Degree reduction of Bézier curves and filter banks

We consider the degree elevation and reduction of Bézier curves as the filter bank process. The process consists of the synthesis filters and the analysis filters. Using the relationship of basis changes, we find what these filters are and how these filters are related. Explicit forms of each filter are given and the best degree reduced Bézier curves in the L2-norm, L∞-norm, and L1-norm are obtained easily from the analysis filters.