Random signals have been used as test signals in various fields. Among the various types of random signals, a white and normally-distributed random signal is most frequently used. A normal random signal is usually generated on the basis of the central limit theorem. This theorem is approximately realized by adding
n binary random numbers with a weighted adder.
The purpose of this paper is to find out the optimum sets of
n weights of the weighted adder which can generate a best-approximated normal random signal on condition that
n is constant. First the characteristic function of a distribution obtained by the adder is represented as the function of the
n weights. And the low order cumulants of the distribution are led from the characteristic function. These cumulants are best-approximated to those of a normal distribution, when all weights have the same value. The uniformity of the weights, however, make an obtained distribution discrete. Therefore the effect of the dispersion of the weights is taken into consideration. The characteristic function obtained from dispersed weights can be expressed by the nominal value of the weights and the variance of the dispersion. The optimum variances of the weights are determined for several
n's from minimization of difference between the two characteristic functions of an obtained distribution and a normal one. This result shows that economic rough resistors should be used as the input resistances of the weighted adder.
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