A Mellin transform approach to wavelet analysis

作者：Alotta Gioacchino^*; Di Paola Mario; Failla Giuseppe

来源：Communications in Nonlinear Science & Numerical Simulation, 2015, 28(1-3): 175-193.

DOI：10.1016/j.cnsns.2015.04.001

• Mellin transform
• Fractional calculus
• Wavelet analysis
• linear systems

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 functionf(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.

• 出版日期2015-11