Abstract
In this article, special properties of m-D first order discrete recursive processes are discussed. The results are interpreted in view of the well-known results of 1-D processes and their significance within the general theory of m-D systems is highlighted. In particular it is demonstrated that first order m-D processes share the same properties as 1-D first order processes in many aspects. This includes robustness against nonlinear effects and shift-varying conditions as well as stability under zero and non-zero input conditions, the effect of spectral transformations and the dynamic behavior in the space- (time-) domain. It is shown that the results in the 1-D theory follow from the developed m-D theory by formally settingm=1. This pertains to the closed form representation of the impulse response, the robustness properties and the stability conditions.
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Bauer, P.H. Robustness and stability properties of first order multi-dimensional (m-D) discrete processes. Multidim Syst Sign Process 1, 75–86 (1990). https://doi.org/10.1007/BF01812208
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DOI: https://doi.org/10.1007/BF01812208