On the computation of rational approximations to continuous functions

For each t, x(t) in Eq. (6) is composed of a linear combination of identically and independently distributed random variables. I t might be suspected that as N ~ the distribution of x(t) approaches a normal distribution with mean-zero and variance equal to R(0). Care must be exercised, however, since the A,~ coefficients are functions of N, as evidence by Eqs. (5). In other words, each case must be analyzed individually, as R(r ) = cos r provides an example of a case in which the central limit theorem does not hold. The authors have tested a few cases, using a chi-squared goodness-of-fit test, and obtained results which indicate that when the central limit theorem applies, convergence is quite rapid. For example, let