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An orthogonality condition of convolution type is derived for scaling functions satisfying a twoscale relation. In two spaces of the shifted scaling functions, one of which includes the other space, a...n inner product different from the $ L^2 $ inner product is introduced. The finer scaling function space is decomposed into the coarser one and its orthogonal complement. A wavelet function is constructed so that its shifted functions form an orthonormal basis in the orthogonal complernent. Such wavelets contain the Daubechies' compactly supported wavelets as a special case. Also, a symmetric and almost compactly supported wavelet is obtained.続きを見る
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Mendeley出力
doi-tr-131