Zusammenfassung
In den Kapiteln 4 und 5 wurden bereits zwei Zeit-Frequenz-Verteilungen behandelt: das Spektrogramm und das Skalogramm. Beide Verteilungen entstehen durch lineare Filterungen des zu analysierenden Signals und eine anschließende Bildung des Betragsquadrats. In diesem Kapitel werden Zeit-Frequenz-Verteilungen behandelt, die nicht über lineare Filterungen gewonnen werden und die im Gegensatz zum Spektrogramm bzw. Skalogramm nicht in ihrer Auflösung durch die Unschärferelation eingeschränkt sind. Obwohl bei diesen Methoden nicht in jedem Fall sichergestellt werden kann, daß die Verteilungen positiv sind, lassen sich damit in speziellen Anwendungsfällen extrem aussagekräftige Erkenntnisse gewinnen.
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Literatur
Y. Meyer: “Ondelettes et fonction splines,” Séminare EDP, École Polytechnique, Paris, Dez. 1986.
J. Morlet, G. Arens, I. Fourgeau, and D. Giard: “Wave propagation and sampling theory,” Geophysics, 47, pp. 203–236, 1982.
J. Morlet: “Sampling theory and wave propagation,” in NATO ASI series, vol. 1, Issues in Acoustic signal/image processing and recognition, C.H. Chen (ed.), pp. 233–261, Springer, New York, 1983.
O. Rioul and M. Vetterli: “Wavelets and signal processing,” IEEE Signal Processing Magazine, October 1991.
M.B. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and L. Raphael: Wavelets and Their Applications, Jones and Bartlett Publishers, Boston, 1992.
M.J. Shensa: “The discrete wavelet transform: Wedding the a trous and Mallat algorithms,” IEEE Trans. on Signal Processing, vol. 40, no. 10, pp. 2464–2482, Oct. 1992.
G. Strang: “Wavelets and dilation equations: A brief introduction,” SIAM Review, vol. 31, no. 4, pp. 614–627, December 1989.
B. Boashash and A. Riley: “Algorithms for time-frequency signal analysis,”in Time-Frequency Signal Analysis, B. Boashash (ed. ), Longman Cheshire, 1992.
H.I. Choi and W.J. Williams: “Improved time-frequency representation on multicomponent signals using exponential kernels,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-37, no. 6, pp. 862–871, 1989.
T.A.C.M. Claasen and W.F.G. Mecklenbräuker: “The Wigner distribution–a tool for time-frequency signal analysis–parts I-III,” Philips J. Res., 35, pp. 217–250, 276–300, 372–389, 1980.
L. Cohen: “Generalized phase-space distribution functions,” J. of Math. Phys., 7, pp. 781–786, 1966.
L. Cohen: “Introduction: A primer on time-frequency analysis,” in Time-Frequency Signal Analysis, B. Boashash (ed.), Longman Cheshire, 1992.
L. Cohen: Time frequency analysis, Prentice-Hall, Englewood Cliffs, N.J.,1995.
N.G. De Bruijn: “A theory of generalized functions, with applications to Wigner distribution and Weyl correspondence,” Nieuw Archief voor Wiskunde (3), vol. XXI, pp. 205–280, 1980.
P. Flandrin and O. Rioul: “Affine smoothing of the Wigner-Ville distribution,” in Proc. International Conference on Acoustics, Speech, and Signal Processing, Albuquerque, NM, pp. 2455–2458, April 1990.
L.E. Francks: Signal Theory, Prentice-Hall, Englewood Cliffs, New Jersey,1969.
F. Hlawatsch and G.F. Boudreaux-Bartels: “Linear and quadratic time-frequency signal representations,” IEEE Signal Processing Magazine, April 1992.
A.J.E.M. Janssen: “Positivity of time-frequency distribution functions,” Sig-nal Processing, vol. 14, pp. 243–252, 1988.
J.E. Moyal: “Quantum mechanics as a statistical theory,” Camb. Phil. Soc., 45, pp. 99–124, 1949.
A.W. Rihaczek: “Signal energy distribution in time and frequency,” IEEE Trans. on Inf. Th., vol. IT-14, no. 3, pp. 369–374, 1968.
O. Rioul and P. Flandrin: “Time-scale energy distributions: A general class extending wavelet transforms,” IEEE Trans. Signal Processing, July 1992.
E.F. Velez and H. Garudadri: “Speech analysis based on smoothed Wigner-Ville distributions,” in Time-Frequency Signal Analysis, B. Boashash (ed.), Longman Cheshire, 1992.
J. Ville: “Theorie et applications de la notion de signal analytique,” Cables et Transmission, 2 A, pp. 61–74, 1948.
H.L. Van Trees: Detection, Estimation, and Modulation Theory, Part III,Wiley, New York, 1971.
E.P. Wigner: “On the quantum correction for thermodynamic equilibrium,”Physical Review, 40, pp. 749–759, 1932.
Y. Zhao, L.E. Atlas, and R.J. Marks II: “The use of cone-shaped kernels for generalized time-frequency representations of non-stationary signals,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-38, no. 7, pp. 1084–1091, 1990.
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© 1996 B. G. Teubner Stuttgart
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Mertins, A. (1996). Zeit-Frequenz-Verteilungen. In: Signaltheorie. Informationstechnik. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-05686-7_6
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