Skip to main content
Log in

Transfer Function Computation for Multidimensional Systems

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

A theoretically interesting technique is proposed for the determination of the coefficients of the determinantal polynomial and the coefficients of the adjoint polynomial matrix of a given n-D system, described by the Fornasini-Marchesini state space model. The proposed algorithms are based on the discrete Fourier transform (DFT), and easily can be implemented. An example is included to illustrate the application of the algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N.K. Bose, Applied Multidimensional Systems Theory, Van Nostrand, 1982.

  2. T. Venkateswarlu and C. Eswaran, ''Realization of Multidimensional Digital Transfer Functions with Separable Numerator and Denominator Polynomials,'' Multidimensional Systems and Signal Processing, vol. 10, 1999, pp. 201-211.

    Google Scholar 

  3. T. Venkateswarlu, C. Eswaran, and A. Antoniou, ''Realization of Multidimensional Digital Transfer Functions,'' Multidimensional Systems and Signal Processing, vol. 1, 1990, pp. 179-198.

    Google Scholar 

  4. K. Galkowski, ''State Space Realizations on N-D systems,'' Wroclaw Technical University, Monograph No. 76, 1994.

  5. G.E. Antoniou, ''Minimal State Space Realization of Multidimensional Systems Using Continued Fraction Expansions,'' Control Theory and Advanced Technology, vol. 7, no. 1, 1991, pp. 129-145.

    Google Scholar 

  6. G.E. Antoniou, S.J. Varoufakis, and P.N. Paraskevopoulos, ''M-Dimensional Continued Fraction Inversion,'' IEE Proceedings, Part G, vol. 136, pt. G, no. 6, 1989, pp. 307-312.

    Google Scholar 

  7. N.E. Mastorakis, ''Approximate Stable Multidimensional Polynomial Factorization into Linear m-D Polynomial Factors,'' Kybernetika, vol. 32, no. 3, 1996, pp. 275-288.

    Google Scholar 

  8. N.E. Mastorakis, ''Multidimensional Spectral Factorization Through the Reduction Method of Multidimensional Polynomial Factorization,'' Journal of Applied Mathematics and Computer Science, vol. 5, no. 1, 1995, pp. 11-19.

    Google Scholar 

  9. G.O. Glentis, et al.,''Transfer Function Determination of Multidimensional Singular Systems Using the FFT,'' Inter. J. Systems Science, vol. 24, no. 1, 1993, pp. 211-218.

    Google Scholar 

  10. E. Fornasini and E. Marchesini, ''Doubly Indexed Dynamical Systems: State Space Models and Structural Properties,'' Math. System Theory, vol. 12, no. 1, 1978, pp. 59-72.

    Google Scholar 

  11. G.E. Antoniou, G.O.A. Glentis, S.J. Varoufakis, and D.A. Karras, ''Transfer Function Determination of Singular Systems Using the DFT,'' IEEE Trans. Circuit Syst., vol. CAS-36, 1989, pp. 1140-1142.

    Google Scholar 

  12. D.E. Dudgeon and R.M. Mersereau, Multidimensional Digital Signal Processing, Prentice Hall, 1984.

  13. T. Kaczorek, Linear Control Systems, John Wiley Publishers, vol. 2, 1993.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Antoniou, G.E. Transfer Function Computation for Multidimensional Systems. Multidimensional Systems and Signal Processing 13, 419–426 (2002). https://doi.org/10.1023/A:1019936615341

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019936615341

Navigation