基于 GCTST 变换研究多尺度函数的构造与性质

摘要

V Strela提出的两尺度相似变换（TST ）在研究多小波的构造与性质中发挥着十分重要的作用。在文中，我们提出了广义共轭两尺度相似变换（GCTST ）的概念。利用广义逆矩阵的分解及单边逆的相关理论，详细地研究了GCTST变换对矩阵符号特征值影响，这种技巧在其他相关文献中很少使用。证明了GCTST可以保持多尺度函数的逼近阶，平衡非平衡的多尺度函数及保持对称性等。通过最后的算例，说明GCTST是可行的有效的，而且可以减少或增加多尺度函数的重数。%Two-scale similarity transform (TST)presented by V .Strela is an important role in studying the multi-wavelet .The concept of general conjugate two-scale similarity transform (GCTST )is introduced in this paper .GCTST is the most universal gener-alization of TST .We discuss how the GCTST change the eigenvalue of the matrix by using the general inverse matrix theory ,which the former authors hardly use .Then we show that GCTST can keep the approximation order of the multi-scaling function ,balance the unbalanced multi-scaling function and keep the symmetry of the multi-scaling function .By the two examples ,we conclude that the GCTST transform is feasible and efficient .GCTST also change the multiplicity of the multi-scaling function .