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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 universal multi-dimensional all-phase digital filter design method is proposed. Based on one-dimensional prototype all-phase digital filter (APDF), a multidimensional APDF with arbitrary parallelepiped passband is designed by multidimensional decimation transformation and retains the Nyquist and zero-phase characteristics. A new type of windowed APDF with excellent performance was designed by using a new type of optimized window function. As a one-dimensional prototype filter, an inseparable multi-dimensional windowed APDF was generated. The experimental results show that the performance of multi-dimensional windowed APDF based on the new optimized window is better than that of the multi-dimensional windowed APDF based on rectangular window, Kaiser window and Hamming window under the same filter length, and better than the traditional Chebyshev Approximation method designed multi-dimensional digital filter; it has good pass-band characteristics, the transitional steep, stopband attenuation surface is very flat, minimal ripple, to meet the higher attenuation index.