16 bit vs 24 bit vs 35 bit vs 36 bit vs 64 bit DAC sampling

There are no "stair steps" in digital audio.

Correct, but only after reconstruction filtering.

For people who want to learn about it, you really ought to go back to the original journal articles by the pioneers in telecom int he 1960s - from the Bell Labs Technical Journal and the Lenkurt Demodulator, the Demodulator being very accessible and written for the client base, not researchers.

Slowly a set of blogs on this and related topics is appearing on Sonogy Research's blog as well.


Digital has several challenges. IMNSHO, bit depth is not at the front of the line.

@itsjustme 

What do you perceive as the greatest challenges and areas for digital to excel?

Thanks. 

1. timing/jitter (read the blog at sonogy research.com).
2. noise on the ground of digital signals, that either pollutes the analog ground or impacts jitter (back to #1)
3. Filtering - the reconstruction part, both by shifting the frequencies so they are easier to filter (that's what over sampling or up sampling essentially achieves) or building better filters.  A filter can bee deep, or linear, but typically not both. So the bit I wrote about "only after the reconstruction filter" means these filters can be imperfect.  Can be?  Are.  I'll also point out that that @cleeds said "its math".  True enough, but there is an ocean of difference between theoretical math, and practical implementations. Analog is perfect in theory too.

4. part B of the filters is that there are some very small signals that need to be amplified or impedance transformed at the output of a DAC.  Both present good old analog amp challenges, not all that different from a moving coil cartridge.
5. never underestimate the impact of regular old audio blocking and tackling.  Power supplies. Amps.  grounding.  parts selection.  Do you know how many DACs depend on relatively pedestrian chip opamps and ok-but-not-awesome power supplies?  Most.  You know why?  Its easy and cheap compared to doing it from scratch.

Nyquist goes to Hz sampling (the vertical aspect in the time domain) and the step landings - horizontal bits - would become narrower with higher Hz sampling rate.

This is a bit confusingly worded. Harry Nyquist inferred from Shannon’s work (its basically a corollary) that sampling at **higher than** 2X the highest frequency allows the original waveform to be reconstructed perfectly. yes it is the X coordinate of what becomes a Cartesian graph, when viewed as PAM. (pulse amplitude modulation).

The caveats are:

1. higher than, not = 2X. At precisely 2X you can get the wrong answer. Its called an alias.  For example a 1 kHz 1V sine wave sampled at precisely 2X could land samples all at zero (silence) all at 1V (perfect recreation), all at 0.5V (off by half) or anywhere in the middle.
   
   
2. perfect reconstruction. Not in this world.
   
   
3. ...but we can get very close. Likely much closer than a) analog does (maybe 60-70 dB on a good day) and also b) likely distortion below the levels of our hearing
   
   
4. another issue is that one ought not measure distortions as "all created equal". Music theory tells us that, if pleasure is the desired result, this is not so. Dissonance and consonance are pretty well understood.
   
   
5. In the end arguing for "perfection" misses the point that no system is perfect, and vinyl is a long way from perfect, as is tape.

on the topic of bit depth used in recording nad mastering, there are many reasons why more than 16 bits are used.  And, today, almost ALL recording and mastering is done at 24 bits. Must be better for us right?
No.
reason #1 is so that if levels are off ( remember 0vU levels sets?) there is sufficient headroom to keep all 16 bits int he end product.  You can record too high and not clip, or too low and not lose bits on the low end.

#2 is so that in the inevitable (regrettable too) mixing, processing etc. the fidelity lost is below the least significant of the 16 bits. I won get into how digital level math is done but if you think about it it may become clear that you have both Least common denominator (speaking loosely) issues and truncation issues.

So it allows for sloppy production.  OK, tha's harsh, btu not too far off.  It also allows for multi-track mix-down. Yuk again, but reality especially in rock/grunge/pop/hip-hop/rap.

Want to hear what properly level-set and unmixed 16 bits can do? Listen to old Verve or Mercury Living Presence.  Old 3 channel analog recordings. Careful levels sets. Loving attention to detail. Minimal processing. Superb.  16 bits