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The Use of Wavelet Transform and Frames in NVH Applications
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Abstract
In this study, the recent developments in the theory of linear time-frequency localization techniques are reviewed, and their applications to the analysis and synthesis of transient vibrations are investigated. Particular attention is given to the wavelet transform, wavelet frames and multiresolution concepts. The introduction of the basic wavelet theory and the related algorithms are followed by physical applications. In the first part, the continuous wavelet transform is employed as an analysis tool to study the propagation of transient structural and acoustic waves that are induced by impulsive forces. The time-scale representations generated by the wavelet transform are utilized to track the spectral evolutions of the transient wave interferences, and also to identify the characteristic signatures of the sources and the dispersive properties of the propagator. In the second part, the wavelet frame expansions and multiresolution concepts are utilized to construct the transient vibration response of a wide-band system. The forcing function is decomposed into multiresolution bands and convolved with the corresponding wavelet response functions. Then, the outputs generated at different resolution levels are combined together to form the system response. The examples demonstrate the effectiveness of the self-adjusting (zooming) window structure of the wavelet transform during both the analysis and synthesis of wide-band transient vibration responses.
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Önsay, T., "The Use of Wavelet Transform and Frames in NVH Applications," SAE Technical Paper 951364, 1995, https://doi.org/10.4271/951364.Also In
References
- Önsay, T. Haddow, A. G. 1994 “Wavelet Transform Anlysis of Transient Wave Propagation in a Dispersive Medium,” Journal of the Acoustical Society of America 95 3 1441 1449
- Önsay, T. 1994 “Application of Wavelet and Gabor Transforms to the Analysis of Transient Wave Propagation,” Proceedings of the Third International Congress on Air- and Structure-Borne Sound and Vibration Montreal 717 726
- Önsay, T. 1994 “Wavelet Frame Expansions and Wavelet Response Functions,” Journal of the Acoustical Society of America 96 5 3340
- Önsay, T. 1994 “Characterization of Transient Vibrations in Mechanical Systems: Time-Frequency Localization with Wavelets and STFT,” Ph.D. Dissertation Michigan State University
- Cohen, L. 1989 “Time-Frequency Distributions- A Review,” Proceedings of the IEEE 77 7 941 981
- Hlawatsch, F. Boudreaux-Bartels, G.F. 1992 “Linear and Quadratic Time-Frequency Signal Representations,” IEEE Signal Proc. Mag. 9 2 21 67
- Strang, G. 1989 “Wavelets and Dilation Equations: A Brief Introduction,” SIAM Review 31 4 614 627
- Benedetto, J.J. Frazier, M.W. 1994 Wavelets: Math. and Applications Boca Raton CRC Press
- Morlet, J. et al. 1982 “Wave Propagation and Sampling Theory- Part I: Complex Signal and Scattering in Multilayered media,” Geophysics 47 2 203 221
- Gabor, D. 1946 “Theory of communications,” J. of the Institution of Electrical Engineers 93 3 429 457
- Meyer, Y. 1990 Ondelettes et Opérateurs I II Paris Hermann Éditeurs des Sciences et des Arts
- Meyer, Y. 1992 Wavelets and Applications Proc. of the International Conference, Marseille 1989 Paris Masson
- Meyer, Y. 1993 Wavelets Algorithms and Applications Philadelphia Society for Industrial and Appl. Math
- Daubechies, I. 1988 “Orthonormal Bases of Compactly Supported Wavelets,” Comm. on Pure and Applied Math 41 7 909 996
- Daubechies, I. 1990 “The Wavelet Transform, Time-Frequency Localization and Signal Analysis” IEEE Trans. on Information Theory 36 15 961 1005
