We consider the design of an orthogonal symmetric/antisymmetric multiwavelet from its matrix product filter by matrix spectral factorization (MSF). As a test problem, we construct a simple matrix product filter with desirable properties, and factor it using Bauer's method, which in this case can be done in closed form. The corresponding orthogonal multiwavelet function is derived using algebraic techniques which allow symmetry to be considered. This leads to the known orthogonal multiwavelet SA1, which can also be derived directly. We also give a lifting scheme for SA1, investigate the influence of the number of significant digits in the calculations, and show some numerical experiments.

翻译：我们从矩阵产品过滤器中通过矩阵光谱系数化(MSF)来考虑一个正对/对称多波体的设计。作为一个测试问题,我们建造了一个带有理想属性的简单矩阵产品过滤器,并用Bauer的方法来计算。在这种情况下,可以封闭方式进行。相应的正对/对称多波体功能是使用对称法技术产生的。这导致已知的正对多波体SA1,也可以直接得出。我们给SA1提供了一个提振计划,调查计算中重要数字数目的影响,并展示一些数字实验。