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Nonessential singularities of the second kind and stability for multidimensional digital filters

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Abstract

In this paper, certain problems concerning nonessential singularities of the second kind (NSSKs), especially continuous NSSKs for 3-D digital filters, are discussed. It is shown that continuous NSSKs, both inT 2 U and onT 3, may exist in stable systems. Based on the Weierstrass theorem of multidimensional complex analysis, the existence criteria of continuous NSSKs inT 2 U and onT 3 are obtained. Certain basic properties of this type of singularities are given. A stability condition for a transfer functionH(Z) with continuous NSSKs and the inverse ofH(Z) is derived. Furthermore, for isolated NSSKs, a new necessary and sufficient condition for stability is developed for a class of systems.

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Authors and Affiliations

  1. Institute of Information Science, Northern Jiao-Tong University, 100044, Beijing, People's Republic of China

    Lizhi Wang & Du Xiyu

  2. Department of Automation, Tsinghua University, 100084, Beijing, People's Republic of China

    Fei Xia

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  1. Lizhi Wang
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  2. Du Xiyu
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  3. Fei Xia
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Wang, L., Xiyu, D. & Xia, F. Nonessential singularities of the second kind and stability for multidimensional digital filters. Multidim Syst Sign Process 3, 363–380 (1992). https://doi.org/10.1007/BF01940231

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  • DOI: https://doi.org/10.1007/BF01940231

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