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首页> 外文期刊>IEEE Transactions on Automatic Control >Semi-infinite linear programming: a unified approach to digital filter design with time- and frequency-domain specifications
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Semi-infinite linear programming: a unified approach to digital filter design with time- and frequency-domain specifications

机译：半无限线性规划：采用时域和频域规范的统一数字滤波器设计方法

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摘要

Using the recently developed semi-infinite linear programming techniques and Caratheodory's dimensionality theory, we present a unified approach to digital filter design with time and/or frequency-domain specifications. Through systematic analysis and detailed numerical design examples, we demonstrate that the proposed approach exhibits several salient features compared to traditional methods: 1) using the unified approach, complex responses can be handled conveniently without resorting todiscretization; 2) time-domain constraints can be included easily; and 3) any filter structure, recursive or nonrecursive, can be employed, provided that the frequency response can be represented by a finite-complex basis. More importantly, the solutionprocedure is based on the numerically efficient simplex extension algorithms. As numerical examples, a discrete-time Laguerre network is used in a frequency-domain design with additional group-delay specifications, and in a H{sub}∞ -optimal envelopeconstrained filter design problem. Finally, a finite impulse response phase equalizer is designed with additional frequency domain H{sub}∞ robustness constraints.
机译：利用最近开发的半无限线性规划技术和Caratheodory的维数理论，我们提出了一种具有时域和/或频域规范的数字滤波器设计的统一方法。通过系统分析和详细的数值设计算例，证明了所提方法与传统方法相比具有几个显著特点：1）使用统一方法，无需诉诸离散化即可方便地处理复杂的响应;2）可以很容易地包含时域约束;3）可以采用任何递归或非递归的滤波器结构，前提是频率响应可以用有限复基表示。更重要的是，求解过程基于数值高效的单纯形扩展算法。作为数值示例，离散时间拉盖尔网络用于具有附加群延迟规范的频域设计，以及 H{sub}∞ 最优包络约束滤波器设计问题。最后，设计了一种具有附加频域H{sub}∞鲁棒性约束的有限脉冲响应相位均衡器。

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