Atte Aalto

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.

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.

Output error minimizing back and forth nudging method for initial state recovery

Abstract We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and simulated outputs — given that the observer gains are chosen suitably and the system is exactly observable. If the system’s generator A is essentially skew-adjoint and dissipative (with not too much dissipation), the colocated feedback has to be corrected by the operator e A t e A ∗ t in order to obtain such convergence. In some special cases, a feasible approximation for this operator can be found analytically. The case with wave equation with constant dissipation will be presented.

Convergence of discrete-time Kalman filter estimate to continuous time estimate

ABSTRACT This article is concerned with the convergence of the state estimate obtained from the discrete-time Kalman filter to the continuous time estimate as the temporal discretisation is refined. The convergence follows from Martingale convergence theorem as demonstrated below; however, surprisingly, no results exist on the rate of convergence. We derive convergence rate estimates for the discrete-time Kalman filter estimate for finite and infinite dimensional systems. The proofs are based on applying the discrete-time Kalman filter on a dense numerable subset of a certain time interval [0, T].

Modal Locking Between Vocal Fold Oscillations and Vocal Tract Acoustics

jects are treated in the companion article [3]. Such 38 glides are particularly interesting when the fo range 39 intersects an isolated acoustic resonance of the supra40 or subglottal cavity. Since the lowest formant F1 usu41 ally lies high above fo in adult male phonation, this 42 situation is more typical in females and children when 43 they are producing vowels with low F1 such as [i]. 44 As reported in Section 5, simulations reveal (in addi45 tion to other observations) a characteristic locking be46 haviour of fo at the VT acoustic resonance1 fR1 ⇡ F1. 47 This article has two equally important objectives. 48 Firstly, we pursue better understanding of the time49 domain dynamics of glottal pulse perturbations near 50 fR1 of [i]. An acoustic and flow-mechanical model 51 of the speech apparatus is a well-suited tool for this 52 purpose. Secondly, we introduce and validate a com53 putational model that meets these requirements. The 54 proposed model has been originally designed to be a 55 glottal source for a high-resolution 3D computational 56 acoustics model of the VT which is being developed 57 for medical purposes. There is also an emerging ap58 plication for such models as a development platform 59 of speech signal processing algorithms [5, 6, 7]. Since 60 perturbations of fo near F1 are a widely researched, 61 yet quite multifaceted phenomenon, as discussed next, 62 it is a good candidate for model validation experi63 ments. 64