Characteristic Frequencies, Polynomial-Exponential Trajectories, and Linear Exact Modeling with Multidimensional Behaviors
Characteristic Frequencies, Polynomial-Exponential Trajectories, and Linear Exact Modeling with Multidimensional Behaviors
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特征频率、多项式指数轨迹和具有多维行为的线性精确建模
DOI：
10.1137/s0363012904441738
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
E. Zerz
中科院分区：
文献类型：
--
作者：
E. Zerz
线性、平移不变的多维行为的特征频率与其非零指数轨迹相对应。研究属于行为的固定特征频率的多项式指数轨迹集：导出测试以确定该空间是否是有限维的，如果是，则构造基础。如果它是无限维的，则仅考虑多项式部分达到一定次数的多项式指数轨迹，并给出这些空间的维度随着次数界限趋于无穷大而渐近增长的特征。对偶问题涉及线性精确建模，即构建所谓的最强大的非证伪模型（MPUM）：给定一组有限的多项式指数轨迹，目标是构建包含数据和尽可能少的其他内容的行为。
The characteristic frequencies of a linear, shift-invariant multidimensional behavior correspond to its nonzero exponential trajectories. The set of polynomial-exponential trajectories belonging to a fixed characteristic frequency of a behavior is investigated: A test is derived for determining whether this space is finite-dimensional, and if so, a basis is constructed. If it is infinite-dimensional, one considers only the polynomial-exponential trajectories up to a certain degree of the polynomial part, and a characterization is given of the asymptotic growth of the dimensions of these spaces as the degree bound tends to infinity. A dual problem is concerned with linear exact modeling, that is, the construction of the so-called most powerful unfalsified model (MPUM): Given a finite set of polynomial-exponential trajectories, the goal is to construct a behavior that contains the data and as little else as possible.