforms. At best, humans can only reliably hear differences in overall amplitude down to 0.1dB in the midband, and they are far less sensitive to differences in overall amplitude very high frequencies close to the bandwidth limit of digital systems.
The 128 states that canonical DSD has at Fs represent a dynamic range of about 44dB. 16 bit digital systems have the same dynamic range across the audible spectrum--98dB.
Clearly what is lost with sigma delta systems is dynamic range at the higher frequencies down to about the middle of the frequency spectrum. This is not easy to hear, but many things audiophiles obsess about are not actually that easy to hear either. In a complex recording, high frequency dynamic range is what makes it easier to separate different sounds.
In a photograph, the smallest details represent something called "resolution." That is analogous to what is lost with sigma delta systems, which should also be called resolution.
June 14 further thoughts:
One of the problems with observing this difference in information is that it may not be audible over one listening. There is only so much information a human listener gathers in each listening. Subsequent listenings may gather a slightly disjoint set of information. Possibly never is the sum of all information completed, except for standard recordings.
But clearly the larger the initial amount of information, the more likely variance between the information gathered in the first listening and each subsequent one. This difference makes a recording sound "real" as opposed to "canned." A canned sound may be fine the first time, but then it gets boring, precisely because there is no more information to be gathered, it was all apparent the first time.
So we definitely want a recording to have as much information as possible, particularly in audible ranges, and extending to lesser degrees beyond.
By stepping back from the information available even with far earlier PCM systems, DSD deprives us of information, as of course to lesser degrees generally all sigma delta devices (I' do calculations in a later essay).
At Fs, the standard sampling rate frequency (44.1kHz I believe, or perhaps it's 48kHz), a 16 bit system has 65536 "states." A 1 bit system operating at 64Fs has 2 states per bit times 64 or 128 states--thus it has 65536 / 128 or 1/512 as many possible states. Now that is huge information loss! (Quad DSD has 1/128 as many states as 16 bit digital. The new PS Audio DAC has 10x the DSD rate or 1/51 as many states as 16 bit digital.)
But what information is lost? DSD with noise shifting has standard specifications superior to 16 bit digital in almost every way. It has higher frequency response, lower midband noise, etc. So how can information be lost? And given this huge information loss, how come so few audiophiles notice it and so many audiophiles strongly believe, nevertheless, that DSD is a superior system to 16 bit PCM--and even high resolution PCM (which has far more states than 16 bit digital)? Surely DSD is not a "lossy compression" system like MP3, which has issues which are far clearer on a technical or listening basis. Strangely, DSD is a "lossy expansion" system which uses more bits to encode less information about amplitude, and it's very hard to see what is actually being lost.
The reason the limitations of DSD systems go unnoticed is that human hearing and most technical measurements don't actually deal with small changes in amplitude that do not cause detectable differences in continuous waveforms. At best, humans can only reliably hear differences in overall amplitude down to 0.1dB in the midband, and they are far less sensitive to differences in overall amplitude very high frequencies close to the bandwidth limit of digital systems.
The 128 states that canonical DSD has at Fs represent a dynamic range of about 44dB. 16 bit digital systems have the same dynamic range across the audible spectrum--98dB.
Clearly what is lost with sigma delta systems is dynamic range at the higher frequencies down to about the middle of the frequency spectrum. This is not easy to hear, but many things audiophiles obsess about are not actually that easy to hear either. In a complex recording, high frequency dynamic range is what makes it easier to separate different sounds.
In a photograph, the smallest details represent something called "resolution." That is analogous to what is lost with sigma delta systems, which should also be called resolution.
June 14 further thoughts:
One of the problems with observing this difference in information is that it may not be audible over one listening. There is only so much information a human listener gathers in each listening. Subsequent listenings may gather a slightly disjoint set of information. Possibly never is the sum of all information completed, except for standard recordings.
But clearly the larger the initial amount of information, the more likely variance between the information gathered in the first listening and each subsequent one. This difference makes a recording sound "real" as opposed to "canned." A canned sound may be fine the first time, but then it gets boring, precisely because there is no more information to be gathered, it was all apparent the first time.
So we definitely want a recording to have as much information as possible, particularly in audible ranges, and extending to lesser degrees beyond.
By stepping back from the information available even with far earlier PCM systems, DSD deprives us of information, as of course to lesser degrees generally all sigma delta devices (I' do calculations in a later essay).
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