Characteristics of power-law distributed AE signals

A simple model of the measurement chain frequently used in Acoustic Emission (AE) experiments furnishes interesting results in the case of power-law distributed AE events; the importance of such systems is remarkable as more and more physical processes are being shown to possess scale invariant statistics. The aim of this study is to characterize the response of a simple harmonic 1D resonator subject to an excitation signal having a power-law amplitude distribution. Specific realizations of excitations signals are analyzed not only to put into evidence certain features of the resultant time series but also to analyze the transitions that take place varying the parameters of the applied noise signal. The response of the simple harmonic resonator to the AE signals is obtained using a spectral method relying on the linearity and time invariance of the resonator's response. The principle of superposition ensures that each component of the input signal can be treated separately; output signal are obtained by convolving input signals with the response function of the resonator. The statistical characteristics of the output signal exhibit several regimes which depend both on the resonator's and the AE distribution's parameters.