arXiv subjects

Jarmo Malinen

Publications and source records attributed to Jarmo Malinen.

16 recordsLinked to original sources

arXiv2024

Student behaviour and engagement with adaptive exercises on a thermodynamics course

A teaching experiment was carried out in a university-level thermodynamics course using adaptive and interactive e-learning material, created in the new Moodle question type Stateful extending the original e-learning platform STACK. The system collects data about the students that is used to algorithmically classify them according to their behaviour in solving problems. It is observed that the classification of this data predicts students' success in the other parts of the course for a majority of students. Also, the classification is statistically consistent with Thermodynamic Concept Survey and Maryland Physics Expectation Survey.

physics.ed-ph↗

arXiv2021

Distributed solution of Laplacian eigenvalue problems

The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval $(0,Λ)$. A novel domain decomposition Ritz method, partition of unity condensed pole interpolation method, is proposed. This method can be used in distributed computing environments where communication is expensive, e.g., in clusters running on cloud computing services or networked workstations. The Ritz space is obtained from local subspaces consistent with a decomposition of the domain into subdomains. These local subspaces are constructed independently of each other, using data only related to the corresponding subdomain. Relative eigenvalue error is analysed. Numerical examples on a cluster of workstations validate the error analysis and the performance of the method.

math.NA↗

arXiv2020

Efficient solution of symmetric eigenvalue problems from families of coupled systems

Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower diagonal block and the range of the coupling blocks remains unchanged. Such block structure naturally arises when studying the effect of a subsystem to the eigenmodes of the full system. The proposed method is based on interpolation of the resolvent function after some of its singularities have been removed by a spectral projection. Singular value decomposition can be used to further reduce the dimension of the computational problem. Error analysis of the method indicates exponential convergence with respect to the number of interpolation points. Theoretical results are illustrated by two numerical examples related to finite element discretisation of the Laplace operator.

math.NA↗

arXiv2019

Numerical modelling of coupled linear dynamical systems

Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc., the first step is to discretise them into finite-dimensional LDSs using, e.g., the finite element method, autoregressive techniques, and interpolation. The finite-dimensional component systems may satisfy various types of energy (in)equalities due to passivity that require translation into a common form such as the scattering passive representation. Only then can the component systems be coupled in a desired feedback configuration by computing pairwise Redheffer star products of LDSs. Unfortunately, a straightforward approach may fail due to ill-posedness of feedback loops between component systems. Adversities are particularly likely if some component systems have no energy dissipation at all, and this may happen even if the fully coupled system could be described by a finite-dimensional LDS. An approach is proposed for obtaining the coupled system that is based on passivity preserving regularisation. Two practical examples are given to illuminate the challenges and the proposed methods to overcome them: the Butterworth low-pass filter and the termination of an acoustic waveguide to an irrational impedance.

math.OC↗

arXiv2019

Notes on glottal flow and acoustic inertial effects

This text is a compilation of some of the notes that the author has written during the development of the low-order model "DICO" [2, 8, 10, 11] for vowel phonation and the even more rudimentary glottal flow model [9] for processing high-speed glottal video data. The following subject matters are covered: (i) Incompressible, laminar, lossless flow models for idealised rectangular and wedge shape vocal fold geometries. Equations of motion and the pressure distribution are computed in a closed form for each model using the unsteady Bernoulli's theorem; (ii) The assumption of incompressibility and energy loss (i.e., irrecoverable pressure drop) of the airflow in airways (including the glottis) is discussed using steady compressible Bernoulli theorem as the main tool; (iii) Inertia of an uniform waveguide is studied in terms of the low-frequency limit of the the (acoustic) impedance transfer function. It is observed that the inductive loading in the boundary condition sums up with the waveguide inertance in an expected way; (iv) It is shown that an acoustic waveguide, modelled by Webster's lossless equation with Dirichlet boundary condition at the far end, will produce the expected mass inertance of the fluid column as the low-frequency limit of the impedance transfer function.

physics.flu-dyn↗

arXiv2017

An acoustic glottal source for vocal tract physical models

A sound source was proposed for acoustic measurements of physical models of the human vocal tract. The physical models are produced by Fast Prototyping, based on Magnetic Resonance Imaging during prolonged vowel production. The sound source, accompanied by custom signal processing algorithms, is used for two kinds of measurements: (i) amplitude frequency response and resonant frequency measurements of physical models, and (ii) signal reconstructions at the source output according to a target waveform with measurements at the mouth position of the physical model. The proposed source and the software are validated by measurements on a physical model of the vocal tract corresponding to vowel [a] of a male speaker.

physics.ins-det↗

arXiv2017

Modal locking between vocal fold and vocal tract oscillations: Simulations in time domain

During voiced speech, the human vocal folds interact with the vocal tract acoustics. The resulting glottal source-resonator coupling has been observed using mathematical and physical models as well as in in vivo phonation. We propose a computational time-domain model of the full speech apparatus that, in particular, contains a feedback mechanism from the vocal tract acoustics to the vocal fold oscillations. It is based on numerical solution of ordinary and partial differential equations defined on vocal tract geometries that have been obtained by Magnetic Resonance Imaging. The model is used to simulate rising and falling pitch glides of [a, i] in the fundamental frequency (f_o) interval [150 Hz, 320 Hz]. The interval contains the first vocal tract resonance f_R1 and the first formant F1 of [i] as well as the fractions of the first resonance f_R1/4 and fR1/3 of [a]. The simulations reveal a locking pattern of the fo-trajectory at f_R1 of [i] in falling and rising glides. The resonance fractions of [a] produce perturbations in the pressure signal at the lips but no locking. All these observations from the model behaviour are consistent and robust within a wide range of feasible model parameter values and under exclusion of secondary model components.

