关键词: 正交多尺度函数;正交多小波, 逼近阶, 平衡阶

Abstract:

Generalizing the definition of m-order approximation of two-scale orthonormal multiwavelets to the case that the scale factor is equals to a(a ≥2), a sufficient and necessary condition is proposed for orthonormal multiwavelets with scale a to have m-order approximation, by studying the factorization of a-scale matrix symbol; Based on the m-balanced definition of orthonormal multiscaling functions with
scale a, three sufficient and necessary conditions are investigated for such orthonormal multiwavelets to have m-order balance; Then,
verify the theory by means of an example.

Key words: Orthonormal multiscaling function, Orthonormal multiwavelets, Approximation order, Balancing order