In this paper, a new trial for the signal processing is proposed along the same line as a previous study on the extended regression analysis based on the Bayes' theorem. This method enables us to estimate a response probability property of complicated systems in an actual case when observation values of the output response are roughly observed due to the quantization mechanism of measuring equipment. More concretely, the main purpose of this research is to find the statistics of the joint probability density function before a level quantization operation which reflects every proper correlation informations between the system input and the output fluctuations. Then, the output probability distribution for another kind of input is predicted by using the estimated regression relationship. Finally, the effectiveness of the proposed method is experimentally confirmed by applying it to the actually observed input-output data of the acoustic system.

A specific signal in most of actual environmental systems fluctuates complicatedly in a non-Gaussian distribution form, owing to various kinds of factors. The nonlinearity of the system makes it more difficult to evaluate the objective system from the viewpoint of internal physical mechanism. Furthermore, it is very often that the reliable observation value can be obtained only within a definite domain of fluctuating amplitude, because many of measuring equipment have their proper dynamic range and the original random wave form is unreliable at the end of amplitude fluctuation. It becomes very important to establish a new signal processing or an evaluation method applicable to such an actually complicated system even from a functional viewpoint. This paper describes a new trial for the signal processing along the same line of the extended regression analysis based on the Bayes' theorem. This method enables us to estimate the response probability property of a complicated system in an actual situation, when observation values of the output response are saturated due to the dynamic range of measuring equipment. This method utilizes the series expansion form of the Bayes' theorem, which is applicable to the non-Gaussian property of the fluctuations and various kinds of correlation information between the input and output fluctuations. The proposed method is newly derived especially by paying our attention to the statistical information of the input-output data without the saturation operation instead of that on the resultantly saturated observation, differing from the well-known regression analysis and its improvement. Then, the output probability distribution for another kind of input is predicted by using the estimated regression relationship. Finally, the effectiveness of the proposed method is experimentally confirmed too by applying it to the actual data observed for indoor and outdoor sound environments.