Correct if I'm wrong but I would say more that the ladder step is a representation of "how digital audio" works, but that it's misrepresentation of "how analog audio coming from digital audio" works
No, it's actually a misrepresentation of both.
Consider sampling—taking an instantaneous reading of an analog signal. That reading is truly only valid for the instant it represents—it does not represent the entire period till the next sample.
But, I have to add something that usually goes unsaid, and muddies the water a bit. Like I said before, to make the sampling process practical, we "sample and hold" the input—this is just so that the super-accurate measurements we take (24-bit sampling is insanely accurate) have time to settle to a stable reading. The reading is still of a point in time, we just lengthen the time to make it easier to read.
More significantly, outputting accurate impulses is hard to do with accuracy. So we do, essentially, output steps instead of impulses, ahead of filtering. But unlike the sampling process, this does truly f'up the result. But, the error it causes is known precisely and is easily compensated for.
In other words, for DACs, we essentially do it wrong then fix it—it's simply easier to do that than to to try to do it right in one shot. Extending the impulses to steps causes a sinc-shaped frequency rolloff at the top end. It's easy to compensate for with inverse filtering. I could elaborate on why it's so much easier and repeatable to make steps than impulses, if asked, but I'm already wordy.
Of course, modern converters are usually even more complex, but I'm describing the most fundamental aspects common to all, including the basic R-2R ladder DACs.
So, yeah, it gets a little sticky when complaining that "steps" are wrong, despite steps being used in practical implementations. But the fact is, if you're describing sampling theory, viewing as steps
is wrong. Even if we might use them when it comes time to build a practical converter.
