Direct algorithm for computation of derivatives of the Daubechies basis functions

摘要

We extend the direct algorithm for computing the derivatives of the compactly supported Daubechies N-vanishing-moment basis functions. The method yields exact values at dyadic rationals for the nth derivative (0 ⩽ n ⩽ N − 1) of the basis functions, when it exists. Example results are shown for the first derivatives of the basis functions from the Daubechies N-vanishing-moment extremal phase orthonormal family (for N = 3, 4, and 5), and the CDF(2, N) spline-based biorthogonal family (for N = 6, 8, and 10).