A Matrix Euclidean Algorithm for minimal partial realization

A matrix Euclidean algorithm for minimal partial realization

A Matrix Euclidean Algorithm induced by State Space Realization

An eecient algorithm is developed for determining the greatest common left divisor (GCLD) of two polynomial matrices. Knowing this divisor allows for several immediate applications: In coding theory, a noncatastrophic convolutional encoder can be derived from an arbitrary one. In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found. In linear algeb...

Minimal stable partial realization

An asymptotically stable minimal order realization of a partial sequence of Markov parameters is achieved by reducing the problem to a standard but minimal one in decision algebra. Summary—In this paper two equivalent sets of necessary and sufficient conditions for the existence of an asymptotically stable partial realization are developed. Both sets are expressed as multivariable polynomial eq...

Euclidean Algorithm for Laurent Polynomial Matrix Extension

In this paper, we develop a novel and effective Euclidean algorithm for Laurent polynomial matrix extension (LPME), which is the key of the construction of perfect reconstruction filter banks (PRFBs). The algorithm simplifies the dual-chain approach to the construction of PRFBs in the paper [5]. The algorithm in this paper can also be used in the applications where LPME plays a role.

A Euclidean Algorithm for Binary Cycles with Minimal Variance

The problem is considered of arranging symbols around a cycle, in such a way that distances between different instances of a same symbol be as uniformly distributed as possible. A sequence of moments is defined for cycles, similarly to the well-known praxis in statistics and including mean and variance. Mean is seen to be invariant under permutations of the cycle. In the case of a binary alphab...