Compactly Supported Discrete Orthogonal Interpolation Bases

Classical interpolation is the basis of function space,which can be basically divided into orthogonal space and non-orthogonal space.Although non-orthogonal bases are sometimes useful mathematical tools,orthogonality is undoubtedly a very important attribute for a basis.Orthogonality is often relaxed when another attribute that contradicts orthogonality needs to be satisfied.An interesting example is the biorthogonal wavelet bases which lack orthogonality.In this paper,the definition of infinite dimensional discrete orthogonal basis is given,and this new interpolation method,namely discrete orthogonal interpolation basis method,is further studied.When When we deal with digital signals and apply discrete orthogonal basis,the computations involved in it are intensive in terms of speed and storage.According to the orthogonality of sym wavelet filter,a set of linear compactly supported discrete orthogonal interpolation bases and three sets of nonlinear compactly supported discrete orthogonal interpolation bases are designed.Finally,the application of this interpolation method is introduced in detail,and numerical experiments are carried out with the designed compactly supported discrete orthogonal interpolation basis.The results show that the interpolation approximation effect of the compactly supported discrete orthogonal interpolation is better than that of the linear one,and the larger the support interval of the interpolation basis,the better the interpolation approximation effect.All the algorithms in this paper are programmed in Mathematical version 10.0.