(1) The average value of the quantity x(r+nh) and y(nh), where x and y are randomly varying functions of the quantity nh and n being an integer which varies from N to +N and r and h are constants. (2) The limit of the quantity defined in (1) as N becomes very large. (3) The average value φ(r) defined by (1/2T) ∫ x(r+t)y(t) dt. (4) The limit of the quantity φ(r) defined in (3) as T goes to infinity. If x and y are different variables, the correlation function is called the cross correlation function of the two variables. If they are the same variable, it is called the auto correlation function of x.