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本文研究了在数学期望为零的高斯过程输入情况下,h(lx)具有h~(k+p)(lx)=l~ph~(k)(lx)(其中:h~(k)(lx)=(?)~(k)h(lx)/(?)x~k,l为某个实数)性质的输出相关函数。 文中利用上述性质,由Price定理导出一常微分方程。将求非线性系统输出相关函数的问题,变成解常微分方程的问题。 所得结果表明:这类非线性系统的输出相关函数具有相同的形式。不同的h(lx)仅影响其系数。 在此基础上,文中将一般非线性系统的特性f(x)用具有上述性质的函数族来表示,然后直接引用文中前面所得的结果,非常简便地得出了一般非线性系统的输出相关函数的计算公式。
In this paper, we study the case that h (lx) has h ~ (k + p) (lx) = l ~ ph ~ (k) (lx) where the mathematical expectation is zero lx) = (?) ~ (k) h (lx) / (?) x ~ k, l is a real number) output correlation function. In this paper, we use the above properties to derive an ordinary differential equation by the Price theorem. The problem of finding the correlation function of nonlinear system output becomes the problem of solving differential equations. The results show that the output correlation functions of these nonlinear systems have the same form. Different h (lx) only affects its coefficient. On this basis, the characteristic f (x) of a general nonlinear system is represented by a family of functions with the above properties, and then the results obtained in the previous paper are directly used to obtain the output correlation function of a general nonlinear system The formula.