Shou Zhi YANG
A general procedure for constructing a class of compactly supported orthogonal interpolation multiscaling functions and multiwavelets with dilation factor a are introduced. Let {Vj} be a multiresolution analysis generated by a multiscaling function Φ(x) = [φ1(x), φ2(x), …, φa(x)]T, where the subspace Vj denotes the L2 (R)-closed linear span of {a-j/2φ(?)(ajx - k), j,k ∈ Z, (?) = 1,2,…, a}. The interpolation property here means that φ1(x), φ2(x),…, φa(x) satisfy φj(k+(?)/a) = δk,0δj,(?),j, (?) ∈ {1,2,…, a}. When Φ(x) is orthogonal interpolation, the coefficients in the multiresolution representation can realized by sampling instead of inner products. Thereby, multiwavelets sampling theorem is established, i.e., if a continuous signal f(x) ∈ VN, then f(x) = Σi=0a-1 Σk∈Zf(k/aN+i/aN+1)φi+1 (aNx - k). The corresponding orthogonal multiwavelets are constructed explicitly. What is more, the multiwavelets we construct here are also interpolation. An example is also presented.
