Just exactly what is the probability of encountering that particular signal in real life? You've got a number? As an engineer, I am perfectly happy with solutions that works
almost everywhere.
Ok, you're a fellow engineer so I'm sure we can reach an agreement
The "intersample overs demo" signal is fs/4, well within the Nyquist limit.
I fully agree.
Just exactly what is the probability of encountering that particular signal in real life?
Zero. We agree on that, too.
Like the J-test, it is a specially crafted signal designed to examine the behaviour of any given device in a worst-case scenario.
The clipping occur during the digitization.
I think that is where our disagreement lies. Perhaps it's a poor choice of words on my part, sorry if that's the case.
If by digitisation you mean the interpolation that happens during conversion, then no wonder we can't understand each other!
For me, digitisation is the conversion from analogue to digital via an ADC. Taking an analogue 'real world' signal, as you say, and storing it in digital PCM values.
In this case, the anti-aliasing filter will prevent any weird behaviour like your graph shows - the system is band-limited. There's nothing to worry about in this scenario, and I think you'll agree?
The whole concept of inter-sample overs only makes sense when converting an encoded signal from digital to analogue, if and only if that signal has been:
1) digitally processed after capture or digitisation (think EQ, compressors, limiters, ...)
2) created digitally in the first place (think of digital synthesizers in a DAW, for example).
Does this make more sense to you now?
[EDIT : since @edechamps made a really good point in post #130. Technically, you'll always have a difference between the sample values and the sampled signal itself when going from A to D and from D to A. This is normal, since the only case where sample peaks and interpolated peaks can be equal is when you digitally generate a sine wave which frequency is an integer divisor of the SR, and which phase is either exactly zero or 180°. In practice, however, most people keep enough headroom and then adjust the gain digitally so you're unlikely to experience clipping.]
And so, when you say:
There is even less excuse with synthesized signals, since the maximum level is known in advance
Well, that's partly true.
Firstly, this is something I've been trying to point out. As I said, the production world is slowly moving away from peak meters (which do *not* interpolate like a DAC) to true-peak meters. In other words, by default, most audio workstations, software and plug-ins only display the PCM peak values, not the true upsampled/interpolated value. The consequence is that even a well-meaning engineer in the 2000s could deliver digital masters full of ISPs and never know it, because all the lights were green in the digital domain!