Oversampling in digital audio - why 14 bits can be equal to or better than 16

There is an easy way to convert a 16-bit digital signal from, say, a compact disc into analog audio.

All you have to do is make a device that will produce a voltage that changes in proportion to the value of each 16-bit digital sample. So 0000000000000001 will result in a very low voltage, 1111111111111111 will be a high voltage.

How much more perfect a solution could there be? It seems that this method does the job and nothing more could possibly be required.

Back in the early days of CD though, things were not so easy. It was difficult to build a digital-to-analog converter with sufficient accuracy. Yes it would work, but the output would be subtly yet significantly distorted.

But the engineers at Philips had a plan...

What they would do would be to use 14-bit converters. Yes, two bits would be ignored, but they had found a way that not only would this not matter, the result would sound even better than a 'straight' 16-bit converter.

What they invented, or at least were first to widely implement, was... oversampling.

Yes we have all heard this word, but what does it mean? It's not so hard to understand...

In the digital domain where everything is just numbers and easy to handle, start by calculating 'in-between' samples between those that already exist. This can be done by simple interpolation based on expectations of where those samples would be if they had actually been taken at the original recording.

So now a 44.1 kHz sampled signal becomes a 176.4 kHz sampled signal. And you know what? That signal has as much information in its top 14 bits as the original 16-bit signal has. Mathematically, it works out perfectly. So those bottom two bits are no longer important and don't need decoding.

There are two advantages here. Firstly, a 14-bit DAC can be designed very much more accurately than a 16-bit DAC (even now, greater bit depths are still more difficult to achieve with accuracy).

Secondly, it is true in all digital-to-analog converters that there is a lot of very high frequency (above 20 kHz) digitally generated noise to filter out.

If a signal is sampled at 44.1 kHz, everything above 22.05 kHz must be filtered. And it is a very tough job to design a filter that will allow frequencies up to 20 kHz to pass unhindered, yet will stop everything at 22.05 kHz and above.

But Philips had it easy. In their oversampled converter, the noise was spread out over a much wider bandwidth up to 176.4 kHz, and was therefore easily dealt with by a simple filter that didn't harm audio quality.

So there it is. Oversampling isn't so difficult, is it?