A long time ago, I worked on a project involving nterpolation of sampled data. It was a "13 point moving cubic". Oddly, I remember that term, but nothing else, though I do remember it involved a bunch of coeffciients from a published table. A moving average filter, probably, though perhaps it was a smoother, i.e. not real time.
I have no idea, then or now, the derivation of the formula. Can anybody guess what it was, or the theory, or point me to a reference?