@HugeMan: I will check the analog bandwidth by open my Quad, as soon I have spare time to do it.
@lygra: I appreciate your effort to demonstrate (better: trying to do it) with tons of theories, but I guess that you are mixing many concepts together.
A square wave is yes composed by odd harmonics (I agree with slimfish about the numbering), but the shapes you drawn could never be what the analog section outputs. You missed a VERY important parameter: the phase!
Remembers that here, for simplicity, we are talking about the modulus of a signal (i.e. a square), but we MUST take in account the phase-shift caused by the analog section. We “should” take in account the phase-shift introduced by the sampling also, but…never mind.
Just take a simple square-wave generator and a R-C lowpass filter. Assuming the time-constant similar to the period, what do you expect to see on a scope?
The input is a square-wave, composed of an infinite number of odd-harmonics. The output cuts them at -6db/oct.
That would be having an output shaped as you drawn?..Yes, if only the filter won’t shift the phase, smoothly from 0 to -90 degrees.
Of course, by scoping the output signal you will see an exponential fragment, repeated on each period. Exactly the same as having a switch charging then discharging the capacitor, via the resistor.
All that only for a simple R-C filter, being just-one-pole complex function. Imagine what would be having a 10+ poles network!
Cheers