Yves G. Kamp

Orthogonal polynomial matrices on the unit circle

This paper proposes a natural matrix extension of the classical theory of orthogonal polynomials on the unit circle introduced by Szego. As a result, orthogonal polynomial matrices appear to be a unifying concept in various mathematical aspects of circuit and system theory.

A generalization of the Levinson algorithm for Hermitian Toeplitz matrices with any rank profile

The paper describes a recursive algorithm for solving Hermitian Toeplitz systems of linear equations, without any restriction on the ranks of their nested Toeplitz subsystems. Such a general algorithm is needed, e.g., to obtain the eigenfilters for signal processing applications, or to compute the inverse of a nondefinite Toeplitz matrix. The regular portion of the algorithm is made of the classical Levinson recursion. The singular portion requires solving some well-defined systems of linear equations with gradient structure. The dimension of each of these sytems equals the amplitude of the corresponding singularity.

A simple proof of Rudin's multivariable stability theorem

It is shown how Rudins multivariable stability theorem can be proved by using simple one-variable arguments, exclusively. In particular, no use is made of multivariable homotopy, in contrast with the original proof. The efficacy of the approach presented here is further illustrated by deriving a new stability test as well as elementary and independent proofs for the classical criteria.

Speaker dependent connected speech recognition via phonetic Markov models

In this paper, a method for speaker dependent connected speech recognition based on phonemic units is described. In this recognition system, each phoneme is characterized by a very simple 3-state Hidden Markov Model (HMM) which is trained on connected speech by a Viterbi algorithm. Each state has associated with it a continuous (Gaussian) or discrete probability density function (pdf). With the phonemic models so obtained, the recognition is then performed either directly at word level (by the reconstruction of reference words from the models of the constituting phonemes) or via a phonemic labelling. Good results are obtained as well with a German ten digit vocabulary (20 phonemes) as with a French 80 word vocabulary (36 phonemes).

Pseudo-lossless functions with application to the problem of locating the zeros of a polynomial

This paper contains an investigation of the class of pseudolossless rational functions F(p) = N(p)/D(p) , which are characterized by the property \Re F(p) = 0 for \Re p = 0 . The index of such a function, counting the zeros of the polynomial N(p)+ D(p) in the right half-plane \Re p > 0 , enjoys some very useful decomposition properties. It is shown how an appropriate index theory of pseudo-lossless functions provides a framework in which the most classical results concerning the problem of locating the zeros of a polynomial can be unified, simplified, and generalized.

Low rank matrices with a given sign pattern

Given an

Half-plane Toeplitz systems

m \times n

A simple approach to spectral factorization

sign matrix S, an

A polynomial approach to the generalized Levinson algorithm based on the Toeplitz distance

m \times n

State reduction in hidden Markov chains used for speech recognition

real matrix A is said to be a realization of S if the sign of the