Boundedness of Multidimensional Filters Over a Prescribed Frequency Domain
Boundedness of Multidimensional Filters Over a Prescribed Frequency Domain
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DOI：
10.1109/tsp.2008.929130
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发表时间：
2008-11
影响因子：
5.4
通讯作者：
T. Zhou
中科院分区：
文献类型：
--
作者：
T. Zhou
信号处理往往需要在某些特定的频域上同时确定一个滤波器的大小。基于多元矩阵多项式的跨度结构，给出了多维多输入多输出(MIMO)无限冲激响应(IIR)滤波器在长方体频域上有界性的一个充分条件。该条件通过一个线性矩阵不等式(LMI)来表示，并且可以证明它比由矩阵结构奇异值的上界导出的条件更不保守。此外，利用参数相关的LMI和滤波器的线性分式变换结构，还得到了该有界性验证问题的两个充要条件，并同样用LMI表示。在此基础上，给出了适用于滤波器设计的基于LMI的滤波器输出矩阵和直接传输矩阵的条件。数值算例说明了所得理论结果的有效性和特点。
Signal processing often requires the magnitude of a filter simultaneously upper and lower bounded on some specified frequency domains. In this paper, on the basis of the structure of the span of a multivariate matrix polynomial, a sufficient condition is derived for the boundedness of a multidimensional multiple-input multiple-output (MIMO) infinite-impulse-response (IIR) filter over a cuboid frequency domain. This condition is expressed through a linear matrix inequality (LMI) and can be proved to be less conservative than a condition derived from an upper bound of matrix structured singular value. Moreover, using parameter dependent LMIs and the linear fractional transformation structure of the filter, two necessary and sufficient conditions are also obtained for this boundedness verification problem, which are again expressed by LMIs. Furthermore, LMI based conditions are derived for filter output matrix and direct transmission matrix, which are applicable to filter design. Numerical examples are included to illustrate the efficiency and characteristics of the derived theoretical results.