Abstract
In this work we present the design of an orthogonal wavelet, infinitely oscillating, located in time with decay 1/|t|n and limited-band. Its appli- cation leads to the signal decomposition in waves of instantaneous, well defined frequency. We also present the implementation algorithm for the analysis and synthesis based on the Fast Fourier Transform (FFT) with the same complexity as Mallat’s algorithm.
References
Donoho, D.L. (1995) “Nonlinear solution of Linear Inverse problems by Wavelet-Vaguelet decomposition”, Applied and Computational Harmonic Analysis 2(2): 101–126.
Huang, N.E; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.C.; Tung, C.C.; Liu, H.H. (1998) “The empirical mode decomposition and the Hilbert spectrum for non-stationary time series analysis”, Proc. R. Soc. Lond. A 454: 903–995.
Jaffard, S.; Lashermes, B.; Abry, P. (2007) “Wavelet leaders in multifractal analysis”, in: T. Qian, M. Vai, X. Yuesheng (Esd.) Wavelet Analysis and Applications, Birkhäuser, Basel, Switzerland: 201–246.
Li, L.C. (2010) “A new method of wavelet transform based on FFT for signal processing”, Second WRI Global Congres on Intelligent Systems, IEEE Computer Society: 203–206.
Mallat, S. (2009) A Wavelet Tour of Signal Processing, The Sparse Way. Academic Press–Elsevier, Burlington MA.
Meyer, Y. (1993) Wavelets, Algorithms and Applications. SIAM, Philadelphia PA.
Meyer, Y. (2001) Oscillating Pattern in Image Processing and Nonlinear Evolution Equations. American Mathematical Society, Providence RI.
Serrano, E.; Figliola, A. (2008) Littlewood-Paley spline wavelets: a simple and efficient tool for signal and image processing in industrial applications, Proceedings in Applied Mathematics and Mechanics (PAMM), Wiley InterScience, 7: 1040313–1040314.
Serrano, E.; Fabio, M. (2010) “Diseño de funciones elementales combinando la transformada wavelet y la transformada de Hilbert”, UMA 2010, Tandil, Argentina.
Serrano, E.; Fabio, M.; Aragón, A. (2011) “Caracterización de la frecuencia instantánea en señales tipo pasa-banda”, III MACI, Asociación Argentina de Matemática Aplicada, Computacional e Industrial. Bahía Blanca, Argentina.