任意UAP関数群による雑音model形成の新たな一試み : II.実験的考察(Digital Simulation)

抄録

In the previous paper, starting from a criticism of the Rice representations of normal random noise and generalizing a random noise model in terms of a trigonometric series consisting of uniformly almost periodic (U. A. P. ) functions, a new trial for a mathematical formation of a random noise model was theoretically introduced by using U. A. P. functions consisting of arbitrary component waves. That is, the new mathematical model I_N(t) (cf. Eq. (1)) is characterized by(1) No necessity for introducing any probability distribution law for either amplitude or phase at the outset, and(2) Gaussian distribution characteristic formed automatically in the course of time. Keeping in mind the variety of the component wave form, the arbitrariness of the number of component waves and the complexity of mathematical expressions involved and their statistical treatment, the use of the digital simulation technique is inevitable for the experimental confirmation and is the most successful way for the present study. In this paper, it is experimentally pointed out on the normal probability papers (cf. Figs. 7〜10 and Figs. 13, 14) from various points of view that a cumulative probability distribution Q(I_N) (cf. Eq. (3)) is asymptotically a standard normal distribution as N tends to infinity and the choice of the component wave F(θ) contributes substantially to the speed of convergence tending to Gaussian distribution on several concrete cases where the component wave has respectively the specialized forms (cf. Cases I〜V in §2. 1 and Figs. 7〜14). Furthermore, the characteristic that the nth order moments (n=4, 6, 8) of I_N(t) become asymptotically those of standard Gaussian distribution for a sufficiently large value of N is experimentally confirmed in a special model of random noise formed in terms of trigonometric series consisting of U. A. P. functions(cf. Fig. 15).