> I don't 100% get the band limited signal bit. [...]
If I can venture yet another explanation for this. Consider the projection
π:signals --> signals,
which corresponds to band limiting a signal to 20k[Hz].
Given any signal in the "time basis" x(t) we can transform
it to the "frequency basis" X(f) and in the frequency basis
the action of the filter is to leave all the frequencies
< 20k unchanged and to set to zero all frequencies f > 20k.
This is similar to the way the projection onto the x axis
leaves the x coordinates of vectors unchanged and sets the
y coordinate to zero.
> Can the converter itself not create the signal incorrectly?
>
Let x the signal and π(x) be the band limited version of x.
The video is talking about the general properties of projections,
namely:
π(π(x)) = π(x).
The time you project you change the signal (restricts to subspace f<20k in freq. domain),
but there is no further harm done by projecting multiple times.
If I can venture yet another explanation for this. Consider the projection
which corresponds to band limiting a signal to 20k[Hz]. Given any signal in the "time basis" x(t) we can transform it to the "frequency basis" X(f) and in the frequency basis the action of the filter is to leave all the frequencies < 20k unchanged and to set to zero all frequencies f > 20k. This is similar to the way the projection onto the x axis leaves the x coordinates of vectors unchanged and sets the y coordinate to zero.> Can the converter itself not create the signal incorrectly? >
Let x the signal and π(x) be the band limited version of x. The video is talking about the general properties of projections, namely:
The time you project you change the signal (restricts to subspace f<20k in freq. domain), but there is no further harm done by projecting multiple times.