physics.flu-dyn↗

arXiv2016

Post-processing speech recordings during MRI

We discuss post-processing of speech that has been recorded during Magnetic Resonance Imaging (MRI) of the vocal tract. Such speech recordings are contaminated by high levels of acoustic noise from the MRI scanner. Also, the frequency response of the sound signal path is not flat as a result of severe restrictions on recording instrumentation due to MRI technology. The post-processing algorithm for noise reduction is based on adaptive spectral filtering. The speech material consists of samples of prolonged vowel productions that are used for validation of the post-processing algorithm. The comparison data is recorded in anechoic chamber from the same test subject. Formant analysis is carried out for the post-processed speech and the comparison data. Artificially noise-contaminated vowel samples are used for validation experiments to determine performance of the algorithm where using true data would be difficult. The properties of recording instrumentation or the post-processing algorithm do not explain the consistent frequency dependent discrepancy between formant data from experiments during MRI and in anechoic chamber. It is shown that the discrepancy is statistically significant, in particular, where it is largest at 1 kHz and 2 kHz. The reflecting surfaces of the MRI head and neck coil are suspected to change the speech acoustics which results in "external formants" at these frequencies. However, the role of test subject adaptation to noise and constrained space acoustics during an MRI examination cannot be ruled out.

cs.SD↗

arXiv2015

Spectral Study of the Vocal Tract in Vowel Synthesis: A Comparison between 1D and 3D Acoustic Analysis

A state-of-the-art 1D acoustic synthesizer has been previously developed, and coupled to speaker-specific biomechanical models of oropharynx in ArtiSynth. As expected, the formant frequencies of the synthesized vowel sounds were shown to be different from those of the recorded audio. Such discrepancy was hypothesized to be due to the simplified geometry of the vocal tract model as well as the one dimensional implementation of Navier-Stokes equations. In this paper, we calculate Helmholtz resonances of our vocal tract geometries using 3D finite element method (FEM), and compare them with the formant frequencies obtained from the 1D method and audio. We hope such comparison helps with clarifying the limitations of our current models and/or speech synthesizer.

cs.SD↗

arXiv2015

Modal locking between vocal fold and vocal tract oscillations: Experiments and statistical analysis

The human vocal folds are known to interact with the vocal tract acoustics during voiced speech production; namely a nonlinear source-filter coupling has been observed both by using models and in \emph{in vivo} phonation. These phenomena are approached from two directions in this article. We first present a computational dynamical model of the speech apparatus that contains an explicit filter-source feedback mechanism from the vocal tract acoustics back to the vocal folds oscillations. The model was used to simulate vocal pitch glideswhere the trajectory was forced to cross the lowest vocal tract resonance, i.e., the lowest formant $F_1$. Similar patterns produced by human participants were then studied. Both the simulations and the experimental results reveal an effect when the glides cross the first formant (as may happen in \textipa{[i]}). Conversely, this effect is not observed if there is no formant within the glide range (as is the case in \textipa{[\textscripta]}). The experiments show smaller effect compared to the simulations, pointing to an active compensation mechanism.

physics.bio-ph↗

arXiv2014

A posteriori error estimates for Webster's equation in wave propagation

We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique.

math.AP↗

arXiv2013

Measurement of acoustic and anatomic changes in oral and maxillofacial surgery patients

We describe an arrangement for simultaneous recording of speech and geometry of vocal tract in patients undergoing surgery involving this area. Experimental design is considered from an articulatory phonetic point of view. The speech and noise signals are recorded with an acoustic-electrical arrangement. The vocal tract is simultaneously imaged with MRI. A MATLAB-based system controls the timing of speech recording and MR image acquisition. The speech signals are cleaned from acoustic MRI noise by a non-linear signal processing algorithm. Finally, a vowel data set from pilot experiments is compared with validation data from anechoic chamber as well as with Helmholtz resonances of the vocal tract volume.

physics.med-ph↗

arXiv2013

Webster's equation with curvature and dissipation

Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of the wave equation satisfy the corresponding Webster's equation when the latter includes additional control signals determined by the solution.

math.AP↗

arXiv2013

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 Webster's 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 Webster's model at the limit of vanishing waveguide intersection.

math.DS↗

arXiv2012

Microspectral analysis of quasinilpotent operators

We develop a microspectral theory for quasinilpotent linear operators $Q$ (i.e., those with $σ(Q) = \{0}$) in a Banach space. When such $Q$ is not compact, normal, or nilpotent, the classical spectral theory gives little information, and a somewhat deeper structure can be recovered from microspectral sets in $\C$. Such sets describe, e.g., semigroup generation, resolvent properties, power boundedness as well as Tauberian properties associated to $zQ$ for $z \in \C$.

math.SP↗

arXiv2012

How far are vowel formants from computed vocal tract resonances?

We compare numerically computed resonances of the human vocal tract with formants that have been extracted from speech during vowel pronunciation. The geometry of the vocal tract has been obtained by MRI from a male subject, and the corresponding speech has been recorded simultaneously. The resonances are computed by solving the Helmholtz partial differential equation with the Finite Element Method (FEM). Despite a rudimentary exterior space acoustics model, i.e., the Dirichlet boundary condition at the mouth opening, the computed resonance structure differs from the measured formant structure by $\approx$ 0.7 semitones for [i] and [u] having small mouth opening area, and by $\approx$ 3 semitones for vowels [a] and [ae] that have a larger mouth opening. The contribution of the possibly open velar port has not been taken into considaration at all which adds the discrepancy for [a] in the present data set. We conclude that by improving the exterior space model and properly treating the velar port opening, it is possible to computationally attain four lowest vowel formants with an error less than a semitone. The corresponding wave equation model on MRI-produced vocal tract geometries is expected to have a comparable accuracy.

math.DS↗