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Since the non-stationary fluctuation of actual acoustic environment like the road traffic noise within a long time interval is usually caused not by the change of merely additional external noise but by the essential change of internal factors themselves, it is reasonable to give as a mathematical model of this non-stationary fluctuation not an additive model but a multiplicative model. In this paper, mainly from a methodological viewpoint, first, the characteristic function method of Mellin transform type for the above multiplicative model is introduced and a new unified expression form of the probability density function within a long time interval is derived in an expansion form based on the probability density function within a short time interval of local stationary type as its first expansion term with distribution parameters reflecting hierarchically various types linear and nonlinear correlation information.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
179--194
Opis fizyczny
Bibliogr. 19 poz., rys., wykr.
Bibliografia
- [1] A. Iketani, Mathematical model and evaluation indexes for road traffic noise [in Japanese], Acoust. Soc. Jpn ., 31, 9, 559-565 (1975).
- [2] M. Ohta et al., A prediction theory of sound level probability distribution in urban district for assessment of establishment of new road and experiment by simulation [in Japanese], Acoust. Soc. Jpn., 31, 2, 72-80 (1975).
- [3] S. Ishii, A study on the calculation method of predicting a road traffic noise [in Japanese], Acoust. Soc. Jpn ., 31, 8, 507-5 17 (1975).
- [4] M. Ohta, A consideration for modelling of non-stationary stochastic phenomena [in Japanese], Systems and Control, 16, 5, 423-426 (1972).
- [5] T. Kariya, Knowledge for prediction, Morikita, Tokyo 1971.
- [6] A. Papoulis, Probability, random variables and stochastic processes, McG raw-Hill Kogakusha, Tokyo 1965.
- [7] E.C. T itchmarsh, Introduction to the theory of Fourier integrals, Oxford 1937.
- [8] G.A . Campbell and R.M. Foster, Fourier integrals for practical applications, Van Nostrand 1948.
- [9] S. Moriguchi, K . Udagawa, S. Hitotum atu, Formula of mathematics II [in Japanese], pp. 307-310, Iwanami 1960.
- [10] K. Yoshida, A. Amamiya, K. Ito , T. Kato, K. Matushima and S. Furuya, Handbook of applied mathematics [in Japanese], pp. 322-323, Maruzen 1969.
- [11] Japanese Industrial Standard Committee, JIS Z 8731-Methods of measurement and description of A-weighted sound pressure level [in Japanese], Japanese Standard Association, Tokyo 1983.
- [12] H. Hironaka, Encyclopedia of mathematical sciences [in Japanese], pp. 484, Maruzen 1991.
- [13] G.E .P . Box and G.M. Jenkins, Some recent advances in forecasting and control, App lied Statis¬tics, 17, 99-109 (1968).
- [14] M.B. Priestley, Evolutionary spectra and non-stationary processes, J.R . Statistical Society, B, 27, 204-237 (1965).
- [15] A.C . Harvey, Tim e series models, Philip Allan Publishers limited, Oxford 1981.
- [16] M. Ohta and T. Koizumi, General statistical treatment of response of a nonlinear rectifying device to a stationary random input, IEEE Trans, on information theory, vol. IT-14, 4, 595-598 (1968).
- [17] M. Ohta, On the composition of waves in the random phase problem, Proc, of 5th Japan National Congreess for Appl. Meeh., pp. 489-492, 1958.
- [18] M. Ohta, A viewpoint in the analysis of non-stationary phenomena [in Japanese], System and Control, 16, 5, 423-426 (1972).
- [19] M. Ohta, A fundamental viewpoint in the analysis problem of stochastic control system-effectiveness of statistical series expansion method [in Japanese], Tians. IECE , 55-D, 8, 562-563 (1972).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT3-0007-0108