基于矩形窗二叉分解的窗函数设计

Design of Window Function Based on Bifurcation of Rectangular Window

在FIR滤波器的窗函数设计方法中,窗的选择直接影响滤波器的性能优劣.为了找到好的窗函数,文中首先给出了一种新结构的频率域数字滤波器结构,经过理论推导找到与其相对应的FIR滤波器结构以及满足线性相位的条件;在分析其幅频特性的基础上,提出一种基于矩形窗二叉分解的窗设计算法.该算法将系统中的窗看作由二叉树中左右低阶的矩形窗卷积形成,并利用递归来形成多级分解而构造不同的窗函数.实验证明,有效的二叉分解得到的窗可使系统传输特性的阻带最小衰减达到-100db以下,并且在通带和阻带中基本无波纹.

In designing FIR filter with window function, how to choose the window has direct effect on the performance of the filter. In order to explore a fine window function to promote the capability of a filter, a novel-structured digital filter in frequency domain is firstly presented, and hence the corresponding FIR model system and condition for linear phrase are given; by analyzing its amplitude-frequency property, a novel algorithm to design windows based on bifurcation of rectangular window is proposed. This algorithm treats that the window of system is formed by convolution of left and right lower-ordered rectangular windows in the dichotomizing tree, therewithal generates multilevel analysis for various window functions in terms of recursion. The experiment proves that the minimum attenuation of the filter with such window is below -100 db, and there′s no ripples across the pass and stop band.