Abstract
In the process of model building, assumptions leading to linearity are routinely made since the resulting models can be thoroughly understood using analytical techniques. Another assumption that is also very commonly used along with linearity is the assumption of invariance, or uniformity, of structure with respect to some set of supporting variables which generally represent time (time-invariance) or space (space-invariance). The assumption of linearity and invariance permits harmonic analysis to be applied. Understanding model behavior and sensitivity to parameter settings is greatly simplified by using frequency domain representations, i.e., Fourier transforms, of appropriate functions.
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References
L. A. Zadeh, “Frequency Analysis of Variable Networks.” Proceedings of the I.R.E., 38, March 1950, pp. 291–299.
P. A. Franaszek and B. Liu, “On a Class of Linear Time-Varying Filters.” IEEE Transactions on Information Theory, IT-3, No. 4, October 1967, pp. 579–587.
R. L. Snyder, “A Partial Spectrum Approach to the Analysis of Quasi-Stationary Time Series.” IEEE Transactions on Information Theory, IT-3, No. 4, October 1967, pp. 579–587.
B. P. Zeigler, Theory of Modelling and Simulation. John Wiley and Sons, New York, 1976.
A. G. Barto, “Linear Cellular Automata and their Homomorphisms.” In: Frontiers in Modelling: Collected Dissertations, edited by B. P. Zeigler, forthcoming.
W. A. Porter and C. L. Zahm, Basic Concepts in System Theory. University of Michigan Technical Report 01656–2-T, Department of Electrical Engineering, 1969.
R. Saeks, “Causality in Hilbert Space.” SIAM Review, 12, No. 3, July 1970.
A. W. Naylor and G. Sell, Linear Operator Theory in Engineering and Science, Holt, Rinehart & Winston, 1971.
N. Y. Foo, “Homomorphic Simplification of Systems.” Ph.D. Dissertation, University of Michigan, Department of Computer and Communication Sciences, 1974.
M. A. Harrison, Lectures on Linear Sequential Machines. Academic Press, 1969.
V. Aladyev, “Survey of Research in the Theory of Homogeneous Structures and Their Applications.” Mathematical Biosciences, 22, 1974.
A. W. Burks (ed), Essays on Cellular Automata. University of Illinois Press, 1970.
H. Yamada and S. Amoroso, “Tessellation Automata.” Information and Control, 14, No. 3, 1969.
A. G. Barto, “Cellular Automata as Models of Natural Systems.” Ph.D. Dissertation, University of Michigan, Department of Computer and Communication Sciences, 1975.
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Springer-Verlag, Berlin, 1963.
A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Alogorithms. Addison-Wesley, Reading, Mass., 1974.
T. W. Cairns, “On the Fast Fourier Transform on Finite Abelian Groups.” IEEE Transactions on Computers, May 1971, pp. 569–571.
P. J. Nicholson, “Algebraic Theory of Finite Fourier Transforms.” J. of Computer and System Sciences, 5, No. 5, 1971.
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© 1978 Springer Science+Business Media New York
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Barto, A.G. (1978). Structurally Invariant Linear Models of Structurally Varying Linear Systems. In: Klir, G.J. (eds) Applied General Systems Research. NATO Conference Series, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0555-3_33
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DOI: https://doi.org/10.1007/978-1-4757-0555-3_33
Publisher Name: Springer, Boston, MA
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