As a quick follow-up to my post on noise shaping, I wanted to make some comments on DSD playback. DSD’s specification flies quite close to the edge, in that its noise shaping causes ultrasonic noise to begin to rise almost immediately above the commonly accepted upper limit of the audio band (20kHz). This means that if DSD is directly converted to analog, the analog signal needs to go through a very aggressive low-pass filter which strips off this ultrasonic noise while leaving the audio frequencies intact. Such a filter is very similar in its performance to the anti-aliasing filters required in order to digitally sample an analog signal at 44.1kHz. These aggressive filters almost certainly have audible consequences, although there is no widely-held agreement as to what they are.
In order to get around that, the playback standard for SACD players provides for an upsampling of the DSD signal to double the sample rate, which we nowadays are referring to as DSD128. With DSD128 we can arrange for the ultrasonic noise to start its rise somewhere north of 40kHz. When we convert this to analog, the filters required can be much more benign, and can extend the audio band’s flat response all the way out to 30kHz and beyond. Many audiophiles consider such characteristics to be more desirable. By the way, we don’t have to stop at DSD128, nor do we have to restrict ourselves to 1-bit formats, but those are entirely separate discussions.
If that was all there was to it, life would be simple. And it isn’t. The problem is that the original DSD signal (which I shall henceforth refer to as DSD64 for clarity) still contains ultrasonic noise from about 20-something kHz upwards. This is now part of the signal, and cannot be unambiguously separated from it. If nothing is done about it, it will still be present in the output even after remodulating it to DSD128. So you need to filter it out before upsampling to DSD128, using a filter with similar performance to the one we just discussed and trashed as a possible solution in the analog domain.
The saving grace is that this can now be a digital filter. There are three advantages that digital filters have over analog filters. The first is that they approach very closely the behavior of theoretically perfect filters, something which analog filters do not. This makes the design of a good digital filter massively easier as a practical matter than that of an equivalent analog filter. The second advantage is that digital filters have a wider design space than analog filters, and some performance characteristics can be attained using them that are not possible using analog filters. The third advantage is that analog filters are constructed using circuit elements which include capacitors, inductors, and resistors - components which high-end audio circuit designers will tell you can (and do) contribute to the sound quality. Well-designed digital filters have no equivalent sonic signatures.
So - good news - the unwanted ultrasonic noise can be filtered out digitally with less sonic degradation than we could achieve with an analog filter. Once the DSD64 is digitally filtered, it can be upsampled to 5.6MHz and processed into DSD128 using a Sigma-Delta Modulator (SDM). It is an unresolved question in digital audio whether a SDM introduces any audible sonic degradation. Together with the question of whether a 1-bit representation is adequate for the purposes of high-fidelity representation of an audio signal, these are the core technical issues at the heart of the PCM-vs-DSD debate.
So the difference between something that was converted from DSD64 to DSD128, and something that was recorded directly to DSD128, is that the former has been filtered to remove ultrasonic artifacts adjacent to the audio frequency band, and the latter has not. If DSD128 sounds better than DSD64 it is because it dispenses with that filtering (and re-modulation) requirement. Such arguments can be further extended to DSD256, DSD512, and the like. The higher the 1-bit sampling frequency, the further the onset of ultrasonic noise can be pushed away from the audio band, and the more benign the filtering can be to remove it for playback.
It is interesting to conclude with the observation that, unlike the situation with 44.1kHz PCM, DSD64 allows the encoded signal to retain its frequency spectrum all the way out to 1MHz and beyond, if you wanted. By contrast, 44.1kHz PCM requires the original analog signal itself to be strictly filtered to eliminate all content above a meager 22.05kHz. DSD64 retains the full bandwidth of the signal, but allows it to be submerged by extremely high levels of added noise. In the end you still have to filter out the noise - and any remaining signal components with it - but at least the original signal is still present.