基于新型优化窗的多维全相位数字滤波器设计

Design of multi-dimensional all phase digital filter based on a new optimized window

提出一种通用的多维全相位数字滤波器的设计方法。基于一维原型全相位数字滤波器(APDF),通过多维抽取变换,设计出具有任意平行六面体通带的多维APDF,并保持奈奎斯特约束特性和零相位特性。利用一种新型优化窗函数设计了性能优异的一维加窗APDF,将其作为一维原型滤波器,生成了不可分离的多维加窗APDF。实例表明,在滤波器长度相同的情况下,基于新型优化窗的多维加窗APDF的性能优于基于矩形窗、凯塞窗和汉明窗的多维加窗APDF,并且优于采用传统切比雪夫逼近法设计的多维数字滤波器;它具有良好的通带特性,过渡带陡峭,阻带衰减曲面非常平坦,波纹极小,可满足更高的衰减指标。

A general method for designing multi-dimensional（MD） all phase digital filter（APDF） is presented in this paper.All such filters with an arbitrary parallelepiped-shaped passband can be designed based on an appropriate one-dimensional（1D） prototype APDF through performing MD decimation transformation.The proposed method can preserve the Nyquist constraint and zero-phase properties from the 1D prototype filter.A novel 1D APDF with a new optimized window is designed and used as 1D prototype filter with superior performance.Thus,a non-separable MD windowed APDF is obtained by using the proposed method.With the same filter length,design examples show that the performance of MD windowed APDF based on the new optimized window is not only superior to that based on Rectangle,Kaiser and Hamming windows,but also better than that of the MD digital filter using the traditional Chebyshev approximation approach.It has better passband property and narrower transition band.More importantly,its stopband attenuation surface is much flatter with rather small ripples,which can satisfy higher-performance attenuation specification.