a variance of one. Then, (7) becomes (8)Cx1x2(A)=A2−2cA+E[b1b2]A2−2cA+1=1−1−E[b1b2]A2−2cA+1. Since A2–2cA+1 has a minimum value at A = c, one can see that, when –1 ≤ c ≤ 0, Cx1x2(A) monotonically increases as A(> 0) increases. Fig. 1(A) and (B)(b) show examples of the function Cx1x2(A) according to negative and positive correlations of nonreferential signals b1 and b2, respectively. When 0 ≤ c ≤ 1, Cx1x2(A) monotonically decreases from Cx1x2(0)=E[b1b2] to Cx1x2(c)=(E[b1b2]−c2∕1−c2) as A varies in [0, c] and then start to monotonically increase to one as A varies in [c, +∞]. Fig. 1(B)(a) shows examples of the function Cx1x2(A) according to positive correlations of nonreferential signals b1 and b2. It should be pointed out that the resulting curve from the absolute values of each curve in Fig. 1(A) decreases to zero and then starts to increase to one when A varies in [0, +∞). Moreover, even a small change of coefficient A may lead to a significant impact on correlation values [for example, see the curve corresponding to Cb1b2=−1 in Fig. 1(A)].
