多次元正規分布の不規則信号発生法

抄録

This paper presents the method of generating N-dimensional normally distributed random signals from a single binary random signal.The main constituents on the basis of this method are the n-stage shift register whose state represented by a vector α(t) is varied irregularly by transmitting the binary random signal, and the N weighted adders whose k-th output is x^k=α(t)^tω^k, where ω^k is the weight vector of the k-th weight adder. It is theoretically shown that, if ω^k is proportional to a k-th degree orthogonal polynominal P^k_n-1, the cross-correlation function of x^k and x^l for different arbitrary k, l is zero, the probability density function of x^k is a normal distribution when n is infinite, and x^k and x^l are statistically independent. Therefore it is possible to generate the N-dimensional normally distributed random signals with an arbitrary covariance matrix by combining the {x^k; k=1, 2, …, N} linearly.
It is made sure by a digital simulation that this method can be put to practical use.