Wavelets with Orthogonality Conditions of Convolution Type
Koichi Kuzume, 幸一 葛目, Koichi Niijima, 耕一 新島 · Kyushu University Institutional Repository (QIR) (Kyushu University) · 1997
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, an 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.