In this paper, in order to evaluate quantitatively the stochastic characteristics of the fluctuating signal, a generalized
n-th order fluctuation rate index is first proposed. Then, the high order equivalence relationship between two time constants of the ideal and the exponential type mean square operations is derived based on the proposed
n-th order fluctuation rate index. More concretely, this equivalence relationship is newly discussed especially concerning the third order fluctuation rate index which occupies the first fundamental position in case of hierarchically evaluating the non-Gaussian property, and the well-known equivalence relationship
T≅2γ(
T: time constant of an ideal type mean squaring operation, γ: time constant of an exponential type mean squaring operation) is again found in a special case with
n=2 from the different viewpoint in the time domain under the above same fluctuation rate index. The effectiveness of the proposed theory has been confirmed well experimentally by the applications to the actual sound data.
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