A 8tudy on the Joint Probability Distribution of Two Random Intensity Variables for the Gaussian Random Wave in the Multidimensional Signal Space

摘要

In the present paper，our attention is focused on finding out how the actualrandom variation itself in time is expressed quantitatively for the randomintensity fluctuation. When we observe simuItaneously one or more noisefluctuations having random phases at two or more different observationpoints with differences in time， position， frequency or propagation constant，we need to consider the joint probability distribution density of the intensityof the multiple correlative random noise variables. We must call our attentionto the fact that the joint moments of high orders give the general correlationof high orders among the multiple correlative random noise variables in theabove，e. g. usual linear correlation is reflected in af irst-order joint moment.From this point of view，an explicit expression of joint gamma probabilitydistribution density for two random intensity fluctuations， after passingthrough am ean squaring circuit and a rectangular band-pass filter，is theoretical1y derived for the white noise in connection with an experimentalconsideration.The statistical method described in this paper seems to be applicable alsoto other wide fields of measurement on random phenomena because of itsgenerality.