Sorry to call you stupid, Martin, but you have it around the wrong way.

He was stating that the 2.8224Mbit/s data stream gives an analogue bandwidth of 1.4112MHz (the Nyquist limit- sampling theory).

This statement is missing a fundamental point about DACs.

In the beginning, there was the R-2R ladder. This allows a digital code to be converted directly into an analogue voltage. The disadvantage is that the resistors have to be very accurate. The limit before the error in the resistors outweighs the LSB is about 12 bits (before things get stupidly expensive).

There had to be another way.

The answer was the oversampling sigma-delta DAC. This works by converting the incoming multi-bit PCM stream into a very fast 1 bit stream. This 1 bit stream has the property that its frequency spectrum looks rather like the original audio signal- with a big pile of quantization noise thrown in (you can't get from 24 bits to 1 bit without introducing noise). Taking care with the encoding mechanism allows most of this quantization noise to be pushed up to ultrasonic frequencies (noise shaping).

All we need now is a simple low pass filter to cut off all this ultrasonic rubbish and we have what seems to be a multibit DAC.

As we have seen, the theoretical maximum bandwidth of a sampled system is one half the sampling frequency. To be able to push the quantization noise out of the audible band into ultrasonic territory requires substantial oversampling. DSD uses 64 times oversampling, ie. the 1 bit sampling clock is 64 times the audio sampling clock (128 times the audio bandwidth).

Soooo.... In stating that the DSD audio stream represents an analogue bandwidth of 1.4MHz, our author making a true statement. This statement is (possibly deliberately) misleading, however. As I have mentioned, most of the high frequency information in this bandwidth is ultrasonic noise, which MUST be filtered out to prevent everyone's tweeters from melting.

The effective sampling rate of our 2.8224MHz DSD stream is exactly 44.1kHz. This is substantially lower than DVD-A's 96kHz or 192kHz.


A little note about oversampling: modern sigma-delta DACs have taken advantage of smaller and faster microchip technology and have moved on from 64 times oversampling to 256 times (who knows what the future holds?).

A little note about 1 bit conversion: I mentioned in a previous post that modern DACs use multibit conversion to achieve better linearity, and mentioned an AES paper on the subject. That paper proves that it is impossible to properly linearise (dither) the output of a 1 bit sigma-delta DAC. Indeed, DAC manufacturers have been using 2, 3 and 4 bit conversion for a number of years. This allows proper dither to be applied to make the output that bit more beautiful.

So there it is, in grey and black. My chief complaint with DSD is that it is stuck in the past. My other major gripe is that it is almost impossible to do any signal processing to it in the digital domain.


Cor - verbal diarrhoea.

Simon.