In this paper a straightforward z-domain procedure for realizing multidimensional transfer functions with either numerator or denominator polynomial separable is presented. This procedure yields structures with minimum number of multipliers. It is shown that the number of delay elements can be reduced by selecting the optimum values for certain parameters. To facilitate this theorems that are applicable for some special cases are presented.
This is a preview of subscription content,to check access.
Access this article
Similar content being viewed by others
S. K. Mitra, A. D. Sagar, and N. A. Pendergrass, “Realizations of Two-Dimensional Recursive Digital Filters,” IEEE Trans. Circuits Syst., vol. 22, 1975, pp. 177–184.
S. Y. Kung, B. C. Levy, M. Morf, and T. Kailath, “New Results in 2–D Systems Theory, Part II: 2–D State Space Methods—Realization and Notions of Controllability, Observability and Minimality,” Proc. IEEE, vol. 65, 1977, pp. 945–961.
D. S. K. Chan, “A Simple Derivation of Minimal and Near-Minimal Realizations of 2–D Transfer Functions,” Proc. IEEE, vol. 66, 1978, pp. 515–516.
S. K. Mitra and S. Chakrabarti, “A New Realization Method for 2–D Digital Transfer Functions,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 26, 1978, pp. 544–550.
E. Fornasini, “On the Relevance of Noncommutative Power Series in Spatial Filter Realization,” IEEE Trans. Circuits Syst., vol. 25, 1978, pp. 290–299.
S. Chakrabarti and S. K. Mitra, “Decision Methods and Realization of 2–D Digital Filters Using Minimum Mumber of Delay Elements,” IEEE Trans. Circuits Syst., vol. 27, 1980, pp. 657–666. (See IEEE Trans. Circuits Syst., vol. 28, 1981, pp. 262–263, for corrections).
V. Ganapathy, D. Raghuramireddy, and P. S. Reddy, “Comments on Decision Methods and Realization of 2–D Digital Filters using Minimum Number of Delay Elements,” IEEE Trans. Circuits Syst., vol. 31, 1984, pp. 308–310.
T. Venkateswarlu, C. Eswaran, and A. Antoniou, “Realization of Multidimensional Digital Transfer Functions,” International Journal on Multidimensional Systems and Signal Proce., no. 1, 1990, pp. 179–198.
S. J. Varoufakis, P. N. Paraskevopoulos, and G. E. Antoniou, “On the Minimal State-space Realization of All Pole and All Xero 2–D Systems,” IEEE Trans. on Circuits and Systems, vol. CAS-34, 1987, pp. 289–292.
G. E. Antoniou, P. N. Paraskevopoulos, and S. J. Varoufakis, “Minimal State-Space Realization of Factorable 2–D Transfer Functions,” IEEE Trans. on Circuits and Systems, vol. CAS-35, 1988, pp. 1055–1058.
K. Galkowski, “The State-Space Realization of an n-Dimensional Transfer Function,” Int. J. Circuit Theory and Applications, vol. 9, 1981, pp. 189–197.
P. N. Paraskevopoulos, G. E. Antoniou, and S. J. Varoufakis, “Minimal State-Space Realization of 3–D Systems,” IEE Proc., vol. 135, Pt.G, 1988, pp. 65–70.
A. J. Kanellakis, P. N. Paraskevopoulos, N. J. Theodorou, and S. J. Varoufakis, “On the Canonical State-Space Realization of 3–D Discrete Systems,” IEE Proc., vol. 136, Pt. G, 1989, pp. 19–31.
S. H. Mentzelopoulou and N. J. Theodorou, “n-Dimensional Minimal State-Space Realization,” IEEE Trans. Circuits and Systems, vol. 38, 1991, pp. 340–343.
A. Kawakami, “A Realization Method of Separable-Numerator 3–D Transfer Functions,” IEICE Trans., vol. J72–A (in Japanese), no. 7, 1989, pp. 1148–1150.
E. Watanabe and A. Nishihara, “Synthesis of Separable-Denominator Multidimensional Digital Lattice Filters,” Electronics and Communications in Japan (in English), Part 3, vol. 77, 1994, pp. 97–105.
About this article
Cite this article
Venkateswarlu, T., Eswaran, C. Realization of Multidimensional Digital Transfer Functions with Separable Numerator or Denominator Polynomials. Multidimensional Systems and Signal Processing 10, 201–211 (1999). https://doi.org/10.1023/A:1008454630134