单位圆周上具有重极点的Z变换与傅里叶变换相互计算的方法

Z-transform and Fourier Transform Mutual Calculation Method with Multiple Poles on Unit Circle

提出了一种单位圆周上具有重极点的Z变换(ZT)与傅里叶变换(DTFT)相互计算的方法。基于分解的基本思路,将单位圆周上具有重极点的ZT分解成单位圆周上含极点和不含极点两部分之和,针对单位圆周上含极点的ZT部分,分区内极点和区外极点两种情况,导出了利用ZT计算DTFT的方法;将序列的DTFT分解成解析部分与不解析部分之和,针对DTFT的不解析部分,分因果序列和反因果序列两种情况,导出了利用DTFT计算ZT的方法。

A mutual calculation method of Z-transform and Fourier transform with multiple poles on unit circle is proposed.Firstly,based on decomposing Z-transform of the sequence into the sum of the two parts including the poles on the unit circle and the poles not on the unit circle,the methods for computing the Fourier transform are derived respectively for the causal sequences and anti-causal sequences by using the Z transform.Then,based on decomposing the Fourier transform of the sequence into the sum of the analytical part and the non-analytical part,the methods for computing the Z-transform are deduced respectively for the causal sequences and anti-causal sequences by using the Fourier transform.