A functional prediction method on the response probability for linear sound systems on energy scale based on the stochastic information and its application to room acoustics.

Abstract

As is well-known, the conventional standard identification methods for stochastic systems are usually employed under the optimum selection of the system order and system parameters, by use of the linear correlation technique and the usual least squares error method. In this paper, a new trial of finding some object-oriented system identification method matched to the prediction of output response probability distribution has been proposed in the functional and hierarchical forms. More explicitly, the indoor sound system on an energy scale is firstly described by a linear time series model supported by the well-known Sabine's equation or Statistical Energy Analysis method. Then, a generalized series expansion type probability density expression matched to an energy state variable has been proposed for the system output response in the form matched to the variety of fluctuation form, under the introduction of statistical information reflected hierarchically in expansion coefficients. Furthermore, instead of the usual system order and system parameters in the time series type system model, several kinds of functionally introduced system orders and system parameters have been estimated hierarchically in the matched form to the above hierarchical structure in the probability density expression. Finally, the validity and the effectiveness of the proposed theory have been experimentally confirmed too by applying it to the actual data observed in a reverberation room.