基于二次规划的2D FIR滤波器设计

2D FIR Filter Design Based on Quadratic Programming

本文提出了一种新型的基于McClenllan变换和二次规划的2DFIR滤波器设计方法。该方法使用McClenllan变换来实现从1D原型滤波器向2D滤波器的频率映射。在设计过程中,使用二次规划方法来求解McClenllan变换的最优系数,通过对二次规划使用一些限制条件,避免了传统的尺度变换问题。与传统的2DFIR滤波器设计方法相比,该方法使映射中1DFIR通带截止频率和阻带截止频率两点误差平方和达到最小,通过实际的扇形滤波器和菱形滤波器设计证明,本文的基于二次规划的方法是一种有效的2DFIR滤波器设计方法。

A novel method is proposed for 2D FIR filter design in this paper, which is based on McClellan transform and quadratic programming algorithm. The McClellan transform is used to map the 1D prototype FIR filter frequency points into 2D frequency contours. A quadratic programming approach is used to determine the optimal coefficients of McClellan transform. A set of constraints are introduced into the quadratic programming algorithm so that the conventional transform scaling problem can be avoided. Compared with conventional 2D FIR filter design method in literatures, the coefficients of the designed 2D FIR filters using the proposed method are optimized by minimizing the sum of squared errors along the desired contours mapped from cut off frequencies in both pass band and stop band. Two practical design examples demonstrate the effectiveness of the proposed method, which include fan filter and diamond filter.