As is well-known, the ordinary regression analysis method is confined to a simplified linear model of the estimation based on the Gaussian property and a least squares error criterion. Then, usually the prediction is done through the transformation based on this regression function. In this paper, a new trial for the regression analysis is proposed especially in the form matched to the complexity of physical phenomena and stochastic signal detection under the existence of background noise. Furthermore, the prediction of the output probability distribution is done based on the regression relationship with less information loss. Finally, the effectiveness of the proposed method is confirmed experimentally by applying it to the actual acoustic data.

In the actual acoustic environment, the stochastic process exhibits various non-Gaussian distribution forms, and there exist potentially various nonlinear correlations in addition to the linear correlation between time series. In this study, a nonlinear ARMA model is proposed, based on the Bayes' theorem, where no artificially pre-established regression function model is assumed between time series, while reflecting hierarchically all of those various correlation informations. The proposed method is applied to the actual data of road traffic noise and its practical usefulness is verified.

In the actual sound environmental systems, it seems to be essentially difficult to exactly evaluate a whole probability distribution form of its response fluctuation, owing to various types of natural, social and human factors. We have reported a unified probability density expression in the standard expansion form of Hermite type orthonormal series taking a well-known Gaussian probability density function (abbr. p.d.f.) as the basis for generally evaluating non-Gaussian, non-linear correlation and/or non-stationary properties of the fluctuation phenomenon. However, in the real sound environment, there still remain many actual problems on the necessity of improving the above standard type probability expression for practical use. First, a central point in this paper is focused on how to find a new probabilistic theory of practically evaluating the variety and complexity of the actual random fluctuations, especially through newly introducing an equvivalence transformation toward the standard type probability expression mentioned above in the expansion form of Hermite type orthonormal series. Then, the effectiveness of the proposed theory has been confirmed experimentally too by applying it to the actual problems on the response probability evaluation of various sound insulation systems in an acoustic room.

In the measurement of actual random phenomenon, the observed data often result in a loss or are distorted due to the existence of a definite dynamic range of measurement instruments. In this study, a trial on the stochastic signal processing for the incomplete data with loss or distortion is newly proposed. Concretely, by regarding the observed data within a finite dynamic measurement range as a random variable with a amplitude saturation, a new unified expression of the probability distribution function matched to this amplitude limitation is derived in a series expansion form. Next, as an application of the above probability expression, a state estimation method based on the above incomplete observations is theoretically proposed through an establishment of wide sence digital filter under the actual situation of existence of the additional noise. Finally, the validity and the effectiveness of the proposed method are experimentally confirmed.

In this paper, a stochastic signal processing method of analog type for the prediction of power state variable is first discussed by considering the effect of an internal mechanism of an instrument with mean squaring operation. Next, in the actual case of quantized observation contaminated by an additive random noise, a wide sense digital filter estimating the power state variable of stochastic systems is proposed. These methods are applied to the actual data measured in acoustic environment.

In this study, an expression of the regression relationship with less information loss is concretely derived in the form suitable to the existence of amplitude constraint of the observed data and the prediction of response probability distribution. The effectiveness of the proposed method is confirmed experimentally by applying it to the actual acoustic data.

A new trial of statistical evaluation for an output response of power linear type acoustic systems with nonstationary random input is proposed. The purpose of this study is to predict the output probability distribution function on the basis of a standard type pre-experiment in a laboratoty. The statistical properties like nonstationarity, non-Gamma distribution property and various type linear and non-linear correlations of input signal are reflected in the form of differential operation with respect to distribution parameters. More concretely, the pre-experiment is carried out for a power linear acoustic system excited only by the Gamma distribution type sandard random input. Considering the non-negative random property for the output response of a power linear system, the well-known statistical Laguerre expansion series type probability expression is first employed as the framework of basic probability distribution expression on the output power fluctuation. Then, the objective output probability distribution for a non-stationary case can be easily derived only by successively employing newly introduced differential operators to this basic probability distribution of statistical Laguerre expansion series type. As an application to the actual noise environment, the proposed method is employed for an evaluation problem on the stochastic response probability distribution for an acoustic sound insulation system excited by a nonstationary input noise.

The noise level distribution owing to only a non-stationary working objective machine has been stochastically expressed by reflecting the temporal change of distribution parameters under a generalized regression model especially with aid of the vibration level observation. The proposed method has been applied to a noise evaluation of non-stationarily operated jigsaw.

For evaluating the output response fluctuation of the actual environmental acoustic system excited by arbitrary random inputs, it is important to predict a whole probability distribution form closely connected with many noise evaluation indexes Lx, Leq and so on. In this paper, a new type evaluation method is proposed by introducing lower and higher order type functional models matched to the prediction of the response probability distribution form especially from a problem-oriented viewpoint. Because of the non-negative property of the sound intensity variable, the response probability density function can be reasonably expressed in advance theoretically by a statistical Laguerre expansion series form. The system characteristic between input and output can be described by the regression relationship between the distribution parameters (containing expansion coefficients of this expression) and the stochastic input. These regression functions can be expressed in terms of the orthogonal series expansion. Since, in the actual environment, the observed output is inevitably contaminated by the background noise, the above regression functions can not be directly employed as the models for the actual environment. Fortunately, the observed output can be given by the sum of the system output and the background noise on the basis of additivity of intensity quantity and the statistical moments of the background noise can be obtained in advance. So, the models relating the regression functions to the function of the observed output can be derived. Next, the parameters of the regression functions are determined based on the least-squares error criteria and the measure of statistical independency according to the level of non-Gaussian property of the function of the observed output. Thus, by using the regression functions obtained by the proposed identification method, the probability distribution of the output reducing the background noise can be predicted. Finally, the effectiveness of the proposed method is confirmed experimentally too by applying it to an actual indoor-outdoor acoustic system.

