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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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Electroglottographic recording of a 52-year-old singer producing a sustained note (vowel /a/) with intensity variation (soft–loud–soft). (a) Singer's attempted intensity of voice production in arbitrary numbers on a nonlinear scale (0, lowest intensity; 1, highest intensity). (b) Narrow-band spectrogram of the electrographic (EGG) signal. (c) EGG signal, extracted at t = 1.22, t = 2.14 and t = 7 s. (d) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.3 π radians, yielding intersection points with the trajectory (red dots). (e) Phasegram: the vertical markers at t = 1.22, t = 2.14 and t = 7 s indicate the time instants at which the signals shown in panel (c) were extracted.
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RSIF20130288F7: Electroglottographic recording of a 52-year-old singer producing a sustained note (vowel /a/) with intensity variation (soft–loud–soft). (a) Singer's attempted intensity of voice production in arbitrary numbers on a nonlinear scale (0, lowest intensity; 1, highest intensity). (b) Narrow-band spectrogram of the electrographic (EGG) signal. (c) EGG signal, extracted at t = 1.22, t = 2.14 and t = 7 s. (d) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.3 π radians, yielding intersection points with the trajectory (red dots). (e) Phasegram: the vertical markers at t = 1.22, t = 2.14 and t = 7 s indicate the time instants at which the signals shown in panel (c) were extracted.

Mentions: Human voice production is governed by complex control parameters, over which the singer has only partial and intuitive control. In the example shown in figure 7, the singer's intended intensity of voice production was varied, attempting to keep all other parameters stable. The plotted intensity is a dimensionless quality, expressed on an arbitrary nonlinear scale (0, lowest intensity; 1, highest intensity; figure 7a). The spectrogram in figure 7b reveals several abrupt transitions, suggesting spontaneous changes in the underlying voice production mechanism, not intended by the singer. They represent unwanted, spontaneous system-level behaviour and violate the traditional aesthetic boundary conditions of classical singing. The findings, corroborated by inspection of the time-domain signal (provided as the audio track in electronic supplementary material, movie S5), are described in table 3.Table 3.


Visualization of system dynamics using phasegrams.

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

Electroglottographic recording of a 52-year-old singer producing a sustained note (vowel /a/) with intensity variation (soft–loud–soft). (a) Singer's attempted intensity of voice production in arbitrary numbers on a nonlinear scale (0, lowest intensity; 1, highest intensity). (b) Narrow-band spectrogram of the electrographic (EGG) signal. (c) EGG signal, extracted at t = 1.22, t = 2.14 and t = 7 s. (d) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.3 π radians, yielding intersection points with the trajectory (red dots). (e) Phasegram: the vertical markers at t = 1.22, t = 2.14 and t = 7 s indicate the time instants at which the signals shown in panel (c) were extracted.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC4043161&req=5

RSIF20130288F7: Electroglottographic recording of a 52-year-old singer producing a sustained note (vowel /a/) with intensity variation (soft–loud–soft). (a) Singer's attempted intensity of voice production in arbitrary numbers on a nonlinear scale (0, lowest intensity; 1, highest intensity). (b) Narrow-band spectrogram of the electrographic (EGG) signal. (c) EGG signal, extracted at t = 1.22, t = 2.14 and t = 7 s. (d) Phase portraits from the above signals, created by plotting the real portion of the Hilbert-transformed EGG signal against its imaginary counterpart. A Poincaré section was created at an angle of 0.3 π radians, yielding intersection points with the trajectory (red dots). (e) Phasegram: the vertical markers at t = 1.22, t = 2.14 and t = 7 s indicate the time instants at which the signals shown in panel (c) were extracted.
Mentions: Human voice production is governed by complex control parameters, over which the singer has only partial and intuitive control. In the example shown in figure 7, the singer's intended intensity of voice production was varied, attempting to keep all other parameters stable. The plotted intensity is a dimensionless quality, expressed on an arbitrary nonlinear scale (0, lowest intensity; 1, highest intensity; figure 7a). The spectrogram in figure 7b reveals several abrupt transitions, suggesting spontaneous changes in the underlying voice production mechanism, not intended by the singer. They represent unwanted, spontaneous system-level behaviour and violate the traditional aesthetic boundary conditions of classical singing. The findings, corroborated by inspection of the time-domain signal (provided as the audio track in electronic supplementary material, movie S5), are described in table 3.Table 3.

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