Jarmo Malinen

When is a linear system conservative

We consider infinite-dimensional linear systems without a-priori well-posedness assumptions, in a framework based on the works of M. Livsic, M. S. Brodskiǐ, Y. L. Smuljan, and others. We define the energy in the system as the norm of the state squared (other, possibly indefinite quadratic forms will also be considered). We derive a number of equivalent conditions for a linear system to be energy preserving and hence, in particular, well posed. Similarly, we derive equivalent conditions for a system to be conservative, which means that both the system and its dual are energy preserving. For systems whose control operator is one-to-one and whose observation operator has dense range, the equivalent conditions for being conservative become simpler, and reduce to three algebraic equations.

Vowel formants from the wave equation

This article describes modal analysis of acoustic waves in the human vocal tract while the subject is pronouncing [o]. The model used is the wave equation in three dimensions, together with physically relevant boundary conditions. The geometry is reconstructed from anatomical MRI data obtained by other researchers. The computations are carried out using the finite element method. The model is validated by comparing the computed modes with measured data.

The Cayley Transform as a Time Discretization Scheme

We interpret the Cayley transform of linear (finite- or infinite-dimensional) state space systems as a numerical integration scheme of Crank–Nicolson type. The scheme is known as Tustins method in the engineering literature, and it has the following important Hamiltonian integrator property: if Tustins method is applied to a conservative (continuous time) linear system, then the resulting (discrete time) linear system is conservative in the discrete time sense. The purpose of this paper is to study the convergence of this integration scheme from the input/output point of view.

Recording Speech during MRI : Part II

We design and construct a recording arrangement for speech during an MRI scan of the speakers vocal tract. We concentrate on the acoustic environment around the test subject inside the MRI machine. The data thus obtained is used for construction and validation of a numerical model of the vocal tract.

Recording speech during magnetic resonance imaging

We discuss recording arrangements for speech during an MRI scan of the speakers vocal tract. The image and sound data thus obtained will be used for construction and validation of a numerical model for the vocal tract.

ACOUSTIC WAVE GUIDES AS INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Websters model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Websters model at the limit of vanishing waveguide intersection.

Laplace and Cayley transforms – an approximation point of view

We interpret the Cayley transform of linear (finite-or infinite-dimensional) state space systems as a numerical integration scheme of Crank–Nicolson type. If such a scheme is applied to a conservative system, then the resulting discrete time system is conservative in the discrete time sense. We show that the convergence of this integration scheme is equivalent to an approximation of the Laplace transform.

Automated Segmentation of Upper Airways from MRI: Vocal Tract Geometry Extraction

A method for automatically extracting a triangulated surface mesh of the human vocal tract from 3D MRI data is proposed. The algorithm is based on a combination of anatomic landmarking, seeded region growing, and smoothing. More precisely, a mask is automatically created for removing unwanted details not associated with the vocal tract from the MRI voxel data. The mask then is applied to the original MRI data in order to produce an outcome on which marching cubes algorithm for triangulated surface extraction can be used. The proposed method can be used for processing large datasets, e.g., for validation of numerical methods in speech sciences as well as for anatomical studies.

Tustin's method for final state approximation of conservative dynamical systems

Abstract We study a Crank–Nicolson type time discretisation (known as Tustins method in engineering literature) for a conservative, infinite-dimensional linear dynamical system whose transfer function is scalar and inner. We show that this discretisation approximates the state trajectory at any given time. We first prove the result for canonical Hankel range realisations, and the general case is then obtained using the state space isomorphism.

Wave propagation in networks: A system theoretic approach

Abstract We consider dynamical systems defined on graph structures. The dynamics on the edges are governed by partial differential equations that are interconnected at the graph vertices through algebraic conditions involving the boundary conditions of the PDEs. We show that a variety of such wave propagation problems on networks are solvable (forward in time) and energy passive or conservative — given that the governing PDEs are solvable on the separate edges. We treat these problems in the operator theoretic boundary control system framework.