Special interpolations defined in terms of our custom Interpolation class.
Consider the signal to be piecewise constant, where the leading value is used for filling the interval [0,1).
Consider the signal to be piecewise cubic, with smooth connections at the nodes. It uses a cubic curve which has node values x0 at 0 and x1 at 1 and derivatives (x1-xm1)2 and (x2-x0)2, respectively. You can see how it works if you evaluate the expression for t=0 and t=1 as well as the derivative at these points.