Abstract
ABSTRACT In this paper, we will discuss integral wavelet transforms and orthogonal multiresolution analysis associatedwith spline functions in shift-invariant spaces of B-splines. A recurrence relation formula and the corresponding algorithm about the B-wavelets will also be given. Keywords: Integral wavelet transform, orthogonal multiresolution analysis, orthogonal scaling function, shift- invariant space, recurrence relation of B-wavelets, Bezier coefficients. 1 Introduction Let Nm(X) be the cardinal B-spline function of order m and S(Nm(X)) be the shift-invariant space of Nm(X) that is defined as the span of the integer translations of Nm(X). Thus, Sm E S(Nm(X)) can be written as Sm(X) = ;: CjNm(X _ j), X E R, j E Z. (1)Throughout, we will always assume that Sm(X) 5 a finite linear combination of {Nm(X _ j)}. In author's paper7 we have discussed window Fourier transforms and wavelet series expansions associated with Sm(X) because of two reasons. First, the basic function of a cardinal B-spline interpolation from S(Nm(X))can be expressed as Sm (x) ; the wavelet function associated with Sm (x) can then be used for numerical analysis.5
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