Algebraic multidimensional phase unwrapping and zero distribution of complex polynomials-characterization of multivariate stable polynomials
Algebraic multidimensional phase unwrapping and zero distribution of complex polynomials-characterization of multivariate stable polynomials
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复多项式的代数多维相位展开和零分布-多元稳定多项式的表征
DOI：
10.1109/78.678480
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
K. Sakaniwa
中科院分区：
文献类型：
--
作者：
I. Yamada;K. Kurosawa;H. Hasegawa;K. Sakaniwa
我们定义了任何有限范围的多维信号的多维展开相位，这些信号可能在单位多圆盘的可分辨边界上具有零点。利用这个定义，我们推导出多元稳定多项式可以简单地用所提出的去包裹相位来刻画。给出了多维有限范围信号精确相位展开问题的严格符号代数解。这种解基于新开发的通用Sturm序列，不需要任何数值求根或数值积分技术。此外，还证明了所提出的代数相位展开算法可以用来确定任意一元复多项式的精确零分布，而不会遇到所谓的奇异情况问题。
We define the multidimensional unwrapped phase for any finite extent multidimensional signal that may have its zero on the distinguished boundary of the unit polydisc. By using this definition, we deduce that multivariate stable polynomials can be simply characterized in terms of the proposed unwrapped phase. A rigorous symbolic algebraic solution to the exact phase unwrapping problem for multidimensional finite extent signals is also proposed. This solution is based on a newly developed general Sturm sequence and does not need any numerical root finding or numerical integration technique. Furthermore, it is shown that the proposed algebraic phase unwrapping algorithm can be used to determine the exact zero distribution of any univariate complex polynomial without suffering the so-called singular case problem.