Man. We were going so well. Why do we have to fall apart like this?
It's "
inter-sample" overs, and it means overshoots
between samples.
Samples between samples would be inter-sample samples.
In the context of OS DACs, there is some overlap between inter-sample samples and inter-sample overs, but they're not quite the same thing.
Inter-sample samples are a digital representation of an inter-sample peak. That is, until they hit the 0dBFS threshold, at which point they can no longer represent the original inter-sample peak accurately and they will instead represent a clipped inter-sample peak.
You're right in saying that for the purpose of this thread we can forget about all the inter-sample peaks that don't exceed 0dBFS, but it is important to know what those look like, because we are trying to make sure that the ISPs above 0dBFS behave just like (or mostly like) the ones that are below that threshold.
Given the required analog headroom voltage-wise, a NOS DAC followed by an analog low-pass filter will do just that (you showed this yourself in the last couple of graphs you posted). It will reconstruct an inter-sample peak at 0dBFS just like it reconstructs an ISP at -1dBFS, at -2dBFS and at every other value it's able to hold. An OS DAC won't be able to do this.
"We didn't have this problem until oversampling DACs were invented" means exactly what it sounds like: NOS DACs didn't introduce digital clipping because they weren't oversampling.
You're getting there. A square wave is an infinite series of odd sine waves decaying in amplitude at a fixed rate.
In the time domain, if you keep adding those sine waves on top of each other you'll get a square wave.
One crucial thing to understand is that changing the shape of the wave in the time domain also changes the harmonic content in the frequency domain.
I'm sure you're also familiar with the spectrum of a square wave in the frequency domain. You'll get a series of vertical lines getting smaller and smaller representing the odd harmonics.
But what wave would we get in the time domain if instead of having those odd harmonics in the frequency domain we had that ultrasonic,
high frequency noise you mentioned (specifically around the sampling frequency)?
Yep, we'd get a Zero-Order-Hold train.
If you think about it, a ZOH train is not exactly a square wave. If it's not exactly a square wave in the time domain, it won't be exactly a square wave in the frequency domain either. Instead of having odd harmonics we'll have what are called "images" of the original signal at multiples of FS, which are exactly the high frequency noise you want to filter out.