Yeah this is the part that breaks people’s heads.
Both PCM and DSD describe a waveform by plotting amplitude over a fixed sampling time interval. They are both subject to Nyqvist’s rule. They both have quantisation noise. From a mathematical perspective they are the same kind of animal.
In a practical sense, for the purpose of encoding and reproducing audio, they have some important differences. By using 16 or more bits of resolution per sample, PCM aims to capture all (or nearly all) of the sub-Nyqvist frequencies with an effectively inaudible amount of quantisation noise. DSD uses ultra high sampling rates to exploit the fact that the extremely high quantisation noise of 1-bit samples can be shaped so that its energy falls in frequencies which are far higher than the actual passband of interest. (Shaped dither is also used in PCM to improve the noise floor at lower frequencies and move the energy of quantisation noise into higher, less audible parts of the spectrum.)
So while 16/44.1 PCM with random dither has a flat -96dB noise floor from 0 to 22.05kHz, 1/2822.4 PCM aka DSD64 would have a noise floor of -6dB from 0 to 1.4MHz without noise shaping! Using noise shaping we can get a very good SNR in the audio passband, with an increasing amount of noise pushing up towards 0dB at much higher frequencies. Then we just get rid of that unwanted noise using a low-pass analog filter.
There are therefore some differences in how you create useful 1-bit PCM audio samples vs 16- or 24-bit audio samples. Most ADCs are actually high sample rate low-resolution devices these days anyway, using noise shaping and sigma-delta modulation to create something more like a DSD stream that then gets mathematically filtered and converted to PCM. In that sense a pure DSD recording is closer to the original than most PCM recordings.
There are differences in how you process the data digitally. High resolution PCM can be scaled, mixed and processed in quite a linear fashion with relatively slight increases in noise. DSD can’t be treated that way because even the slightest modification gives you back your -6dB noise floor.
Maybe most importantly there are differences in the machinery needed to do D-to-A conversion. Ted’s core insight with the DS is that a DSD stream needs nothing more than a positive/negative voltage switched according to the data stream, followed by a gentle analog low pass filter. That’s so different to a traditional audio DAC that it’s probably why people think DSD and PCM are completely different things… the physical machinery for D-to-A conversion is so different that they are mostly one or the other.
But at the mathematical core, this is the truth: DSD is a special case of PCM.