OK, I get it now. Thanks for the explanation. I would just never in a lifetime call it a "filter". That's extremely poor naming.
If they called it a choice of basis or influence function, it would've been so much clearer.
If they called it a choice of basis or influence function, it would've been so much clearer.
I would think that conceptually that a basis function is different form a filter function because a basis function is usually about transforming a point in one space to some different space, and basis functions come in a set that’s the size of the dimensionality of the target space. Filters, even if you can think of the function as a sort of basis, aren’t meant for changing spaces or encoding & decoding against a different basis than the signal. Filters transform the signal but keep it in the same space it started from, and the filter is singular and might lose data.
May be better if I just link to what others say about filters than me trying to blabber on https://en.wikipedia.org/wiki/Filter_(signal_processing)