Extension of the Background/biResonant decomposition to the estimation of the kurtosis coefficient of the response

Based on the observation of the existence of different timescales, this paper provides an approximate method to compute the kurtosis coefficient of the response of a linear-time-invariant system subjected to a low-frequency non Gaussian input. While the kurtosis coefficient is formally obtained by a multidimensional integration of the corresponding spectrum, the proposed method only requires the estimation of a single definite integral. The speedup performance is three to four orders of magnitude and the approximation is very accurate as it corresponds to the leading order expansion of the formal solution, with the ratio of the identified timescales considered as a small parameter.