A PCM only style of DAC such as a Schiit would be unable to play a DSD file. However, presently, the only way you would encounter a DSD file would be if you purchased DSD downloads or played rips of SACDs.
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Here are Mike Moffat's comments on DSD from a Headfi article. Mike is the cofounder of Schiit and developed the first ever standalone DAC back in the 1980s.
"I have never published my DSD opinions. Here they are. I say opinions because the design of audio gear should adhere to hard science. The user's response however, is totally in that user's psyche. When I worked in Peru, there were tribes in the Amazon region who spoke in vocabularies limited to grunts and delighted in eating insects they found under logs. Then there are people like myself who prefer meat, coffee, dairy, sometimes things green or fruity, starches, and lots of salt.
In the early days of digital audio, multibit reigned. It was suitable, but expensive, derived as it was from weapons guidance and medical science. Note the use of the word science. Analog numbers were converted to digital, and the reverse yielded the same number. Nothing was averaged, no noise was added, no economic engineering geniuses were allowed to make anything cheaper with smoke and mirrors.
The earliest DACs were pretty marginal, but natural selection led to the Burr-Brown PCM-63, an amazing multibit DAC, still pretty good today. About that time, Burr Brown was sold to Texas Instruments. There began to appear delta-sigma dacs, which is a fancy name for reduced bit width DACs which used the above alluded to tricks of averaging and noise shaping to make up for the data they threw away. Soon we had TI, Wolfson, Crystal Semiconductor, Phillips, and many more manufacturers of these (now marketed as audio - read dogschiit) DACs. Why stoop to make them?? Simple - they're cheaper! Never mind they can't be used in medical imaging or defense applications because of their inherent data loss/hallucination. Too late, the audio customer had far cheaper gear. The chip makers sold lots of parts.
Enter DSD, the ultimate extension of this idea. More noise and less bitwidth. You get for free with the bargain, the elimination of the nasty anti-alias filter effects used in the recordings. Cool, huh. This idea works well just as soon as every recording studio on the planet switches over. When that happens (right), what about the old recordings like all of those from SACD days of yore!! Oops, they are already recorded with the filter in place... Unfortunately, they are the bulk of the current DSD catalog available. Can you get DSD from iTunes?? Download DSD from Amazon?? Oh...
What about 1, 2, 4, or 87.6x native DSD recordings. Yeah there's a few - I really loved the Folsom Prison Castrati Singers doing Handel soprano motets. My all time fave is the Orkney Island shepherd's Poems and Cries of Ecstacy with the sheep. The plaintive cries and bleats of all involved were immaculately suspended in perfect panoramic image. Even the subtle sounds of the shepherds gently placing the sheep's rear legs in their boots were clearly audible.
Nobody ever explained to me how to design a multi-rate 1x, 2x, etc DSD DAC without a real expensive adaptive filter. Do you optimize it for 1X? 2X? 5.76X? Trouble is, then all of the other rates are compromised. Maybe the over $10K DACs do that. I haven't figured out how to make an over $10K DAC yet, maybe someone will teach me.
In conclusion - this is opinion, mine with respect to DSD: How can I express just how underwhelmed I am. Adjectives such as stillborn, faith-based, and ludicrous come to mind.
But wait - I actually built the Loki DSD DAC! How can I be such a hypocrite! The answer is that I will try almost anything once. If I don't like it, I won't do it again. But I could be wrong - if servers ever get big/cheap enough that iTunes and Amazon offer DSD downloads AND major label music providers begin to provide native DSD recordings in substantial numbers - then I will cook and eat a crow at RMAF. Meanwhile, all you DSDers - enjoy the grubs!! Buy a Loki!"