Abstract
A new class of rectangular zero prime multivariate polynomial matrices are introduced and their inverses are computed. These matrices are ideal for use in multidimensional systems involving input-output transformations. We show that certain multivariate polynomial matrices, when transformed to the sequence space domain, have an invertible subsequence map between their input and output sequences. This invertible subsequence map can be used to derive the polynomial inverse matrix together with a set of pseudo-inverses. All computations are performed using elementary operations on the ground field without using any polynomial operations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bose, N.K. (ed.): Multidimensional Systems: Progress, Directions and Open Problems. Reidel, Dordrecht, The Netherlands (1985)
Youla, D.C., Gnavi, G.: Notes on n-dimensional system theory. IEEE Trans. Circuits and Systems 26, 105–111 (1979)
Youla, D., Pickel, P.: The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices. IEEE Trans. Circuits and Systems 31(6), 513–517 (1984)
Park, H., Kalker, T., Vetterli, M.: Grobner bases and multidimensional FIR multirate systems. Journal of multidimensional systems and signal processing 8, 11–30 (1997)
Fornasini, E., Valcher, M.E.: nD polynomial matrices with applications to multidimensional signal analysis. Multidimensional Systems and Signal Processing 8, 387–408 (1997)
Fornasini, E., Valcher, M.E.: Algebraic aspects of 2D convolutional codes. IEEE Trans. Inform. Theory IT-40(4), 1068–1082 (1994)
Weiner, P.A.: Basic properties of multidimensional convolutional codes. In: Codes, Systems and Graphical Models. IMA Volumes in Mathematics and Its Applications, vol. 123, pp. 397–414. Springer, New York (2001)
Luerssen, H.G., Rosenthal, J., Weiner, P.A.: Duality between multidimensional convolutional codes and systems. In: Colonius, F., Helmke, U., Wirth, F., Prätzel-Wolters, D. (eds.) Advances in Mathematical Systems Theory, A Volume in Honor of Diederich Hinrichsen, Birkhauser, Boston, pp. 135–150 (2000)
Vologiannidis, S., Karampetakis, N.: Inverses of multivariable polynomial matrices by discrete fourier transforms. Multidimensional Systems and Signal Processing 15(4), 341–361 (2004)
Lobo, R.G., Bitzer, D.L., Vouk, M.A.: Locally invertible multivariate polynomial matrices. In: Ytrehus, Ø. (ed.) WCC 2005. LNCS, vol. 3969, pp. 481–490. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lobo, R.G., Bitzer, D.L., Vouk, M.A. (2006). Locally Invertible Multivariate Polynomial Matrices. In: Ytrehus, Ø. (eds) Coding and Cryptography. WCC 2005. Lecture Notes in Computer Science, vol 3969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779360_33
Download citation
DOI: https://doi.org/10.1007/11779360_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35481-9
Online ISBN: 978-3-540-35482-6
eBook Packages: Computer ScienceComputer Science (R0)