Interpolation is the process of moving from the discrete-time world to the continuous-time world. We are given a sequence $$x[n]$$ and we would like to build a continuous-time function $$x(t)$$ that somehow "embeds" the sequence in continuous time.

We are first going to look at polynomial interpolation for finite-length data sets. Then we are going to study another method called local interpolation, where a single interpolation "shape" (or kernel) can be applied sequentially to sequences of arbitrary length. Finally, we will see how the two approaches converge to the same ideal method when the original signal is infinite-length.