A unified pole-zero module for linear transfer functions |
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Authors: | Bostwick F. Wyman Michael K. Sain |
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Affiliation: | Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA;Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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Abstract: | A new module-theoretic tool is presented for the study of linear time-invariant input/output maps (‘transfer functions’). For suitable subrings of the field k(s) of rational functions, an O-module called the structure module can be attached to each transfer function. This structure module naturally contains the classical (Kalman) pole module as a submodule which gives the (Wyman-Sain) multivariable zero module as the corresponding factor module. A posteriori the resulting exact sequence splits, and the structure module is isomorphic to the direct sum of the pole module and the zero module. Calculations over local rings echo valuation-theoretic results obtained by Kung and Kailath. |
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Keywords: | Pole module Multivariable zero module |
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