Interpolation by Nonuniform B-Spline through Uniform B-Spline Filter Banks

For knots spaced uniformly, the B-spline interpolation can be represented by an interpolator with a B-spline filter. In this paper, a B-spline filter bank is designed to describe the nonuniform B-spline interpolation. Signals considered here are those that can be split into several uniform subsequences by decimation. The decimated signals are then interpolated by the uniform B-spline functions to recover signals. However, aliasing cannot be eliminated through direct interpolation on the decimated subsequence. By using a bank of multilevel filters, aliasing can be removed to obtain that nonuniform B-spline interpolation is carried out by uniform B-spline interpolation.