Tab.2: Correlation probability and SNR 
  
Probability with objective function*! 
SNR a b C d 
< 0.10 0.00 0.00 0.00 0.00 
0.13 0.00 0.00 0.00 0.36 
0.18 0.06 0.12 0.00 0.47 
0.25 0.44 0.17 0.00 0.67 
0.31 0.44 0.38 0.00 0.63 
0.39 0.57 0.57 0.00 0.93 
0.43 0.71 0.79 0.00 0.86 
0.49 0.62 0.59 0.15 0.77 
  
0.57 0.88 0.94 0.06 1.00 
0.66 0.88 0.88 0.00 0.94 
0.76 1.00 1.00 0.17. 1.00 
0.86 0.94 1.00 p.25 = 1,00 
LE 0.96 0.92 1,00 0.25 . 1.00 
1.25 1.00 1.00 9.33 1.00 
1.75 1.00 1.00 0.83 1.00 
3.50 1.00 1.00 0.95 1.00 
7.50 1.00 1.00 0.98 1.00 
> 10.00 1.00 1.00 1.00. 1.00 
  
+) a = product moment correlation coefficient 
b = intensity coefficient (global variances) 
c = Laplace coefficient 
d 
= phase correlation coefficient 
For an easier interpretation it is convenient to develop a mathematical expression of 
the relationship between probability and SNR. 
  
Mathematical approximation of correlation probability and SNR 
To obtain an analytical expression of the connection between noise and correlation 
probability P, the P-values are plotted versus the corresponding logarithmic SNR. We 
get an S-shaped curve with an almost linear increase in the medium domain (see fig.9). 
For an analytical formulation we have to approximate the probability functions consi- 
dering the boundary conditions 
limp=20 
SNR ^ 0 
and 
limp=0 
SNR + » 
An easy analytical solution can be given by the 'logistic growth curve' 
| (6) 
142 31780 
  
which has been set up first by VOLTERRA for population processes (WHISTON. 1974).