Digital recording is everywhere, but there remains a fascination about pure analog. Comments like ‘more musical’ and ‘less tiring’ are often made.

A popular misconception is that, in conversion, much information is lost between the sample-points, leading to the notion that more samples could provide a better result.

However, in today’s converters, the sample rate at the analog-digital interface is almost always much higher than Nyquist’s theorem would suggest – in fact between 64 and 128 times higher. Co-incidentally, DSD (direct stream digital) is 64 times oversampled too. Today’s converters have something else in common with DSD – very few bits in each sample. Yet strangely, by the time we end up with something that you can record on your hard disk, the sample-rate has been reduced to something typically between 44.1kHz and 192kHz and, magically, we end up with as many as 24 bits.

This raises the question of resolution, precision or accuracy – or how many bits a converter is. So, when the change in a signal is smaller than the least significant bit in the converter, can the change be recorded or captured?  If you think about it, it must be possible, if the business end of a converter is between one and six bits. Otherwise, how could we ever derive 16, never mind, 24 bits from it?

We don’t have space to explain in detail here, so I’ll just have to summarise: today’s over-sampling converters employ noise shaping in their one to six-bit modulator stages to push noise out of the audio band. The noise itself dithers the converter, miraculously resolving and capturing changes smaller than the bottom bit. Then a low pass filter is applied to band limit the source audio, remove aliasing products and the high-frequency noise products resulting from noise-shaping. In an A/D, the next step is down-sampling to the desired rate, such as 44.1kHz or 96kHz.

The lower-order bits (extending to 16, 20 or 24 as we choose) are the product of our mathematical calculations, a bit like the remainder figures after the decimal point when we try to work out what 1/3 is in decimal. We keep as many as we need and, once again, we dither and optionally noise-shape when we truncate the result, but this does not limit resolution of the fine detail.

So, near perfect resolution of large and small signals un-constrained by the supposed number of bits is a feature of both DSD and so-called PCM (pulse code modulation) systems and, in fact, they both share broadly the same kind of sampling circuit.
Prism Sound’s recent UK and US university seminar programme included a demonstration on how we can fade a signal up and down between, say, ­120dB and ­100dB without distortion in a dithered 16-bit system with 93dB dynamic range and hear it quite clearly – even more so if we noise shape down to 16 bits.