A constructive algorithm for 2-D spectral factorization with rational spectral factors

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 47, Issue 9, 2000, Pages 1309-1318

  Basu, Sankar ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ELECTRIC NETWORK SYNTHESIS; MATRIX ALGEBRA; PARAMETER ESTIMATION; POLYNOMIALS; SIGNAL THEORY; SPECTRUM ANALYSIS; WAVELET TRANSFORMS;

HERMITIAN POLYNOMIAL MATRICES; SPECTRAL FACTORIZATION;

SYSTEM THEORY;

EID: 0034262699     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.883325     Document Type: Article

References (24)

1. B. D. O. Andersen and J. B. Moore, Linear Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1971.
2. Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
3. S. Basu, ;Multidimensional filter banks and wavelets - A system theoretic perspective,; J. Franklin Inst., Invited Paper, vol. 335B, pp. 1367-1409, 1998. Special issue on Signal Processing.
4. ;A framework for 2-D hyperstability theory based provably convergent adaptive 2-D IIR filtering,; SIAM J. Contr. Opt., Nov. 1991.
5. C. Berg, J. P. R. Christensen, and P. Ressel, Harmonic Analysis on Semi-groups. New York: Springer-Verlag, 1984.
6. N. K. Bose, Applied Multidimensional Systems. New York: Van Nostrand Reinhold, 1981.
7. M. P. Ekstrom and J. Woods, ;Two dimensional spectral factorization with applications in digital filtering,; IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-24, pp. 115-128, Apr. 1976.
8. W. Habicht, ;Über the Zerlegung strikter definiter Formen in Quadrate,; Comment. Math. Helv., vol. 12, pp. 317-322, 1940.
9. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities. Cambridge, MA: Cambridge University Press, 1951.
10. D. Hilbert, ;Über Ternäre Definite Formen,; Acta Mathematica, vol. 32, pp. 169-197, 1893.
11. N. Jacobson, Basic Algebra, Volume 2. San Francisco, CA: Freeman.
12. A. Kummert, ;The synthesis of two-dimensional passive n-ports containing lumped elements,; Multidimensional Syst. Signal Processing, vol. 1, no. 4, pp. 351-362, 1990.
13. ;Spectral factorization of two-variable para-Hermitian polynomial matrices,; Multidimensional Syst. Signal Processing, vol. 1, no. 3, pp. 327-339, 1990.
14. T. Y. Lam, Algebraic Theory of Quadratic Forms. New York: W. A. Benjamin, 1973.
15. E. Landau, ;Über die Darstellung definiter Funktionen durch Quadrate,; Mathematische Annalen, vol. 62, p. 272, 1906.
16. S. Lang and J. Tate, Collected Papers of Emil Artin. Reading, PA: Addison-Wesley, 1965.
17. T. Marzetta, ;Two-dimensional linear prediction: Autocorrelation arrays, minimum-phase prediction error filters and reflection coefficient arrays,; IEEE Trans. Acoust. Speech, Signal Processing, vol. ASSP-28, pp. 725-733, Dec. 1980.
18. T. S. Motzkin, ;The arithmetic-geometric inequality,; in Inequalities, O. Shisha, Ed. New York: Academic, 1967.
19. R. W. Newcomb, Linear Multiport Synthesis. New York: McGraw-Hill, 1966.
20. P. Whittle, ;On Stationary processes in a plane,; Biometrica, vol. 41, pp. 434-449, Dec. 1954.
21. M. R. Wohlers, Lumped-Distributed Passive Networks: A Generalized and Advanced Viewpoint. New York: Academic, 1969.
22. ∞ Optimal Control. Boston, MA: Birkhauser, 1997.
23. R. Saeks, ;The factorization problem - A survey,; IEEE Proc., vol. 64, pp. 90-95, 1976.
24. D. C. Youla, ;On the factorization of rational matrices,; IEEE Trans. Inform. Theory, vol. IT-18, pp. 172-189, July 1961.