Optimal Design of Filters for Multirate Systems

本研究的目的是开发设计最佳多速率数字滤波器的程序。用于最优性的准则是从表示过滤器的线性算子的范数中导出的。当应用于线性时不变滤波器的设计时，这种最优性度量降低到通常的切比雪夫频域误差准则。对于多速率系统，该方法给出了滤波器最优性的新准则。这提供了一个定量的、分析的设计过程，产生比常用的直观设计方法更好的过滤器。开发适当误差函数的方法使用了周期时变线性系统的奇异值分解和分析技术。高效设计算法的开发是基于半无限规划和类似remez的多重交换方法。本研究旨在确定多速率滤波器的性能限制，并提供改进的滤波器。目前的设计可以与可达到的最佳设计进行比较，以确定可能的改进。

Parks The objective of this research is to develop procedures for the design of optimum multirate digital filters. The criterion used for optimality is derived from the norm of a linear operator that represents the filter. When applied to the design of linear, time-invariant filters this measure of optimality reduces to the usual Chebyshev frequency domain error criterion. For multirate-systems, this approach leads to a new criterion for filter optimality. This provides a quantitative, analytic design procedure that yields better filters than intuitive design methods that are in common use. The methods for the development of appropriate error functions use techniques from singular value decomposition and analysis of periodically time-varying linear systems. The development of efficient design algorithms is based on semi-infinite programming and Remez-like multiple exchange methods. This research is expected to establish limits for performance of multirate filters as well as to provide improved filters. Present designs can be compared with the best attainable to determine possible improvements.