The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.

Alotta, G., Di Paola, M., Failla, G. (2015). A Mellin transform approach to wavelet analysis. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION, 28(1-3), 175-193 [10.1016/j.cnsns.2015.04.001].

### A Mellin transform approach to wavelet analysis

#### Abstract

The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin transform expression, with fractional moments obtained from a set of algebraic equations whose coefficient matrix applies for any scale a of the wavelet transform. Robustness and computationally efficiency of the proposed approach are shown in the paper.
##### Scheda breve Scheda completa Scheda completa (DC) 2015
Alotta, G., Di Paola, M., Failla, G. (2015). A Mellin transform approach to wavelet analysis. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION, 28(1-3), 175-193 [10.1016/j.cnsns.2015.04.001].
File in questo prodotto:
File
1-s2.0-S1007570415001252-main.pdf

Solo gestori archvio

Dimensione 3.49 MB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/173371`
• ND
• 9
• 8