Multi-dimensional filter bank systems achieving the highest performance of running approximation under given limited resources
Multi-dimensional filter bank systems achieving the highest performance of running approximation under given limited resources
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多维滤波器组系统在给定有限资源下实现运行逼近的最高性能
DOI：
10.1109/ispacs.2013.6704559
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Yuichi Kida and Takuro Kida
中科院分区：
文献类型：
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作者：
延原寛史;岡本好弘;仲村泰明;山下正人;大沢 寿;村岡裕明;Yuichi Kida and Takuro Kida
运行近似使用有限支持的插值函数，并将信号从初始端依次插值到信号的另一端。当给定任意误差算子的连续最坏情况测度时，我们给出了向量信号在一定扩展向量滤波器组中的最佳多维运行逼近，该扩展向量滤波器组同时使各种最坏情况误差测度（包括错误率测度）最小化。这种多维最佳运行（扫描型）近似使用有限数量的样本值，这些样本值随着变量向量x在n维变量向量空间上的移动而步进更新。进一步，当给定一组具有大于1的不同整数采样间隔的通信群时，我们利用离散数学中埃及分数的Muirhead定理，给出了这些通信系统的可能带宽资源总和最大化的解。我们提供了一个精确的总结，过去的最佳插值逼近多维矢量信号，或更准确地说，多变量矢量信号，在Hilbert空间的扩展滤波器组，这是由Kida给出的。然后，我们将[20]中的一维结果推广到在给定多维传输滤波器组和任意连续最坏情况误差测度的条件下的多维矢量信号的逼近。这个问题已经研究多年，但有的结果需要对信号的带宽进行复杂的扩展，有的结果只能证明一维情况。因此，对于多维矢量信号的运行逼近问题，目前还没有得到精确的解决。基于图论中已知的k色数定理，定义了彩色多维多翼信号及其在彩色变量-向量空间中互不干扰的多维多翼近似。我们证明了这些多维多翼近似的主干成为所提出的运行近似。在这些讨论中，我们提出了一种扩展的多维向量滤波器组理论，该理论在给定的有限资源下实现了最高的运行近似性能。
Running approximation uses interpolation functions with limited supports and interpolates a signal in turn from an initial side to the other end of the signal. When continuous worst-case measures of arbitrary operators of error are given, we present the optimum multi-dimensional running approximation of vector-signals in a certain extended vector-filter bank that minimizes various worst-case measures of error, including a measure of error-rate, simultaneously. This multi-dimensional optimum running (scan-type) approximation uses a finite number of sample values which are updated step-like with movement of the variables-vector x on an n-dimensional variables-vector-space. Further, when a family of communication groups having different integer sampling-intervals larger than one is given, we present a solution of maximizing sum of possible band-widths resources of these communication systems by referring Muirhead's theorem in discrete mathematics for Egyptian fractions. We provide an exact summary of past optimum interpolation approximations of multi-dimensional vector-signals, or more exactly, multi-variables-vector-signals, in extended filter banks on a Hilbert space which are given by Kida. Then, we extend past one-dimensional results in [20] to approximation of multi-dimensional vector-signals under the condition that a multi-dimensional transmission filter bank and an arbitrary continuous worst-case-measure of error are given. This problem has been studied for many years, but one result requires complex extension of band-width of signals and others can prove one-dimensional case only. Hence, it is not solved exactly yet with respect to running approximation of multi-dimensional vector-signals. Based on known theorem of k-chromatic number in graph theory, we define a new concept of colored multi-dimensional multi-wing signals and the corresponding multi-dimensional multi-wing approximations that do not interfere each other in colored variables-vector-spaces. We show that backbone of these multi-dimensional multi-wing approximations becomes the presented running approximation. Throughout these discussions, we present a theory of extended multi-dimensional vector filter banks that achieves the highest performance of running approximation under given limited resources.