- Daubechies, I. 1992 Ten Lectures on Wavelets Philadelphia Society for Industrial and Applied Math
- Rioul, O. Vetterli, M. Oct. 1991 “Wavelets and Signal Processing,” IEEE Signal Proc. Mag. 14 38
- Mallat, S.G. 1989 “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Trans. on Pattern Analysis and Mach. Int. 11 7 674 693
- Mallat, S.G. 1989 “Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 ( R ),” Trans. of the Math. Society of America 315 1 69 87
- Battle, G. 1987 “A Block Spin Costruction of Ondelettes. Part I: Lemarie Functions,” Communications in Math. Physics 110 601 615
- Frazier, M. Jawerth, B. 1988 “The φ -Transform and Application to Distribution Spaces,” Cwikel M. et al. Lecture Notes in Math Berlin Springer-Verlag 233 246
- Chui, C.K. 1992 An Introduction to Wavelets New York Academic Press
- Chui, C.K. 1992 Wavelets: A Tutorial in Theory and Applications New York Academic Press
- Coifman, R.R. Wickerhauser, M.V. 1992 “Entropy-Based Algorithms for Best Basis Selection,” IEEE Trans. on Information Theory 38 2 713 718
- Beylkin, G. et al. 1991 “Fast Wavelet Transforms and Numerical Algorithms I,” Comm. on Pure and Applied Math 44 141 183
- Wickerhauser, M.V. 1992 “Acoustic Signal Compression with Wavelet Packets,” 679 700
- Alpert, B.K. 1992 “Wavelets and Other Bases for Fast Numerical Linear Algebra,” 181 216
- Duffin, R. J. Schaeffer, A. C. 1952 “A Class of Nonharmonic Fourier Series,” Trans. of the American Math. Society 72 341 366
- Heil, C. E. Walnut, D. F. 1989 “Continuous and Discrete Wavelet Transform,” SIAM Review 31 4 628 666
- Vetterli, M. Herley, C. 1992 “Wavelets and Filter Banks: Theory and Design,” IEEE Trans. on Sig. Processing 40 9 2207 2232
- Holschneider, M. et al. 1989 “A Real-Time Algorithm for Signal Analysis with the Help of the Wavelet Transform,” 286 297
- Dutilleux, P. 1989 “An Implemantation of the ‘Algorithme á Trous’ to Compute the Wavelet Transform,” 298 304
- Rioul, O. Duhamel, P. 1992 “Fast Algorithms for Discrete and Continuous Wavelet Transforms,” IEEE Trans. on Information Theory 38 2 569 586
- Shensa, M. 1992 “The Discrete Wavelet Transform: Wedding the Á trous and Mallat Algorithms,” IEEE Trans. on Sig. Processing 40 10 2464 2482
- Farge, M. 1992 “The Continuous Wavelet Tansform of Two-Dimensional Turbulent Flows,” 275 302
- Rabiner, L.R. Allen, J.B. 1980 “On the Implementation of a Short-Time Spectral Analysis Method for System Identification,” IEEE Trans. on Acoustics, Speech, and Sig. Proc. 28 1 69 78
- Nawab, S. H. Quatieri, T. F. 1988 “Short-Time Fourier Transform,” Advanced Topics in Signal Processing Lim, J. S. Oppenheim, A.V. Englewood Cliffs Prentice Hall
- Combes, J.M. et al. 1987 “Wavelets: Time-Frequency Methods and Phase Space,” Berlin Springer-Verlag
- Ruskai, M.B. et al. 1992 Wavelets and Their Applications Boston Jones and Bartlett
- Grossmann, A. et al. 1985 “Transforms Associated to Square Integrable Group Representations. I. General Results,” J. of Math. Physics 26 10 2473 2479
- Goupillaud et al. 1984 “Cycle-Octave and Related Transforms in Seismic Signal Analysis,” Geoexploration 23 85 102
- Hodges, C. H. et al. 1985 “The use of the sonogram in structural acoustics and an application to the vibrations of cylindrical shells,” J. Sound and Vibration 101 203 218
- Wahl, T. J. Bolton, J. S. 1993 “The application of the Wigner distribution to the identification of structure-borne noise components,” J. Sound and Vibration 163 101 122
- Tewfik, A.H. et al. 1992 “On the Optimal Choise of a Wavelet for Signal Representation,” IEEE Trans. on Inf. Theory 38 2 747 765
- Young, R. M. 1980 An Introduction to Nonharmonic Fourier Series New York Academic Press