Generally speaking, in the actual situation of evaluating or predicting the stochastic random phenomena, it is sometimes inevitable to consider the undesirable modelling error generated from an incomplete situation in the actual measurement (i.e., the observations in an actual environmental field are very often given under the unsatisfactory situation without keeping the idealized physical property assumed abstractively in the theoretical research), together with the inevitable additional background noise of arbitrary distribution type. Thus, the unified statistical treatment for the resultant data contaminated by these additional noises of different type is newly proposed in this paper from the system-theoretical viewpoint closely related to environmental field, based on Bayes' theorem and the information criterion. Its computer-aided identification algorithm is derived in a very compact form matched to the recurrence processing of succesive observations. Finally, the validity and the effectiveness of our theoretical result are experimentally confirmed through the application to the actual data of environmental noise in room acoustics.

In direct connection with the signal information processing, a practical method of identification and probabilistic prediction for sound insulation systems is theoretically proposed in the object-oriented expression forms by introducing a few functional system parameters. Concretely, a trial of identification of the above functional system parameters and the output probabilistic prediction for a panel thickness change of double-wall type sound insulation system, especially, under the existence of a strong background noise inside of the reception room, is newly proposed based on one of wide sense digital filters and SEA (Statistical Energy Analysis) method. Finally, by using the actual music sound of an arbitrary distribution type, the effectiveness of the proposad method is confirmed experimentally by applying it to some problems of predicting the cumulative probability distribution of the transmitted sound level fluctuation.

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.

It often occurs in the acoustic environment that a specific signal is contaminated by the additional noise of non-Gaussian distribution type. In order to extract exactly the various statistical information of only specific signal from the observed noisy data, a stochastic signal processing by use of digital computer is essential. In this study, a stochastic method for estimating the probability function of the specific signal embedded in the additional noise is first theoretically proposed in a suitable form for the quantized level observation. Then, the effectiveness of the proposed method is experimentally confirmed by applying it to the observed data in the acoustic environment.

A ner trial of statistical evaluation for a nonstationary traffic flow and its traffic noise is proposed as a prediction method of its probability distribution function by considering the temporal change of distribution parameters especially from a structural viewpoint. First, a headway distribution of the nonstationary traffic flow passing through within a road segment is proposed on the basis of an Erlang distribution by reflecting a temporal change of its distribution parameters. Then, an initial phase density concerning with asynchronous counting method and the probability of counting n cars over a long time interval are derived from the above nonstationary expression of headway distribution. Thus, the statistics of noise intensity at an observation point has been predicted by combining the above probabilistic factors and deterministic factors related to noise propagation environment with use of a compound stochastic process model. Finally, te effectivenss of the proposed theory has been confirmed experimentally by applying it to the actual traffic flow on a highway.

It often occurs in an environmental phenomenon in our daily life that a specific signal is partially or completely contaminated by the additional external noise. In this study, a digital filter for estimating a specific signal fluctuating impulsively under the existence of an actual external noise with various kinds of probability distribution forms is proposed in an improved form of already reported digital filter. The effectivenss of the proposed theory is experimentally confirmed by applying it to the estimation of an actual impulsve signal in a room acoustic.

In the measurement of actual random phenomenon, the observed data often contain the fuzziness due to the existence of confidence limitation in measuring instruments, permissible error in experimental data, some practical simplification of evaluation procedure and a quantized error in digitized observation. In this study, by introducing the well-known fuzzy theory, a state estimation method based on the above fuzzy observations is theoretically proposed through an establishment of wide sense digital filter under the actual situation of existence of the background noise in close connection of the inverse problem. The validity and effectiveness of the proposed method are experimentally confirmed by applying it to the actual fuzzy data observed in an acoustic environment.

In this paper, a new restoration method for the X-ray images with optical blurs and quantum mottles is proposed by considering the physical formation process of X-ray images. More specifically, the optical blurs are first deterministically cleared away by using the transfer characteristic of the laser scanning, the characteristic of the radiographic screen-film system, the logarithmic transformation of the optical density and a digital inverse filter based on the point spread function. Next, as a restoration method for remaining quantum mottles, a wide sense digital filter of a stochastic type using the statistical properties of quantum mottles is newly derived on the basis of a Bayes' theorem matched to the recursive image processing. Finally, in order to confirm the effectiveness of the proposed method, it is applied to one of the actual medical images.

This paper describes a trial of evaluating the proper characteristics of multiple sound insulatain systems from their output responses contaminated by unknown background noises. The unknown parameters of sound insulation systems are first estimated on the basis of hte linear time series on an intensity scale, describing functionally the input-output relation of the systems. Then, their output probability distributions are predicted when an arbitrary input noise passes through these insulation systems.

Under a contamination of background sound noises, it seems difficult especially in a real working situation to evaluate various type statistics of only an objective sound signal fluctuation. In many cases of the noise evaluation, some signal processing method have been employed to eliminate the effect of background sound noises by first measuring emitted sound levels. In this study, a new evaluation method of sound level fluctuation is proposed in principle on the basis of the measurement of heterogeneous physical quantity other than sound pressures or sound levels to eliminate the effect of background sound noises. Though the theoretical analysis on acoustical emission caused by a mechanical vibration seems very difficult in a working situation, the sound noise fluctuation emitted only from an objective sound source can be effectively evaluated through its related vibration measurement by employing a fairly unified stochastic method proposed on the basis of a generalized regression analysis between sound and vibration. Here, the regression coefficients are determined by employing the least squares error method to minimize the mean square of estimation error to illustrate well the sound data by means of vibration data. Finally, the effectiveness of proposed method has been experimentally applied to the sound noise evaluation of a jigsaw.

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.