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Visualization of system dynamics using phasegrams.

Herbst CT, Herzel H, Svec JG, Wyman MT, Fitch WT - J R Soc Interface (2013)

Bottom Line: A phasegram can be interpreted as a bifurcation diagram in time.In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known.Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

View Article: PubMed Central - PubMed

Affiliation: Department of Cognitive Biology, Laboratory of Bioacoustics, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria. christian.herbst@univie.ac.at

ABSTRACT
A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

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(a) Schematic of the two-mass model of the vocal folds. Each vocal fold is approximated by two coupled oscillators. The springs and dampers represent the viscoelastic properties of the vocal folds. The time-varying lateral displacements x1l and x1r were taken as the input to phasegram analysis. (b) Excised larynx set-up: sika deer larynx mounted on an air supply tube, EGG electrodes attached on thyroid cartilage at level of vocal folds.
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RSIF20130288F4: (a) Schematic of the two-mass model of the vocal folds. Each vocal fold is approximated by two coupled oscillators. The springs and dampers represent the viscoelastic properties of the vocal folds. The time-varying lateral displacements x1l and x1r were taken as the input to phasegram analysis. (b) Excised larynx set-up: sika deer larynx mounted on an air supply tube, EGG electrodes attached on thyroid cartilage at level of vocal folds.

Mentions: In previous research, a simplified two-mass model of voice production was created in order to study the effect of asymmetries on vocal fold vibration [28]. In this model, each vocal fold is represented by two coupled oscillators (defined by their mass, stiffness and damping coefficients; figure 4a). This model provides 2 d.f. per vocal fold. It allows for the two masses of each vocal fold to oscillate with a phase difference (the lower mass typically leading the vibration), thus capturing the most essential mechanism of self-sustaining vocal fold vibration: the transfer of aerodynamic energy into tissue vibrations [29]. The model has the option of simulating the effect of asymmetrical vocal fold anatomy/configuration, which is a well-known cause of pathological voice production and voice nonlinearities [30,31].FigureĀ 4.


Visualization of system dynamics using phasegrams.

Herbst CT, Herzel H, Svec JG, Wyman MT, Fitch WT - J R Soc Interface (2013)

(a) Schematic of the two-mass model of the vocal folds. Each vocal fold is approximated by two coupled oscillators. The springs and dampers represent the viscoelastic properties of the vocal folds. The time-varying lateral displacements x1l and x1r were taken as the input to phasegram analysis. (b) Excised larynx set-up: sika deer larynx mounted on an air supply tube, EGG electrodes attached on thyroid cartilage at level of vocal folds.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4043161&req=5

RSIF20130288F4: (a) Schematic of the two-mass model of the vocal folds. Each vocal fold is approximated by two coupled oscillators. The springs and dampers represent the viscoelastic properties of the vocal folds. The time-varying lateral displacements x1l and x1r were taken as the input to phasegram analysis. (b) Excised larynx set-up: sika deer larynx mounted on an air supply tube, EGG electrodes attached on thyroid cartilage at level of vocal folds.
Mentions: In previous research, a simplified two-mass model of voice production was created in order to study the effect of asymmetries on vocal fold vibration [28]. In this model, each vocal fold is represented by two coupled oscillators (defined by their mass, stiffness and damping coefficients; figure 4a). This model provides 2 d.f. per vocal fold. It allows for the two masses of each vocal fold to oscillate with a phase difference (the lower mass typically leading the vibration), thus capturing the most essential mechanism of self-sustaining vocal fold vibration: the transfer of aerodynamic energy into tissue vibrations [29]. The model has the option of simulating the effect of asymmetrical vocal fold anatomy/configuration, which is a well-known cause of pathological voice production and voice nonlinearities [30,31].FigureĀ 4.

Bottom Line: A phasegram can be interpreted as a bifurcation diagram in time.In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known.Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

View Article: PubMed Central - PubMed

Affiliation: Department of Cognitive Biology, Laboratory of Bioacoustics, University of Vienna, Althanstrasse 14, 1090 Vienna, Austria. christian.herbst@univie.ac.at

ABSTRACT
A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

Show MeSH
Related in: MedlinePlus