Lagrange interpolation converges poorly. Something like B-spline interpolation converges much better, but requires a linear-phase IIR pre-filter (=not causal).Lagrange interpolation approximates sinc interpolation in the sense that if you crank up the order of Lagrange interpolation, it will converge to sinc interpolation. So, my first shot at the problem would be to find a Lagrange interpolant of sufficiently high order and search for an extremal point in the region of interest (i.e. between t = n-1 and t = n or something).
Practically speaking, since you can't really solve high-order polynomials directly anyway, it's probably better idea to just oversample until something like Catmull-Rom is good enough.
Statistics: Posted by mystran — Fri Mar 07, 2025 7:58 am