FIR滤波器设计的半无穷维二次优化方法

Semi-infinite Quadratic Optinization Techniques for the Design of Fir Digital Filters

Parks-McClellan方法是FR滤波器设计中常用的设计方法。这种方法基于最小最大误差判据，使得设计的滤波器响应与期望滤波器响应之间的最大误差最小化，但是忽略了误差能量。该文基于半无穷维二次优化（SDO）技术给出一个设计FIR数字滤波器的新方法。该方法把FIR滤波器设计问题转化为SIQO模型．在峰值误差满足给定指标的条件下，使得设计滤波器与理想滤波器之问的误差能量最小化。与ParksMcCellan方法相比，该文方法在牺牲较少的最大阻带增益的情况下极大地降低了阻带误差能量。设计实例证实了该方法的有效性。

Parks-McClellan method is awidely used method for the design of FIR fil-ters The method has mininized the maxinum error between the desired filter and the designed one regardless of the error energy. This paper proposes a new method for the design of FIR filter by using son i-infinite quadratic optinization （SIQO） techniques This method form ulates the FIR filter design into SIQO model, which minimizes the error energy between the desired filter and the designed one subject to the specifications of the peak error.In comparisonwith the Parks-McCiellan method, the new method has greatly reduced stopband error energy with the slight increase of maxinum stopband gain Design examples show the effectiveness of the new method.