いわゆる「ウィーナー・ヒンチンの公式」とパワースペクトルについて
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概要
- 論文の詳細を見る
The expression "Wiener-Khintchine's formula" often appears in the literature of science and technology. But the suitability of the naming is doubtful. Here, the related treatises and monographs are widely surveyed and the following result is obtained. That is, the content of the "formula" is different according to the authors who adopt the name, and though considerably many authors use this term, a lot of authors do not mention such expression at all and the name has not been established yet. Further the author carefully examines the original works of both Wiener and Khintchine and outlines the three fundamental concepts appearing in the "formula" together with the relations among them. In Wiener's the autocorrelation function by time average for a definite function is introduced and the power spectrum is defined as the inverse Fourier-Stieltjes transform of the autocorrelation function. In the author's opinion, what Wiener did was nothing but the definition of the power spectrum and the physical meaning of the power spectrum has not been made clear until now. While, in Khintchine's the notions of the autocorrelation function by ensemble average and the spectral distribution function for a stationary stochastic process are considered. After all, the author comes to the conclusion that the expression "Wiener-Khintchine's formura" must be fabricated by someone by connecting the convenient parts of the works of two great mathematicians. Naturally, the author will not support this term.
- 湘南工科大学の論文
- 1992-03-31