I had a semester long master's level course in Digital Signal Processing, EE-638, at Purdue University.

There's plenty of mind-bending stuff in that course, but bit depth is one of the easier things to understand.

In a 16 bit A/D, there is 1 of 2^16 possible values the A/D converter stuffs the conversion into. That's 1 of 65,536 shelves to put the data on. When the A/D puts the data on a shelf, it's called quantization in the amplitude domain. Many books visualize this as a stair-step kind of a picture. 65,536 possible steps to be on.

In a 24 bit A/D, there is 1 of 2^24 shelves, or 1 of 16,777,216 possible steps to put the data on, to represent the same possible overall magnitude of the signal.

What this means is that the step height for 24 bit is way smaller than in a 16 bit recording. In fact, there are 256 of the 24 bit steps in a single 16 bit step.

So, why should we care?

Well, when the data is converted back to analog from the digital representation, there is a bit of noise that is generated taking that step value, and then doing the magic back to analog.

The easiest situation to think about is a signal that is nominally zero. The A/D process has to take the zero and decide is it going on the smallest shelf or the next largest shelf. Basically, 0000000000000000 or 0000000000000001 in the binary representation, for a 16 bit signal. For a 24 bit signal, it's 000000000000000000000000 or 000000000000000000000001. (those of you that know signed/little/big endian, etc. work with me here!)

IF the signal happens to be set on the 0....01 shelf in either case, when it's converted back to analog, that actually is something bigger than zero and a tiny bit of noise results in the analog signal.

For a 24 bit recording, this noise, known as quantization noise, is 48 dB quieter than in a 16 bit recording.

So again, why should we home recording types care?

Well, this 'which shelf?' decision happens for every single shelf, not just the lowest two shelves.

With 24 bit, this means you can record with your signal much less 'hot' and still get pristine A/D and ultimately D/A representation. With 16 bit recording, it's more of a concern to maximize the analog signal range to cover as much of the 2^16 values, so that those steps matter less when converting back D/A. With 24 bit recording, one almost has to work hard to make the signal level be so quiet that quantization noise factors into the output story/sound.

That was one takeaway from that class that sunk in. The other was how D/A conversion actually does recreate a smooth analog signal and not a stair-stepped analog signal, through the output anti-aliasing filter impulse responses of each sample. That's a discussion for a different day.

Last edited by rockstar_not; 05/10/15 03:31 PM.
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