Digital Filters Design for Signal and Image Processing

10.4. Bibliography

[BAR 93] BARRET M., Etude de la stabilité des filtres numénques récursifs bidimensionnels, PhD Thesis, University of Paris-Sud, Orsay, December 1993.

[BAR 94] BARRET M., BENIDIR M., “On the boundary of the set of Schur polynomials and applications to the stability of 1-D and 2-D digital recursive filters”, IEEE Trans. on Automatic Control, vol. 39, p. 2 335-2 339, November 1994.

[BEN 99] BENIDIR M., BARRET M., Stabilité des filtres et des systémes linéaires, Dunod, Paris, 1999.

[FRI 78] FRIEDLANDER B., KAILATH T., MORF M., LJUNG L., “Extended Levinson and Chandrasekhar equations for general discrete-time linear estimation problems”, IEEE Trans. on Automatic Control, vol. AC-23, no. 4, p. 653-659, August 1978.

[MIG 99] MIGNOTTE M., STEFUANESCU D., Polynomials: An algorithmic approach, Springer-Verlag, 1999.

¹ The Laurent series decomposes as the sum of a power series in z and a power series in z⁻¹. We recall that the convergence domain of a power series in z is a disk centered at the origin, of possibly infinite radius of the domain , then the series converges absolutely and if |z| > R, then the series diverges.

² A complex number ξ is the zero or root of a polynomial P(z) when P(ξ) = 0. The multiplicity order of ξ is then the integer k > 0, so that and , where ...