全相位多维多抽样率数字滤波器设计

Design of All Phase Multidimensional Multirate Digital Filter

基于一维全相位数字滤波器(APDF),提出了通用的全相位多维多抽样率数字滤波器设计方法.该方法适用于抽取/内插矩阵为任意有理数情况,能够保持奈奎斯特特性和零相位特性,可将一维APDF的优良特性继承到多维滤波器.由一维APDF的波纹和过渡带参数,导出了结果滤波器的通带、阻带波纹和过渡带向量的估算公式.另外,研究了一种根据理想通带参数寻找对应抽取/内插矩阵的方法,并给出了抽取/内插矩阵分别为整数和有理数时的2个实例.在滤波器长度相同的情况下,与传统方法相比,所设计的全相位多维多抽样率滤波器过渡带略宽,但通带波纹和阻带波纹更小,阻带衰减更大,具有良好的幅频特性.

A general method for designing all phase multidimensional（MD）multirate digital filter was presented based on one-dimensional（1D）all phase digital filter（APDF）,which is applicable to arbitrary rational decima-tion/expansion matrix.The resulting MD multirate filters inherit excellent properties,such as zero phase property and Nyquist constraint property,from 1D APDF.Their passband and stopband ripples and transition band vector were estimated in terms of the ripples and transition band of 1D prototype filter.Furthermore,a method of computing the corresponding matrix was studied according to the specifications of the ideal passband.Two design examples were given with integer and rational decimation/expansion matrix respectively.Under the condition of the same filter length,compared with traditional method,the resulting all phase MD multirate filters using the proposed method have better amplitude-frequency response characteristics.Except for slightly wider transition band,the pass band and stopband are much flatter with rather small ripples.