Abstract
To ensure safe and economical operation and product quality, manufacturing machines and processes are constantly monitored and evaluated for their working conditions, on the basis of signals collected by sensors, which are generally presented in the form of time series (e.g., time-dependent variation of vibration, pressure, temperature, etc.). To extract information from such signals and reveal the underlying dynamics that corresponds to the signals, proper signal processing technique is needed.
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References
Bracewell, R (1999) The Fourier transform and its applications. 3rd edn. McGraw-Hill, New York
Chui CK (1992) An introduction to wavelets. Academic, New York
Cohen L (1989) Time-frequency distributions – a review. Proc IEEE 77(7):941–981
Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex Fourier series. Math Comput 19:297–301
Daubechies I (1988) Orthonormal bases of compactly supported wavelets. Comm Pure Appl Math 4:909–996
Daubechies I (1992) Ten lectures on wavelets. SIAM, Philadelphia, PA
DeVore RA, Jawerth B, Lucier BJ (1992) Image compression through wavelet transform coding. IEEE Trans Inf Theory 38(2):719–746
Fourier J (1822) The analytical theory of heat. (trans: Freeman A). Cambridge University Press, London, p 1878
Gabor D (1946) Theory of communication. J IEEE 93(3):429–457
Grossmann A, Morlet J (1984) Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15(4):723–736
Grossmann A, Morlet J, Paul T (1985) Transforms associated to square integrable group representations. I. General results. J Math Phys 26:2473–2479
Grossmann A, Morlet J, Paul T (1986) Transforms associated to square integrable group representations. II: examples. Ann Inst Henri Poincaré 45(3):293–309
Haar A (1910) Zur theorie der orthogonalen funktionen systeme. Math Ann 69:331–371
Herivel J (1975) Joseph Fourier. The man and the physicist. Clarendon Press, Oxford
Jaffard S, Yves Meyer Y, Ryan RD (2001) Wavelets: tools for science & technology. Society for Industrial Mathematics, Philadelphia, PA
Körner TW (1988) Fourier analysis. Cambridge University Press, London
Littlewood JE, Paley REAC (1931) Theorems on Fourier series and power series. J Lond Math Soc 6:230–233
Mackenzie D (2001) Wavelets: seeing the forest and the trees. National Academy of Sciences, Washington, DC
Mallat SG (1989a) A theory of multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 11(7):674–693
Mallat SG (1989b) Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans Am Math Soc 315:69–87
Mallat SG (1998) A wavelet tour of signal processing. Academic, San Diego, CA
Meyer Y (1989) Orthonormal wavelets. In: Combers JM, Grossmann A, Tachamitchian P (eds) Wavelets, time-frequency methods and phase space, Springer-Verlag, Berlin
Meyer Y (1993) Wavelets, algorithms and applications. SIAM, Philadelphia, PA
Newland DE (1993) Harmonic wavelet analysis. Proc R Soc Lond A Math Phys Sci 443(1917) 203–225
Oppenheim AV, Schafer RW, Buck JR (1999) Discrete time signal processing. Prentice Hall PTR, Englewood Cliffs, NJ
Qian S (2002) Time-frequency and wavelet transforms. Prentice Hall PTR, Upper Saddle River, NJ
Ricker N (1953) The form and laws of propagation of seismic wavelets. Geophysics 18:10–40
Rioul O, Vetterli M (1991) Wavelets and signal processing. IEEE Signal Process Mag 8(4):14–38
Strömberg JO (1983) A modified Franklin system and higher-order spline systems on Rn as unconditional bases for Hardy space. Proceedings of Conference on Harmonic Analysis in Honor of Antoni Zygmund, vol 2, pp 475–494
Jean B. Joseph Fourier, http://mathdl.maa.org/images/upload_library/1/Portraits/Fourier.bmp
Dennis Gabor, http://nobelprize.org/nobel_prizes/physics/laureates/1971/gabor-autobio.html
Alfred Haar, http://www2.isye.gatech.edu/~brani/images/haar.html
Paul Levy, http://www.todayinsci.com/L/Levy_Paul/LevyPaulThm.jpg
Jean Morlet, http://www.industrie-technologies.com/GlobalVisuels/Local/SL_Produit/Morlet.jpg
Stephane Mallat, http://www.cmap.polytechnique.fr/~mallat/Stephane.jpg
Yves Meyer, http://www.academie-sciences.fr/membres/M/Meyer_Yves.htm
Ingrid Daubechies, http://commons.princeton.edu/ciee/images/people/DaubechiesIngrid.jpg
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Gao, R.X., Yan, R. (2011). From Fourier Transform to Wavelet Transform: A Historical Perspective. In: Wavelets. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1545-0_2
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