But if each bit is being mapped to a discrete voltage, isn't that in fact a stairstep signal?
Taking the opportunity of your wording to make an important point to the topic in gereal:
There is the temptation to mentally connect discrete samples over time, but in fact they only exist for the
moment of their designated time. In other words, they are not a train of steps, but a train of impulses. Taking readings (sampling)
n times a second is mathematically equivalent to multiplying the analog signal by a unit pulse train of that rate.
The DAC stair steps NTK refers to is a practical implementation measure. Unfortunately, it confuses people, because (as Monty explained) digital audio is not about stair steps. However, converting the digital values to impulses, for DAC output, is less practical than "zero order hold" output as a staircase. (Impulses are narrow, so the energy represented is highly affected by an errors from one to the next. Stair steps have a lot of area, and it's easier to main a precise constant level for the sampling period. In other words, it's easier to get acceptable signal to noise by stretching the sample level over the entire period than to flash it briefly. BTW, someone may point out it's impossible to generate a perfect impulse, but we never needed perfect; audio has a limited bandwidth, so the impulses can too. You
can make a DAC that outputs impulses into the "reconstruction" filter, it would just be a needlessly difficult design.)
A staircase is wrong, but fortunately it's wrong in a precise mathematical way that is easy to correct for in the final analog result. Most important for the audio band, the "staircasing" of the signal gently rolls off the highest frequencies. That's easy to compensate for.
