The Design Of Six-band Orthogonal Filter-banks

In the past thirty years,the general theory of multi-band wavelets has gradually matured,but the design of M-band linear phase orthogonal wavelets is still very difficult,especially when the number of channels of multi-band wavelet is relatively large.The design problems of two kinds of six-band linear phase orthogonal filter banks are mainly studied in this paper.The first kind is six-band linear phase orthogonal filter banks of equal length,that is to say,the filter bank has one center of symmetry,and the other one is six-band linear phase orthogonal filter banks with multi-center of symmetry.For the six-band orthogonal filter banks with one center of symmetry,according to the semi-rank factorization theory of the poly-phase matrix of multi-band orthogonal wavelet,the design problem of the multi-band linear phase orthogonal wavelet can be solved concisely and effectively by constructing the starting matrix and the orthogonal projection matrix.For the design of linear phase orthogonal filter banks with multi-center of symmetry and different lengths,semi-rank factorization can also be used to construct them.This decomposition method has the completeness of linear phase,so it is also called complete factorization.In this paper,the concept of minimal starting block matrix is introduced,and three cases of six-band orthogonal filter banks with two symmetrical centers are discussed.Finally,the six-band linear phase orthogonal filter banks are optimized.