Construction Of Discrete Biorthogonal Interpolation Base

It is well known that 2-band orthogonal wavelet has no linear phase except haar wavelet.This greatly limits the use of wavelets in practical applications.However,linear phase is crucial because it can eliminate phase In addition to distortion,in terms of boundary value processing of a finite-length signal,only a simple symmetric expansion can be performed for accurate processing.In addition,the linear phase property can be used to make the algorithm faster and more efficient.Because the wavelet has no explicit expression,it restricts the application of wavelet in other fields,such as numerical solutions of partial differential equations.In order to be able to use the good properties of wavelets in practical applications,we have relaxed the orthogonality requirements and proposed the concept of discrete biorthogonal interpolation basis.This paper designs two sets of discrete bi-orthogonal interpolation bases based on the wang-1 filter coefficients.The discrete points on the basis function are used to form a bi-orthogonal 2-cyclic matrix.The interpolation function can be obtained by using vectors instead of integration.Application of experimental data shows that the linear approximation effect of discrete bi-orthogonal and dis-crete orthogonal basis interpolation is the same,but the non-linear interpo-lation approximation effect has more advantages.It breaks the limitations of orthogonal wavelet and makes the wavelet theory in There has been further development in function interpolation.This article is an exploratory article,and further theoretical research is needed.