Mobius 函数及其在逆 Z 变换计算中的应用

Mbius Function and Its Application in Computing Inverse Z Transform

该文首先对一维Ｍｏｂｉｕｓ函数的一个性质作了证明，并定义了二维Ｍｏｂｉｕｓ函数，给出其有关性质的证明。文中重点讨论了运用二维Ｍｏｂｉｕｓ函数及二维序列的有限长傅里叶变换在单位双圆上的有限样值点，来计算无限长二维时域序列的逆Ｚ变换的问题。并将二维双边序列的逆Ｚ变换问题全部转化为第一象限问题来讨论，所得公式非常便于计算机实现。

This paper proves a characteristic of a 1D Mbius function, defines a 2D Mbius function and proves its characteristic . It emphasizes on computing inverse Z transform for 2D infinite length time domain series, that is by using 2D Mbius function and finite values of X(Z 1,Z 2) sampled in unit bicircle. These samples are just the finite length 2D discrete Fourier transform. All the problems of computing inverse Z transform for 2D infinite length series are transfered into quadrant 1 and discussed here. This method is convenient to computer calculation.