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The optimum running approximation of band-limited signals based on new concept of multi-legged-type signals in a hyper domain

机译：基于超域中多腿型信号新概念的带限信号的最佳运行逼近

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摘要

The minimization of the error associated with a running approximation by a filter bank is one of the most important problems of the signal processing. In this paper, for a set of vector-signals such that generalized Fourier transforms have weighted norms smaller than a given positive number, we present the extended optimum running approximation that minimizes various continuous worst-case measures of approximation error at. the same time. In this discussion, we introduce a new concept of multi-legged-type signal that is a combined-signal of many one-dimensional band-limited signals. Backbone of this multi-legged-type signal is constituted with a series of small separable segments of the above one-dimensional signals that are determined by the proposed running approximation. Based on this concept, we propose an approximation method of the multi-legged-type signals and we prove that this approximation is the optimum. Then, we define measures of error that become the proposed measures of error in the position of the backbone made by the corresponding running approximation and become small about the other errors. Based on these measures of error, we prove that the presented extended optimum approximation minimizes various continuous worst-case measures of the running approximation error at the same time. As an application, multiple-input multiple-output/space division multiplexing system is discussed.
机译：与滤波器组的运行逼近相关的误差的最小化是信号处理的最重要问题之一。在本文中，对于一组矢量信号（使广义傅里叶变换的加权范数小于给定正数），我们提出了扩展的最佳运行逼近，该逼近最小化了各种连续的最坏情况下的逼近误差。同一时间。在此讨论中，我们介绍了多腿型信号的新概念，它是许多一维带限信号的组合信号。该多腿型信号的骨干由上述一维信号的一系列小的可分离段组成，这些段由建议的运行近似确定。基于此概念，我们提出了一种多腿型信号的逼近方法，并证明了这种逼近是最优的。然后，我们定义误差度量，这些误差度量通过相应的运行近似而成为建议的骨干位置误差度量，而其他误差则变得很小。基于这些误差度量，我们证明了所提出的扩展最优逼近可同时最小化运行近似误差的各种连续最坏情况度量。作为一种应用，讨论了多输入多输出/空分复用系统。

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