COMPUTATIONAL AND ALGORITHMIC ASPECTS OF CARDINAL SPLINE-WAVELETS

摘要

Pascal triangles are formulated for computing the coefficients of the B-spline series representation of thecompactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al-ternating signs removed,all these sequences are totally positive.On the other hand,truncations of the recipro-cal Euler-Frobenius polynomials lead to finite sequences for orthogonal wavelet decompositions.For this pur-pose,sharp estimates are given in terms of the exact reconstruction of these approximate decomposed compo-nents.