We suggest new closely related methods for numerical inversion of $Z$-transform and Wiener-Hopf factorization of functions on the unit circle, based on sinh-deformations of the contours of integration, corresponding changes of variables and the simplified trapezoid rule. As applications, we consider evaluation of high moments of probability distributions and construction of causal filters. Programs in Matlab running on a Mac with moderate characteristics achieves the precision E-14 in several dozen of microseconds and E-11 in several milliseconds, respectively.

翻译：我们提出新的密切相关方法，用于单位圆上函数的$Z$变换数值逆变换与Wiener-Hopf因式分解。该方法基于积分轮廓的sinh变形、相应的变量替换以及简化梯形法则。作为应用，我们考虑了概率分布高阶矩的评估与因果滤波器的构造。在中等配置的Mac上运行的Matlab程序，分别可在几十微秒内达到E-14精度，在几毫秒内达到E-11精度。