Abstract
To achieve effective signal signature extraction, Chap. 10 introduced several quantitative measures for selecting appropriate base wavelets from a pool of available wavelet families, such as Daubechies, Myer, and Morlet wavelets. This chapter introduces a complimentary technique focusing on wavelet customization. The goal is to design a wavelet that is specifically adapted to the signal of interest. Because such a customized wavelet would have a higher degree of matching with the signal than other wavelets, the effectiveness of signature extraction will improve.
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Aldroubi A, Unser M (1993) Families of multiresolution and wavelet spaces with optimal properties. Numer Funct Anal Optim 14:417–446
Burrus CS, Gopinath R, Guo H (1998) Introduction to wavelets and wavelet transforms: a primer. Prentice Hall, Englewood Cliffs, NJ
Chapa JO, Rao RM (2000) Algorithm for designing wavelets to match a specified signal. IEEE Trans Signal Process 48(12):3395–3406
Cohen A, Daubechies I, Feauveau JC (1992) Biorthogonal bases of compactly supported wavelets. Commun Pure Appl Math 45:485–560
Cui CK, Montefusco L, Puccio L (1994) Wavelet: theory, algorithms, and applications. Academic, New York
Daubechies I (1988) Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math 41:909–996
Daubechies I (1992) Ten lectures on wavelets. Society of Industrial and Applied Mathematics, Pennsylvania, PA
Gopinath RA, Odegard JE, Burrus CS (1994) Optimal wavelet representation of signals and wavelet sampling theorem. IEEE Trans Circuits Syst II Analog Digital Signal Process 41:262–277
Guido RC, Slaets JFW, Koberle R, Almeida LOB, Pereira JC (2006) A new technique to construct a wavelet transform matching a specified signal with applications to digital, real time, spike, and overlap pattern recognition. Digit Signal Process 16:22–44
Gupta A, Joshi SD, Prasad S (2005a) A new approach for estimation of statistically matched wavelet. IEEE Trans Signal Process 53(5):1778–1793
Gupta A, Joshi SD, Prasad S (2005b) A new method of estimating wavelet with desired features from a given signal. Signal Processing 85:147–161
Harris T (1991) Rolling bearing analysis. Wiley, New York
Inman D (1996) Engineering vibration. Prentice Hall, Englewood Cliffs, NJ.
Kaiser G (1994) A Friendly Guide to Wavelets. Birkhauser, Boston, MA
Lou X, Loparo KA (2004) Bearing fault diagnosis based on wavelet transform and fuzzy inference. Mech Syst Signal Process 18:1077–1095.
Lu WS, Antoniou A (2001) Design of signal-adapted biorthogonal filter banks. IEEE Trans Circuits Syst I Fundam Theory Appl 48:90–102.
Lutes L, Sarkani S (1997) Stochastic analysis of structural and mechanical vibrations. Prentice Hall, Englewood Cliffs, NJ
Mallat S (1998) A wavelet tour of signal processing. Academic, Boston, MA
Misiti M, Misiti Y, Oppenheim G, Poggi J (1997) Wavelet toolbox for use with Matlab. The Math Works, Inc., Natick, MA
Shark L, Yu C (2003) Design of optimal shift-invariant orthonormal wavelet filter banks via genetic algorithm. Signal Processing 83:2579–2591
Shark L, Yu C (2006) Design of matched wavelets based on generalized Mexican-hat function. Signal Processing 86:1451–1469
Tewfik AH, Sinha D, Jorgensen P (1992) On the optimal choice of a wavelet for signal representation. IEEE Trans Inf Theory 38:747–765
Yan R, Gao R, Wang C (2009) Experimental evaluation of a unified time-scale-frequency technique for bearing defect feature extraction. ASME J Vib Acoust 131:041012-1-12
Young R (1993) Wavelet theory and its applications. Kluwer Academic Publishers, Boston, MA
Zhang S, Mathew J, Ma L, Sun Y (2005) Best basis-based intelligent machine fault diagnosis. Mech Syst Signal Process 19:357–370
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Gao, R.X., Yan, R. (2011). Designing Your Own Wavelet. In: Wavelets. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1545-0_11
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DOI: https://doi.org/10.1007/978-1-4419-1545-0_11
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