Singular root distribution problem for delta-operator based real polynomials (Q1298215)

Zero location tests for the delta-operator-based polynomials in the case of algorithmic singularity (singular case I and singular case II) are presented. The singular case I with the Schur-Cohn test by Pal and Kailath is modified and transformed into the delta-domain. As the sampling interval vanishes the new algorithm converges to an \(s\)-domain singular case I test associated with the \(s\)-domain Schur-Cohn test. The singular case II is also considered and the difference between the traditional approaches in the \(z\)-domain and the \(s\)-domain reconciled. Numerical examples are given to illustrate better numerical properties of the new test over the Pal-Kailath recursion for fast sampling.