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Efficient inverse $Z$-transform and Wiener-Hopf factorization

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  • Svetlana Boyarchenko
  • Sergei Levendorskiu{i}

Abstract

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.

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  • Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2024. "Efficient inverse $Z$-transform and Wiener-Hopf factorization," Papers 2404.19290, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2404.19290
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    File URL: http://arxiv.org/pdf/2404.19290
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