The 44.1KHz stream of 16 bit samples (pulse code modulated, PCM), gets converted into a digital stream which is high (logic 1) and low (logic 0) for lengths of time in proportion to each sample (effectively, pulse width modulated, PWM). So when one of your 44.1KHz samples is, say, 15000, then during that particular 1/44100 of a second the bitstream will be high for 15000/65536 of the time and low for, er, 50536/65536 of the time.

Yes, if you're willing to do 65536x oversampling, that would be fine. The only problem is that your new sampling rate is 65536 x 44.1kHz = 2.9GHz! Yes, that's billions of samples per second. I don't think there's a single audio system that actually does that.

For example, the TACT 1-bit digital amplifier uses a master clockrate of 90.3kHz, which is only 2048x oversampling. So you would think that you could only get 11-bit precision out of that. In fact, it achieves >110dB SNR and >130dB dynamic range over the audible frequencies, which is more like 20 or 21 bits of precision if my calculations are right. (Of course, a 16-bit CD can't even use all that precision.) What the heck!?

That's exactly the non-intuitive---and frankly, amazing---part about noise shaping. If you measured the noise across the entire frequency range (0-45.2 MHz), you'll find precisely the amount of total noise power that you would expect to see from a 1-bit quantizer: a lot. But by controlling very precisely when the unit switches back and forth between the 0s and 1s, the effect is to shape the frequency response of that noise---so that most of it lies well above the audible range, and is easily filtered out.

You can begin to see this with your 65536x oversampling example. The easiest example is right in the middle of the range---0.5. Obviously I should send out half 1s and half 0s to get that. If I send out 32768 1s followed by 32768 0s, I'll see noise power starting at 44.1kHz---still inaudible, but I'll still need a very strong analog filter to attenuate it. On the other hand, if I send out 1,0,1,0,1,0 instead, I've shifted the noise power all the way up to the gigahertz range. No problem filtering that out!

So that's why 1-bit D/A's don't actually have to go all the way up to 65536x oversampling in order to achieve 16-bit precision in the audible range. I seem to remember some units getting away with only 256x oversampling.

By the way, I have no connection to TACT, nor have I even listened to one, I just think the technology is cool.

Michael Grant
12GB Green
080000266