@porres said:

@manuels said:

Sorry, Im not good at explaining ...

well please help me understand how you are doing interpolation with such graphs, and what are "basis functions" or "kernel" supposed to mean in this context... or please give me some references to check. Your patch just gave me a new dimension to look at interpolation and I wanna get it

Maybe this is the missing piece of the puzzle? ... Interpolation is just a special type of convolution

The term "basis functions" (that I probably used incorrectly) doesn't matter, and by kernel I was just refering to the function (whether piecewise polynomial or continuous) the input signal is convolved with.

The difference between my examples and some of the others you correctly spotted is also mentioned in the linked resource in the section "Smoothed quadratic". One advantage of a (non-interpolating) smoothing function is that no overshoot is produced. But of course, if you need actual interpolation you have to use different functions.

Another related topic is resampling. This thread may also be helpful: Digital Audio Demystified