Applied General Systems Research pp 435-451 | Cite as
Structurally Invariant Linear Models of Structurally Varying Linear Systems
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.
Keywords
Weighting Function Cellular Automaton Discrete Fourier Transform Homomorphic Image Impulse Response FunctionPreview
Unable to display preview. Download preview PDF.
References
- 1.L. A. Zadeh, “Frequency Analysis of Variable Networks.” Proceedings of the I.R.E., 38, March 1950, pp. 291–299.CrossRefGoogle Scholar
- 2.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.Google Scholar
- 3.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.CrossRefGoogle Scholar
- 4.B. P. Zeigler, Theory of Modelling and Simulation. John Wiley and Sons, New York, 1976.Google Scholar
- 5.A. G. Barto, “Linear Cellular Automata and their Homomorphisms.” In: Frontiers in Modelling: Collected Dissertations, edited by B. P. Zeigler, forthcoming.Google Scholar
- 6.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.Google Scholar
- 7.R. Saeks, “Causality in Hilbert Space.” SIAM Review, 12, No. 3, July 1970.Google Scholar
- 8.A. W. Naylor and G. Sell, Linear Operator Theory in Engineering and Science, Holt, Rinehart & Winston, 1971.Google Scholar
- 9.N. Y. Foo, “Homomorphic Simplification of Systems.” Ph.D. Dissertation, University of Michigan, Department of Computer and Communication Sciences, 1974.Google Scholar
- 10.M. A. Harrison, Lectures on Linear Sequential Machines. Academic Press, 1969.Google Scholar
- 11.V. Aladyev, “Survey of Research in the Theory of Homogeneous Structures and Their Applications.” Mathematical Biosciences, 22, 1974.Google Scholar
- 12.A. W. Burks (ed), Essays on Cellular Automata. University of Illinois Press, 1970.Google Scholar
- 13.H. Yamada and S. Amoroso, “Tessellation Automata.” Information and Control, 14, No. 3, 1969.Google Scholar
- 14.A. G. Barto, “Cellular Automata as Models of Natural Systems.” Ph.D. Dissertation, University of Michigan, Department of Computer and Communication Sciences, 1975.Google Scholar
- 15.E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Springer-Verlag, Berlin, 1963.CrossRefGoogle Scholar
- 16.A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Alogorithms. Addison-Wesley, Reading, Mass., 1974.Google Scholar
- 17.T. W. Cairns, “On the Fast Fourier Transform on Finite Abelian Groups.” IEEE Transactions on Computers, May 1971, pp. 569–571.Google Scholar
- 18.P. J. Nicholson, “Algebraic Theory of Finite Fourier Transforms.” J. of Computer and System Sciences, 5, No. 5, 1971.Google Scholar