Iterative Reweighted Least Squares Design of Digital Filters

数字滤波器的迭代重加权最小二乘设计

• 批准号: 9316588
• 负责人: C. Sidney Burrus
• 金额: --
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9316588&HistoricalAwards=false
• 关键词: Iterative; Reweighted; Least; Squares; Design

This research is developing a new and significantly better method for the design of a wide variety of digital filters. The new method is based on a successive approximation algorithm called Iteratively Reweighted Least Squares (IRLS). One form of IRLS, Lawson's algorithm, has been used before but not extensively because of slow and inconsistent convergence. Initial results with the new method using a second order IRLS with a form of path- following or homotopy modification have produced a robust, quadratically converging, efficient, versatile filter design technique. The method finds general L^p approximations with 1=p. It also allows different criteria in different bands for the design of mixed criteria optimal filters. The new method solves, not only the standard filter design problems, but many that the Parks- McClellan Remez algorithm or windowed least wquares will not. Initial results on designing with constrained L^p criteria, complex approximation, and two dimensions show great promise. Robust convergence is crucial for the practical success of any iterative algorithm. We feel that we have a potential breakthrough on that issue. This research is doing a theoretical analysis of the convergence for the more general optimization criteria, developing a practical adaptive filter design program, and presenting it in a form accessible to the practicing engineer. The algorithm will be applied to three filter design problems: a) the constrained least-squares and, more generally, the constrained L^p approximation problem. This is often what people really want when they use a straight Chebyshev or window design. b) The important problems of complex approximation which is important in equalization adaptive filter design. c) The multidimensional filter design and image processing problems. This new approach shows excellent promise and a possible great improvement over present techniques.

这项研究正在开发一种新的和显着更好的方法，用于设计各种数字滤波器。 新方法是基于一个逐次逼近算法称为迭代加权最小二乘法（IRLS）。 一种形式的IRLS，劳森的算法，已经使用过，但没有广泛使用，因为缓慢和不一致的收敛。 使用二阶IRLS与路径跟踪或同伦修改的形式的新方法的初步结果产生了一个强大的，二次收敛，有效的，通用的滤波器设计技术。 该方法发现一般L^p近似1= p。 它还允许在不同的频带不同的标准的混合准则的最佳滤波器的设计。 新方法不仅解决了标准滤波器设计问题，而且解决了Parks- McClellan Remez算法或窗口最小二乘法无法解决的许多问题。 在约束L^p准则、复近似和二维设计方面的初步结果显示出很大的希望。 鲁棒收敛对于任何迭代算法的实际成功都是至关重要的。 我们认为，我们在这个问题上有可能取得突破。 本研究是做一个理论分析的收敛性更一般的优化准则，开发一个实用的自适应滤波器的设计程序，并提出它在一个形式访问的实践工程师。 该算法将应用于三个滤波器设计问题：a）约束最小二乘，更一般地说，约束L^p近似问题。 这通常是人们真正想要的，当他们使用直切比雪夫或窗口设计。 B）在均衡自适应滤波器设计中，复逼近的重要问题。 c）多维滤波器设计和图像处理问题。 这种新方法显示出良好的前景和可能的巨大改进，目前的技术。