Appendix F: Miscellaneous

Random (rnd) Function

A random number generation algorithm uses an uniform distribution random generation routine and the central-limit theorem to derive Gaussian distribution random numbers.

Central-limit theorem: when the independent random variables X1, X2..., and Xn conform to an identical random distribution, the mean and variance of x = (X1 + X2 +... + Xn)/n are given as follows:

E(n) + m

V(n) + s2￿n

Even if the initial random distribution is not normal, if a reasonably large value for n is used, the arithmetical mean x of a considerably large number of variables will be close to the normal distribution.

In actuality, 12 is used for n, uniform random numbers are accumulated n times and their arithmetical mean is derived as the ultimate Gaussian distribution random number.

The following algorithm is used to generate uniform distribution random numbers:

seed [n] + (253.0 seed [n±1] ) 1.0) mod 16777216

ran + seed [n] ￿16777216

F￿6

AWG2021 User Manual