For citation:
Andreyev Y. V., Koroteyev M. V. On chaotic nature of speech signals. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 6, pp. 44-59. DOI: 10.18500/0869-6632-2004-12-6-44-59
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Article
UDC:
621.391
On chaotic nature of speech signals
Autors:
Andreyev Yury Vladimirovich, Moscow Institute of Physics and Technology
Koroteyev Maksim Valerevich, Moscow Institute of Physics and Technology
Abstract:
Phonetic signals are considered from the viewpoint of nonlinear dynamics. Phase portraits of the signals are analyzed in embedding space, dimension and the largest Lyapunov exponent are estimated. It is shown that dimension of speech signals is low and the largest Lyapunov exponent is positive.
Key words:
Reference:
- Markel J, Gray A. Linear Prediction of Speech. Moskow: Svyaz’; 1980. 308 p.
- McHaul J. Linear Prediction. A review. TIIER; 1975;53(2):20–45.
- Ishizaka K, Flanagan JL. Synthesis оf voiced sounds from а two-mass model оf the vocal cords. The Bell System Technical Journal. 1972;51(6):1233–1268. DOI: 10.1002/j.1538-7305.1972.tb02651.x.
- Takens К. Detecting strange attractors in turbulence. Lecture notes in mathematics. Springer-Verlag. 1981;898:366–381. DOI: 10.1007/BFb0091924.
- Noakes L. The Takens embedding theorem. Int. J. Bifurcation and Chaos. 1991;1(4):867–872. DOI: 10.1016/S0362-546X(96)00149-6.
- Farmer JD, Sidorowich JJ. Predicting chaotic time series. Phys. Rev. Lett. 1999;59(8):845–848. DOI: 10.1103/PhysRevLett.59.845.
- Bezruchko BP, Dikanev TB, Smirnov DA. Testing for unambiguity and continuity at global reconstruction of model equations by time series. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(4):69.
- Herzel H, Berry Р, Titze LR, Saleh M. Analysis of vocal disorders with method from nonlinear dynamics. J. Speech Hear. Res. 1994;37:1008–1019. DOI: 10.1044/jshr.3705.1008.
- Tize IR. The physics оf small-amplitude oscillation оf the vocal folds. J. Acoust. Soc. Am. 1988;83(4):1536–1552. DOI: 10.1121/1.395910
- Tokuda I, Tokunaga R, Aihara K. A simple geometrical structure underlying speech signals of the japanese vowel /a/. Int. J. of Bifurcation and Chaos. 1996;6(1):149–160. DOI: 10.1142/S0218127496001892.
- Tokuda I, Miyano T, Aihara K. Surrogate analysis for detecting nonlinear dynamics in normal vowels. J. Acoust. Soc. Am. Dec. 2001;110(6):3207–3217. DOI: 10.1121/1.1413749.
- Broomhead DS, King GP. Extracting qualitative dynamics from experimental data. Phys. D. 1986;20(2-3):217–236. DOI:10.1016/0167-2789(86)90031-X.
- Kantz H, Schrider Т. Nonlinear Time Series Analysis. Cambridge university press. 2000. 304 p.
- Lai YC, Ye М. Recent developments in chaotic time series analysis. Int. J. Bifurcation and Chaos. 2003;13(6):1383–1422. DOI: 10.1142/S0218127403007308.
- Judd K, Mees A. Embedding as a modeling problem. Physica D. 1998;120(3-4):273–286. DOI: 10.1016/S0167-2789(98)00089-X.
- Landa PS, Rosenblum MG. About one method of estimation of the attractor embedding dimension from the experimental results. Tech. Phys. 1989;59(1):13–20.
- Grassberger Р, Procaccia I. Characterization of strange attractors. Phys. Rev. Lett. 1983;50(5):346–349. DOI: 10.1103/PhysRevLett.50.346.
- Eckmann JP, Kamphorst SO, Ruelle D, Ciliberto S. Lyapunov exponents from time series. Phys. Rev. А. 1986;34(6):4971–4979. DOI: 10.1103/PhysRevA.34.4971.
- Landa PS, Rosenblum MG. Comparison of methods of phase space construction and determination of attractor dimensionality from experimental data. Tech. Phys. 1989;59(11):1–6.
- Grassberger P, Procaccia I. Measuring the strangeness оf strange attractors. Physica D. 1983;9(1-2):189–208. DOI: 10.1016/0167-2789(83)90298-1.
Received:
20.12.2004
Accepted:
19.05.2005
Published:
15.06.2005
Journal issue:
- 359 reads